Journal articles: 'Redundancy of Degrees of Freedom'

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BOLOGA, OCTAVIAN, and MIHAI CRENGANIŞ. "Efficient method for position control of a redundant robot." Journal of Engineering Sciences and Innovation 2, no. 2 (2017): 1–8. http://dx.doi.org/10.56958/jesi.2017.2.2.1.

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To begin the work presents some redundancy resolution schemes for robotic arms, i.e., the techniques for exploiting the redundant degrees of freedom in the solution of the inverse kinematics problem. This is obviously an issue of major relevance for motion planning and control purposes. In particular, task-oriented kinematics and the basic methods for its inversion at the velocity (first-order differential) level are first recalled. This paper focuses on modeling and simulations of the inverse kinematics of an anthropomorphic redundant robotic structure with seven degrees of freedom and a workspace similar to human arm. Also the kinematic model of the robotic arm in the MATLAB and Simulink environment is presented. A method of resolving the redundancy of a seven degrees of freedom robotic arm when a degree of freedom has a known variation is presented. The kinematic analysis and virtual simulation share similar results.

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Kazerooni, H., K. G. Bouklas, and J. Guo. "Theory and Experiments on the Compliance Control of Redundant Robot Manipulators." Journal of Dynamic Systems, Measurement, and Control 112, no. 4 (December 1, 1990): 653–60. http://dx.doi.org/10.1115/1.2896191.

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This work presents a control methodology for compliant motion in redundant robot manipulators. This control approach takes advantage of the redundancy in the robot’s degrees of freedom: while a maximum six degrees of freedom of the robot control the robot’s endpoint position, the remaining degrees of freedom impose an appropriate force on the environment. To verify the applicability of this control method, an active end-effector is mounted on an industrial robot to generate redundancy in the degrees of freedom. A set of experiments are described to demonstrate the use of this control method in constrained maneuvers. The stability of the robot and the environment is analyzed.

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Potkonjak, V., and T. Petrović. "Contribution to robots control with parallel degrees of freedom." Robotica 12, no. 6 (November 1994): 569–73. http://dx.doi.org/10.1017/s026357470001691x.

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SummaryThis paper considers some problems concerning the motion and the control of large robots. The problem arises when highly nonuniform motion is required. It results in too strong dynamic loads and the robot cannot operate successfully. The solution is found in the introduction of redundancy in the form of parallel degrees of freedom. Kinematics of such a system follows the distributed positioning concept. The control scheme is developed for a one-dimensional redundant robot.

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Huo, Liguo, and Luc Baron. "KINEMATIC INVERSION OF FUNCTIONALLY-REDUNDANT SERIAL MANIPULATORS: APPLICATION TO ARC-WELDING." Transactions of the Canadian Society for Mechanical Engineering 29, no. 4 (December 2005): 679–90. http://dx.doi.org/10.1139/tcsme-2005-0045.

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This paper introduces the concept of functional redundancy of serial manipulators, and presents a new resolution scheme to solve such redundant robotic tasks requiring less than six degrees-of-freedom. Instead of projecting the secondary task onto the null space of the Jacobian matrix in order to take advantage of the redundancy, the twist of end-effector is directly decomposes into two orthogonal subspaces where the main and secondary tasks lie, respectively. The algorithm has shown to be computationally efficient and well suited to solve functionally-redundant robotic tasks, such as arc-welding.

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Wilhelm, Nikolas, Rainer Burgkart, Jan Lang, Carina Micheler, and Constantin von Deimling. "Exploiting null space potentials to control arm robots compliantly performing nonlinear tactile tasks." International Journal of Advanced Robotic Systems 16, no. 6 (November 1, 2019): 172988141988547. http://dx.doi.org/10.1177/1729881419885473.

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In this article, two new compliant control architectures are introduced that utilize null space solutions to decouple force and position control. They are capable to interact with uncertain surfaces and environments with varying materials and require fewer parameters to be tuned than the common architectures – hybrid or impedance control. The general concept behind these approaches allows to consider manipulators with six degrees of freedom as redundant by creating a virtual redundancy with a reduced work space. It will be demonstrated that the introduced approaches are superior regarding orthogonal separation of the Cartesian degrees of freedom and avoid inner singularities. To demonstrate their performance, the controllers are tested on a standard industrial robot (Stäubli, RX90B, six degrees of freedom) that actuates two different biomechanically inspired models of the human knee joint.

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Dounskaia, Natalia, and Wanyue Wang. "A preferred pattern of joint coordination during arm movements with redundant degrees of freedom." Journal of Neurophysiology 112, no. 5 (September 1, 2014): 1040–53. http://dx.doi.org/10.1152/jn.00082.2014.

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Redundancy of degrees of freedom (DOFs) during natural human movements is a central problem of motor control research. This study tests a novel interpretation that during arm movements, the DOF redundancy is used to support a preferred, simplified joint control pattern that consists of rotating either the shoulder or elbow actively and the other (trailing) joint predominantly passively by interaction and gravitational torques. We previously revealed the preference for this control pattern during nonredundant horizontal arm movements. Here, we studied whether this preference persists during movements with redundant DOFs and the redundancy is used to enlarge the range of directions in which this control pattern can be utilized. A free-stroke drawing task was performed that involved production of series of horizontal center-out strokes in randomly selected directions. Two conditions were used, with the arm's joints unconstrained (U) and constrained (C) to the horizontal plane. In both conditions, directional preferences were revealed and the simplified control pattern was used in the preferred and not in nonpreferred directions. The directional preferences were weaker and the range of preferred directions was wider in the U condition, with higher percentage of strokes performed with the simplified control pattern. This advantage was related to the usage of additional DOFs. We discuss that the simplified pattern may represent a feedforward control strategy that reduces the challenge of joint coordination caused by signal-dependent noise during movement execution. The results suggest a possibility that the simplified pattern is used during the majority of natural, seemingly complex arm movements.

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Wu, J., J.-S. Wang, L.-P. Wang, and T.-M. Li. "Dexterity and stiffness analysis of a three-degree-of-freedom planar parallel manipulator with actuation redundancy." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 221, no. 8 (August 1, 2007): 961–69. http://dx.doi.org/10.1243/09544062jmes456.

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The current paper deals with the dexterity and stiffness of a three-degree of freedom (DOF) planar parallel manipulator with actuation redundancy, which is a subpart of a four-DOF-hybrid machine tool. Based on the kinematics, the dexterity is analysed. The stiffness indices, which are the maximum deflection of the moving platform under the action of a unit force and the minimum eigenvalue of the stiffness matrix of the manipulator, are presented for investigating the stiffness. According to the minimum eigenvalue index, it is proved that actuation redundancy can improve the stiffness of the parallel manipulator. Moreover, the relationship between the singular configuration and the stiffness of the parallel manipulator is discussed. Compared with the corresponding non-redundant parallel manipulator without the redundant link, the redundantly actuated parallel manipulator has better dexterity and higher stiffness.

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Boscariol, Paolo, Roberto Caracciolo, Dario Richiedei, and Alberto Trevisani. "Energy Optimization of Functionally Redundant Robots through Motion Design." Applied Sciences 10, no. 9 (April 26, 2020): 3022. http://dx.doi.org/10.3390/app10093022.

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This work proposes to exploit functional redundancy as a tool to enhance the energy efficiency of a robotic system. In a functionally redundant system, i.e., one in which the number of degrees of freedom required to complete the task is smaller than the number of available degrees of freedom, the motion of the extra degrees of freedom can be tailored to enhance a performance metric. This work showcases a method that can be used to effectively enhance the energy efficiency through motion design, using a detailed dynamic model of the UR5 serial robot arm. The method is based on an optimization of the motion profile, using a parametrized description of the end-effector orientation: the results showcase an increased efficiency that allows energy savings up to 20.8%, according to the energy consumption results according to the electro-mechanical dynamic model of the robot.

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Borovinskaya, Ekaterina. "Redundancy-Free Models for Mathematical Descriptions of Three-Phase Catalytic Hydrogenation of Cinnamaldehyde." Catalysts 11, no. 2 (February 4, 2021): 207. http://dx.doi.org/10.3390/catal11020207.

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A new approach on how to formulate redundancy-free models for mathematical descriptions of three-phase catalytic hydrogenation of cinnamaldehyde is presented. An automatically created redundant (generalized) model is formulated according to the complete reaction network. Models based on formal kinetics and kinetics concerning the Langmuir-Hinshelwood theory for three-phase catalytic hydrogenation of cinnamaldehyde were investigated. Redundancy-free models were obtained as a result of a step-by-step elimination of model parameters using sensitivity and interval analysis. Starting with 24 parameters in the redundant model, the redundancy-free model based on the Langmuir-Hinshelwood mechanism contains 6 parameters, while the model based on formal kinetics includes only 4 parameters. Due to less degrees of freedom of molecular rotation in the adsorbed state, the probability of a direct conversion of cinnamaldehyde to 3-phenylpropanol according to the redundancy-free model based on Langmuir-Hinshelwood approach is practically negligible compared to the model based on formal kinetics.

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KHOUKHI, Amar, Luc BARON, and Marek BALAZINSKI. "A PROJECTED GRADIENT AUGMENTED LAGRANGIAN APPROACH TO MULTI-OBJECTIVE TRAJECTORY PLANNING OF REDUNDANT ROBOTS." Transactions of the Canadian Society for Mechanical Engineering 31, no. 4 (December 2007): 391–405. http://dx.doi.org/10.1139/tcsme-2007-0028.

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In this paper, a multi-objective trajectory planning system is developed for redundant manipulators. This system involves kinematic redundancy resolution, as well as robot dynamics, including actuators model. The kinematic redundancy is taken into account through a secondary criterion of joint limits avoidance. The optimization procedure is performed subject to limitations on actuator torques and workspace, while passing through imposed poses. The Augmented Lagrangian with decoupling (ALD) technique is used to solve the resulting constrained non-convex and non-linear optimal control problem. Furthermore, the final state constraint is solved using a gradient projection. Simulations on a three degrees of freedom planar redundant serial manipulator show the effectiveness of the proposed system.

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Harada, Takashi. "Mode changes of redundantly actuated asymmetric parallel mechanism." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 230, no. 3 (May 26, 2015): 454–62. http://dx.doi.org/10.1177/0954406215588479.

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A novel parallel mechanism which enlarges the workspace by singularity-free mode changes is proposed. The proposed mechanism has inherited the design of Linear DELTA, three translational degree-of-freedom and the moving plate driven by three linear actuators. In addition, the mechanism is extended by redundant actuation by four linear actuators and asymmetric design. New criterions about redundancy and singularity of redundantly actuated parallel mechanism using summation and product of determinants of minor matrices of the transposed Jacobian matrix are proposed. Redundant actuation and asymmetric design enables singularity-free mode changes with loss redundancy but maintains non-singularity, which is evaluated by the proposed criterions. Numerical simulations demonstrate the singularity-free mode changes of the proposed mechanism.

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Sellmann, Florian, Titus Haas, Hop Nguyen, Sascha Weikert, and Konrad Wegener. "Orientation Smoothing for 5-Axis Machining Using Quasi-Redundant Degrees of Freedom." International Journal of Automation Technology 10, no. 2 (March 4, 2016): 262–71. http://dx.doi.org/10.20965/ijat.2016.p0262.

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A new approach for set point generation in the field of 5-axis machining using quasi-redundant degrees of freedom is introduced in this study. In machine tools that possess both rotational and translational axes, no bijective correlation exists between the tool center point and the movement of the machine tool axes based on the manufacturing tolerances. Depending on the manufacturing process, as many as two additional degrees of freedom exist that allow the machine tool axes movement to be optimised within the given manufacturing tolerances with respect to the axes’ inertia. In this study to reduce the mechanical excitation of the machine tool, the jerk of the machine tool axes is minimised. To enhance robustness, the optimisation problem is formulated as a quadratic program with linear constraints. This problem can be solved by using an interior point method. An application example shows that when exploiting quasi-redundancy, the mechanical excitation of the machine tool can be reduced.

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Latash, Mark L. "Abundant Degrees of Freedom Are Not a Problem." Kinesiology Review 7, no. 1 (February 1, 2018): 64–72. http://dx.doi.org/10.1123/kr.2017-0058.

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The problem of motor redundancy has been one of the fundamental, albeit elusive, problems in motor control. Traditionally, it has been viewed as a computational problem for the brain, solved with either optimization methods or by introducing additional constraints to motor tasks. This review suggests that the problem was wrongly formulated, and that the abundant degrees of freedom are not to be eliminated but used to ensure dynamic stability of motor performance, which is vital given the unpredictable intrinsic states and external forces. The idea of synergies as mechanisms ensuring action stability is introduced based on the uncontrolled manifold hypothesis and the theory of control with spatial referent coordinates. The importance of controlled stability is illustrated with the phenomena of anticipatory synergy adjustments. This approach is productive for both basic and applied fields as illustrated, in particular, by changes in motor synergies with neurological disorder and exercise.

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Wang, Congzhe, Yuefa Fang, Sheng Guo, and Changchun Zhou. "Design and kinematic analysis of redundantly actuated parallel mechanisms for ankle rehabilitation." Robotica 33, no. 2 (March 3, 2014): 366–84. http://dx.doi.org/10.1017/s0263574714000241.

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SUMMARYIn this paper, we present the design of two serial spherical mechanisms to substitute for a single spherical joint that is usually used to connect the platform with the base in three degrees of freedom parallel mechanisms. According to the principle derived from the conceptual design, through using the two serial spherical mechanisms as the constraint limb, several redundantly actuated parallel mechanisms are proposed for ankle rehabilitation. The proposed parallel mechanisms all can perform the rotational movements of the ankle in three directions while at the same time the mechanism center of rotations can match the ankle axes of rotations compared with other multi-degree-of-freedom devices, due to the structural characteristics of the special constraint limb and platform. Two special parallel mechanisms are selected to analyze their kinematical performances, such as workspace, dexterity, singularity, and stiffness, based on the computed Jacobian. The results show that the proposed scheme of actuator redundancy can guarantee that the redundantly actuated parallel mechanisms have no singularity, better dexterity, and stiffness within the prescribed workspace in comparison with the corresponding non-redundant parallel mechanisms. In addition, the proposed mechanisms possess certain reconfigurable capacity based on control strategies or rehabilitation modes to obtain sound performance for completing ankle rehabilitation exercise.

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Kim, Ki-Kap, and Yong-San Yoon. "Trajectory planning of redundant robots by maximizing the moving acceleration radius." Robotica 10, no. 3 (May 1992): 195–203. http://dx.doi.org/10.1017/s0263574700007931.

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SUMMARYThe moving acceleration radius (MAR) is proposed as a local performance index quantifying the dynamic uniformity of a redundant robot. MAR can be calculated by a simple sequential algorithm, and the resolution of the redundant joint angles is obtained by maximizing MAR locally. In addition, the reduction of the joint torques is achieved by maximizing the acceleration bound in the direction of work path, while MAR is being kept at a maximum. Also a new differentiation algorithm for angular acceleration is suggested for numerical efficiency as well as accuracy, using a null space operator.A three degrees of freedom planar robot with one degree of redundancy, simulated using these algorithms for various situations, showed a marked improvement in dynamic characteristics.

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Arimoto, Suguru, and Masahiro Sekimoto. "Natural Resolution of Ill-Posed Inverse Kinematics for Redundant Robots: A Challenge to Bernstein’s Degrees-of-Freedom Problem." Journal of Robotics and Mechatronics 18, no. 5 (October 20, 2006): 651–60. http://dx.doi.org/10.20965/jrm.2006.p0651.

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Over half a century ago, A. N. Bernstein observed that “dexterity” in human limb movement emerges from the involvement of multijoint motion with surplus degrees of freedom (DOF). Robotics posits that DOF redundancy in robot may enhance dexterity and versatility. Kinematic redundancy involves the problem of ill-posed inverse kinematics from task-description space to joint space. This problem is conventionally avoided by introducing an artificial performance index and uniquely determining an inverse kinematics solution by minimizing it. Instead of taking this conventional avoidance solution, we propose challenging Bernstein’s DOF problem by introducing two direct novel concepts - stability on a manifold and transferability to a submanifold - in dealing with human multijoint movement in reaching and showing that sensory feedback from task space to joint space together with adequate damping (joint velocity feedback) enables any solution to overall closed-loop dynamics to converge naturally and coordinately to a lower-dimensional manifold describing a set of joint states fulfilling a given motion task. This means that a reaching task is accomplished by sensory feedback with the appropriate choice of a stiffness parameter and damping coefficients without having to consider inverse kinematics. We also show that these concepts cope with the annoying “variability” of redundant joint motion seen typically in skilled human reaching. In conclusion, we propose a virtual spring/damper hypothesis that leads to natural control of skilled movement in redundant multijoint reaching.

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Li, Yong Bo, Min Qiang Xu, and Yu Wei. "Take-Off Motion Planning of Legged Hopping Robot with Redundancy Characteristic." Advanced Materials Research 823 (October 2013): 127–30. http://dx.doi.org/10.4028/www.scientific.net/amr.823.127.

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The planning for four-joint legged hopping robot with two redundant degrees of freedom at the take-off stage is researched. According to the take-off velocity and the boundary condition of centroid motion, the trajectory is planned with variable quartic polynomial interpolation. From inverse kinematics, the motion planning with redundancy characteristic is completed by using the GPM with continuous scale factor. Performance index of avoiding joint limit and optimizing joint driving torque are realized. The data indicates the feasibility and practicability of this algorithm.

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Wang, Yunfeng. "A fast workspace-density-driven inverse kinematics method for hyper-redundant manipulators." Robotica 24, no. 5 (May 26, 2006): 649–55. http://dx.doi.org/10.1017/s0263574706002827.

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Hyper-redundant manipulators have a very large number of redundant degrees of freedom. They have been recognized as a means to improve manipulator performance in complex and unstructured environments. However, the high degree of redundancy also poses new challenges when performing inverse kinematics calculations. Prior works have shown that the workspace density (generated by sampling the joint space and evaluating the frequency of occurrence of the resulting end-effector reference frames) is a valuable quantity for use in ${\cal O}(P)$ inverse kinematics algorithms. Here $P$ is the number of modules in a manipulator constructed of a serial cascade of modules. This paper develops a new “divide-and-conquer” method for inverse kinematics using the workspace density. This method does not involve a high-dimensional Jacobian matrix and offers high accuracy. And its computational complexity is only ${\cal O}({\rm log}_2\,P)$, which makes it ideal for very high degree-of-freedom systems. Numerical simulations are performed to demonstrate this new method on a planar example, and a detailed comparison with a breadth-first search method is conducted.

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Bin Hammam, Ghassan, Patrick M. Wensing, Behzad Dariush, and David E. Orin. "Kinodynamically Consistent Motion Retargeting for Humanoids." International Journal of Humanoid Robotics 12, no. 04 (November 27, 2015): 1550017. http://dx.doi.org/10.1142/s0219843615500176.

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Human-to-humanoid motion retargeting is an important tool to generate human-like humanoid motions. This retargeting problem is often formulated as a Cartesian control problem for the humanoid from a set of task points in the captured human data. Classically, Cartesian control has been developed for redundant systems. While redundancy fundamentally adds new sub-task capabilities, the degree to which secondary objectives can be faithfully executed cannot be determined in advance. In fact, a robot that exhibits redundancy with respect to an operational task may have insufficient degrees of freedom (DOFs) to satisfy more critical constraints. In this paper, we present a Cartesian space resolved acceleration control framework to handle execution of operational tasks and constraints for redundant and nonredundant task specifications. The approach is well suited for online control of humanoid robots from captured human motion data expressed by Cartesian variables. The current formulation enforces kinematic constraints such as joint limits, self-collisions, and foot constraints and incorporates a dynamically-consistent redundancy resolution approach to minimize costly joint motions. The efficacy of the proposed algorithm is demonstrated by simulated and real-time experiments of human motion replication on a Honda humanoid robot model. The algorithm closely tracks all input motions while smoothly and automatically transitioning between regimes where different constraints are binding.

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Zghal, H., R. V. Dubey, and J. A. Euler. "Collision Avoidance of a Multiple Degree of Redundancy Manipulator Operating Through a Window." Journal of Dynamic Systems, Measurement, and Control 114, no. 4 (December 1, 1992): 717–21. http://dx.doi.org/10.1115/1.2897746.

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The problem of collision-free operation of a multiple-degree-of-redundancy manipulator operating through a window is addressed. An efficient gradient projection optimization scheme is presented for the kinematic control of manipulators with multiple degrees of redundancy. This scheme was developed for dextrous robotic and telerobotic applications in space station construction as well as in congested shop floor environment. A performance criterion is defined to maximize the shortest distances between the manipulator links and the edges of the window. Effectiveness of this scheme and the validity of the performance criterion are verified through simulations of the seven-degree-of-freedom NASA Laboratory Telerobotic Manipulator (LTM).

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Lv, Wei, Limin Tao, and Zhengnan Ji. "Sliding Mode Control of Cable-Driven Redundancy Parallel Robot with 6 DOF Based on Cable-Length Sensor Feedback." Mathematical Problems in Engineering 2017 (2017): 1–21. http://dx.doi.org/10.1155/2017/1928673.

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The sliding mode control of the cable-driven redundancy parallel robot with six degrees of freedom is studied based on the cable-length sensor feedback. Under the control scheme of task space coordinates, the cable length obtained by the cable-length sensor is used to solve the forward kinematics of the cable-driven redundancy parallel robot in real-time, which is treated as the feedback for the control system. First, the method of forward kinematics of the cable-driven redundancy parallel robot is proposed based on the tetrahedron method and Levenberg-Marquardt method. Then, an iterative initial value estimation method for the Levenberg-Marquardt method is proposed. Second, the sliding mode control method based on the exponential approach law is used to control the effector of the robot, and the influence of the sliding mode parameters on control performance is simulated. Finally, a six-degree-of-freedom position tracking experiment is carried out on the principle prototype of the cable-driven redundancy parallel robot. The experimental results show that the robot can accurately track the desired position in six directions, which indicates that the control method based on the cable-length sensor feedback for the cable-driven redundancy parallel robot is effective and feasible.

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Zhao, T. S., J. S. Dai, and Z. Huang. "Geometric synthesis of spatial parallel manipulators with fewer than six degrees of freedom." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 216, no. 12 (December 1, 2002): 1175–85. http://dx.doi.org/10.1243/095440602321029418.

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Manipulators with fewer than six degrees of freedom meet specific tasks and have the advantage of reducing structural complexity, design redundancy and cost. In order to construct parallel manipulators for given tasks, this paper develops an algebraic approach to type synthesis of spatial parallel mechanisms with fewer than six degrees of freedom based on the screw theory. With the proposed steps (i.e. describing restraining screws, identifying basic kinematic pair (KP) screws reciprocal to the restraining screws, linearly transforming the basic KP screws to obtain equivalent serial limbs and allocating the serial limbs) new parallel mechanisms can be constructed. The approach converts a mechanism design into a screw algebra operation, in which screws describe kinematic pairs and constraints between links. As examples, synthesis procedures of parallel mechanisms with four degrees of freedom are given, from which five novel parallel mechanisms result.

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Dillon, Joshua S., Max Lee, Zaki S. Ali, Aaron R. Parsons, Naomi Orosz, Chuneeta Devi Nunhokee, Paul La Plante, et al. "Redundant-baseline calibration of the hydrogen epoch of reionization array." Monthly Notices of the Royal Astronomical Society 499, no. 4 (October 1, 2020): 5840–61. http://dx.doi.org/10.1093/mnras/staa3001.

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ABSTRACT In 21-cm cosmology, precision calibration is key to the separation of the neutral hydrogen signal from very bright but spectrally smooth astrophysical foregrounds. The Hydrogen Epoch of Reionization Array (HERA), an interferometer specialized for 21-cm cosmology and now under construction in South Africa, was designed to be largely calibrated using the self-consistency of repeated measurements of the same interferometric modes. This technique, known as redundant-baseline calibration resolves most of the internal degrees of freedom in the calibration problem. It assumes, however, on antenna elements with identical primary beams placed precisely on a redundant grid. In this work, we review the detailed implementation of the algorithms enabling redundant-baseline calibration and report results with HERA data. We quantify the effects of real-world non-redundancy and how they compare to the idealized scenario in which redundant measurements differ only in their noise realizations. Finally, we study how non-redundancy can produce spurious temporal structure in our calibration solutions – both in data and in simulations – and present strategies for mitigating that structure.

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Müller, Andreas. "On the terminology and geometric aspects of redundant parallel manipulators." Robotica 31, no. 1 (April 20, 2012): 137–47. http://dx.doi.org/10.1017/s0263574712000173.

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SUMMARYParallel kinematics machines (PKMs) can exhibit kinematics as well as actuation redundancy. While the meaning of kinematic redundancy has been already clarified for serial manipulators, actuation redundancy, which is only possible in PKMs, is differently classified in the literature. In this paper a consistent terminology for general redundant PKM is proposed. A kinematic model is introduced with the configuration space (c-space) as central part. The notion of kinematic redundancy is recalled for PKM. C-space, output, and input singularities are distinguished. The significance of the c-space geometry is emphasized, and it is pointed out geometrically that input singularities can be avoided by redundant actuation schemes. In order to distinguish different actuation schemes of PKM, a nonlinear control system is introduced whose dynamics evolves on c-space. The degree of actuation (DOA) is introduced as the number of independent control vector fields, and PKMs are classified as full-actuated and underactuated machines. Relating this DOA to degree of freedom allows to classify the actuation redundancy.

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Pennestrı`, Ettore, and Pier Paolo Valentini. "A Review of Formulas for the Mechanical Efficiency Analysis of Two Degrees-of-Freedom Epicyclic Gear Trains." Journal of Mechanical Design 125, no. 3 (September 1, 2003): 602–8. http://dx.doi.org/10.1115/1.1587157.

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This paper, after a rigorous proof of the formulas originally proposed by Radzimovsky, demonstrates the numerical equivalence of the different approaches available for computing the mechanical efficiency of two degrees-of-freedom (d.o.f.) epicyclic gear trains. The paper includes also a discussion on the redundancy of data required by some formulas.

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Wang, Jinsong, Jun Wu, Tiemin Li, and Xinjun Liu. "Workspace and singularity analysis of a 3-DOF planar parallel manipulator with actuation redundancy." Robotica 27, no. 1 (January 2009): 51–57. http://dx.doi.org/10.1017/s0263574708004517.

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SUMMARYThis paper deals with the position workspace, orientation workspace, and singularity of a 3-degree-of-freedom (DOF) planar parallel manipulator with actuation redundancy, which is created by introducing a redundant link with active actuator to a 3-DOF nonredundant parallel manipulator. Based on the kinematic analysis, the position workspace and orientation workspace of the redundantly actuated parallel manipulator and its corresponding nonredundant parallel manipulator are analyzed, respectively. In the singularity analysis phase, the relationship between the generalized input velocity and the generalized output velocity is researched on the basis of the theory of singular value decomposition. Then a method to investigate the singularity of parallel manipulators is presented, which is used to determine the singularity of the redundantly actuated parallel manipulator. In contrast to the corresponding nonredundant parallel manipulator, the redundant one has larger orientation workspace and less singular configurations. The redundantly actuated parallel manipulator is incorporated into a 4-DOF hybrid machine tool which also includes a feed worktable to demonstrate its applicability.

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Berret, Bastien, Enrico Chiovetto, Francesco Nori, and Thierry Pozzo. "Manifold reaching paradigm: how do we handle target redundancy?" Journal of Neurophysiology 106, no. 4 (October 2011): 2086–102. http://dx.doi.org/10.1152/jn.01063.2010.

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How the central nervous system coordinates the many intrinsic degrees of freedom of the musculoskeletal system is a recurrent question in motor control. Numerous studies addressed it by considering redundant reaching tasks such as point-to-point arm movements, for which many joint trajectories and muscle activations are usually compatible with a single goal. There exists, however, a different, extrinsic kind of redundancy that is target redundancy. Many times, indeed, the final point to reach is neither specified nor unique. In this study, we aim to understand how the central nervous system tackles such an extrinsic redundancy by considering a reaching-to-a-manifold paradigm, more specifically an arm pointing to a long vertical bar. In this case, the endpoint is not defined a priori and, therefore, subjects are free to choose any point on the bar to successfully achieve the task. We investigated the strategies used by subjects to handle this presented choice. Our results indicate both intersubject and intertrial consistency with respect to the freedom provided by the task. However, the subjects' behavior is found to be more variable than during classical point-to-point reaches. Interestingly, the average arm trajectories to the bar and the structure of intertrial endpoint variations could be explained via stochastic optimal control with an energy/smoothness expected cost and signal-dependent motor noise. We conclude that target redundancy is first overcome during movement planning and then exploited during movement execution, in agreement with stochastic optimal feedback control principles, which illustrates how the complementary problems of goal and movement selection may be resolved at once.

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Oiwa, Takaaki, Harunaho Daido, and Junichi Asama. "A Calibration Method for a Three-Degrees-of-Freedom Parallel Manipulator with a Redundant Passive Chain." Applied Mechanics and Materials 162 (March 2012): 171–78. http://dx.doi.org/10.4028/www.scientific.net/amm.162.171.

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This paper deals with parameter identification for a three-degrees-of-freedom (3-DOF) parallel manipulator, based on measurement redundancy. A redundant passive chain with a displacement sensor connects the moving stage to the machine frame. The passive chain is sequentially placed in three directions at approximately right angles to one another to reliably detect the motion of the stage. Linear encoders measure changes in lengths of the passive chain and the three actuated chains of the manipulator during traveling of the moving stage. Comparison between the measured length and the length calculated from forward kinematics of the 3-DOF manipulator reveals a length error of the passive chain. The least-squares method using a Jacobian matrix corrects 27 kinematic parameters so that the length errors of the passive chain are minimized. The above calculations were accomplished in both numerical simulations and experiments employing a coordinate measuring machine based on the parallel manipulator. Moreover, a length measurement simulation of gauge block measurement and a measurement experiment using the measuring machine were performed to verify the identified parameters.

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Arata, Jumpei, and Hideo Fujimoto. "Redundant Parallel Mechanism for Haptic Applications." International Journal of Automation Technology 4, no. 4 (July 5, 2010): 338–45. http://dx.doi.org/10.20965/ijat.2010.p0338.

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With haptic devices becoming increasingly common in both industrial field and consumer use, parallel mechanisms have been widely introduced for their high rigidity, output, accuracy and high backdrivability due to their multi-legged structure and fixed base actuators. In general parallel mechanism, redundancy enlarges the working area and avoids singularity. The redundant parallel mechanism we present introduces these advantages into haptic applications. Introducing this mechanism into a multiple degrees-of-freedom (DOF) structure realizes a wide range of working areas in rotation. The redundant parallel mechanism implemented in translational force display device, and multi-DOF force display device demonstrate the advantages of the redundant parallel mechanism in haptic applications. Following an overview, we introduce the prototype implementation and evaluation of these devices and discuss the effectiveness of the redundant parallel mechanism in haptic applications.

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Harada, Takashi. "Design of a Redundantly Actuated Asymmetric Linear DELTA Parallel Mechanism for Singularity-Free Mode Changes." Applied Mechanics and Materials 575 (June 2014): 711–15. http://dx.doi.org/10.4028/www.scientific.net/amm.575.711.

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A novel parallel mechanism which enlarges the workspace by singularity-free mode change is proposed. The proposed mechanism is inherited the design of Linear DELTA which has three degree-of-freedom translational moving plate driven by three linear actuators, in addition, extended it by redundantly actuation by four linear actuators and asymmetric design. New criterions about redundancy and singularity of redundantly actuated parallel mechanism using summation and product of determinants of minor matrices of the transposed Jacobian matrix are proposed. Redundantly actuation and asymmetric design enables singularity-free mode changes with loss redundancy but maintain non-singularity, that are evaluated by the proposed criterions. Numerical simulations demonstrate the singularity-free mode changes of the proposed mechanism.

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Chen, Siheng, and L. Mahadevan. "Rigidity percolation and geometric information in floppy origami." Proceedings of the National Academy of Sciences 116, no. 17 (April 5, 2019): 8119–24. http://dx.doi.org/10.1073/pnas.1820505116.

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Origami structures with a large number of excess folds are capable of storing distinguishable geometric states that are energetically equivalent. As the number of excess folds is reduced, the system has fewer equivalent states and can eventually become rigid. We quantify this transition from a floppy to a rigid state as a function of the presence of folding constraints in a classic origami tessellation, Miura-ori. We show that in a fully triangulated Miura-ori that is maximally floppy, adding constraints via the elimination of diagonal folds in the quads decreases the number of degrees of freedom in the system, first linearly and then nonlinearly. In the nonlinear regime, mechanical cooperativity sets in via a redundancy in the assignment of constraints, and the degrees of freedom depend on constraint density in a scale-invariant manner. A percolation transition in the redundancy in the constraints as a function of constraint density suggests how excess folds in an origami structure can be used to store geometric information in a scale-invariant way.

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Crenganis, Mihai, and Octavian Bologa. "Another Approach for Redundancy Resolution of a 7 DOF Robotic Arm." Applied Mechanics and Materials 762 (May 2015): 305–11. http://dx.doi.org/10.4028/www.scientific.net/amm.762.305.

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In this paper we have presented a method to solve the inverse kinematics problem of a redundant robotic arm with seven degrees of freedom and a human like workspace based on mathematical equations, Fuzzy Logic implementation and Simulink models. For better visualization of the kinematics simulation a CAD model that mimics the real robotic arm was created into SolidWorks® and then the CAD parts were converted into SimMechanics model.

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Ostry, David J., Rafael Laboissière, and Paul L. Gribble. "Command invariants and the frame of reference for human movement." Behavioral and Brain Sciences 18, no. 4 (December 1995): 770–72. http://dx.doi.org/10.1017/s0140525x00040942.

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AbstractWe describe a solution to the redundancy problem related to that proposed in Feldman & Levin's target article. We suggest that the system may use a fixed mapping between commands organized at the level of degrees of freedom and commands to individual muscles. This proposal eliminates the need to maintain an explicit representation of musculoskeletalgeometry in planning movements.

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Rodriguez-Barroso, Alejandro, Roque Saltaren, Gerardo A. Portilla, Juan S. Cely, and Marco Carpio. "Cable-Driven Parallel Robot with Reconfigurable End Effector Controlled with a Compliant Actuator." Sensors 18, no. 9 (August 22, 2018): 2765. http://dx.doi.org/10.3390/s18092765.

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Redundancy in cable-driven parallel robots provides additional degrees of freedom that can be used to achieve different objectives. In this robot, this degree of freedom is used to act on a reconfigurable end effector with one degree of freedom. A compliant actuator actuated by one motor exerts force on both bodies of the platform. Due to the high tension that appears in this cable in comparison with the rest of the cables, an elastic model was developed for solving the kinestostatic and wrench analysis. A linear sensor was used in one branch of this cable mechanism to provide the needed intermediate values. The position of one link of the platform was fixed in order to focus this analysis on the relationship between the cables and the platform’s internal movement. Position values of the reconfigurable end effector were calculated and measured as well as the tension at different regions of the compliant actuator. The theoretical values were compared with dynamic simulations and real prototype results.

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Gao, Changhong, Zhidong Yang, Shupeng Zheng, and Dacheng Cong. "An algorithm for real-time forward kinematics of 6-degree-of-freedom parallel mechanisms." Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering 232, no. 2 (November 11, 2017): 109–20. http://dx.doi.org/10.1177/0959651817739793.

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This article proposes a forward kinematics algorithm based on closed-loop feedback solution for real-time pose estimation of 6-degree-of-freedom parallel mechanisms. First, a feedback forward kinematics algorithm with second-order error dynamics built in joint space is presented and its convergence is analyzed. Taking a Stewart platform as an example, fast convergence and high solving accuracy of the algorithm are shown in simulation. However, while applying the algorithm to forward kinematics of a 6-degree-of-freedom redundantly actuated parallel mechanisms, solving errors will be growing slowly and non-convergent, which is caused by redundancy character of the parallel mechanisms. Then a modified algorithm, of which second-order error dynamics is built in Cartesian space, is developed. Considering velocity information is usually difficult to measure or estimate accurately in reality, the performance of feedback forward kinematics algorithm without joint velocity feedforward is also evaluated. Finally, the algorithm is implemented into real-time degree of freedom control of the redundant parallel mechanisms which is calibrated by a coordinate measuring machine. Experiment results show that the proposed algorithm can solve the pose with relatively high accuracy under static conditions and is effective and feasible for real-time pose estimation of parallel mechanisms.

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Chai, Xinxue, Wei Ye, Qinchuan Li, and Lingmin Xu. "Elastostatic Stiffness Modeling and Performance Evaluation of a 2UPR–2PRU Redundantly Actuated Parallel Manipulator." Machines 10, no. 12 (December 15, 2022): 1219. http://dx.doi.org/10.3390/machines10121219.

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Redundantly actuated parallel manipulators (PMs) have attracted a great deal of attention since they generally have better stiffness than non-redundantly actuated ones. This paper presents an analytical elastostatic stiffness modeling and performance study of a 2UPR–2PRU PM with actuation redundancy, which has two rotational and one translational degrees of freedom (U: universal joint; P: prismatic joint; R: revolute joint). First, the inverse displacement is reviewed and verified briefly. Second, the stiffness matrices of UPR and PRU limbs are deduced by using the principle of strain energy, followed by the overall stiffness matrix of the 2UPR–2PRU PM. Combined with the ANSYS software, the finite element analysis method is then used to verify the correctness and universality of the stiffness models by calculating the deformations of four selected configurations. Finally, the stiffness index based on the virtual work is used to evaluate the performance of the 2UPR–2PRU PM, and the influence of different external loads and operational heights on the stiffness performance is discussed. The relationship between singular configurations and the stiffness index is also presented. The stiffness models and performance distributions of the 2UPR–2PRU PM with actuation redundancy can provide references for the actual applications.

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37

Yoshikawa, Tsuneo. "Control of robots having redundant degrees of freedom." Advanced Robotics 3, no. 1 (January 1988): 61–73. http://dx.doi.org/10.1163/156855389x00181.

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Luo, Xuan, Fugui Xie, and Xin-Jun Liu. "Kinematic calibration of the 3-degree-of-freedom redundantly actuated spatial parallel module of a five-axis hybrid machine." Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture 234, no. 9 (April 17, 2020): 1185–97. http://dx.doi.org/10.1177/0954405420911299.

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As a new type of manufacturing equipment, redundant hybrid machines have the theoretical advantage over the traditional serial machines in efficiently processing large structural parts with high material removal ratio and complex parts with curved surfaces. In order to solve the accuracy problem of the redundantly actuated spatial parallel module of a five-axis hybrid machine, an improved kinematic calibration method is proposed in this article. First, different from error modeling for the corresponding non-redundant parallel module, the geometric error model of the redundantly actuated spatial parallel module considers the deformations at active joints caused by actuation redundancy as an error source. Then, the applicable error model is developed using projection technique to remove the need of active joints’ stiffness measurement or modeling. Later, the practical error model is derived from model reduction method to avoid using additional sensors or gratings. Finally, three forms of relative measurement and step identification are adopted for the calibration work, and the bilinear interpolation compensation function is introduced to ensure the calibration effect. On this basis, the kinematic calibration of the redundantly actuated spatial parallel module is conducted. The max position errors are reduced from original −0.192 to 0.075 mm after RM1 and SI1, and then further reduced to 0.014 mm after bilinear interpolation compensation, while the max orientation errors are reduced from −0.017° and 0.249° to −0.005° and −0.007° after RM2 and SI2, and RM3 and SI3, respectively. A contrasting experiment is also carried out with the previous method for the corresponding non-redundant parallel module. As a result, the proposed method shows better convergence value and speed in identifying error parameters, and therefore the effectiveness and efficiency of the proposed method for the redundantly actuated spatial parallel module are validated.

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AlAttar, Ahmad, Francesco Cursi, and Petar Kormushev. "Kinematic-Model-Free Redundancy Resolution Using Multi-Point Tracking and Control for Robot Manipulation." Applied Sciences 11, no. 11 (May 21, 2021): 4746. http://dx.doi.org/10.3390/app11114746.

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Robots have been predominantly controlled using conventional control methods that require prior knowledge of the robots’ kinematic and dynamic models. These controllers can be challenging to tune and cannot directly adapt to changes in kinematic structure or dynamic properties. On the other hand, model-learning controllers can overcome such challenges. Our recently proposed model-learning orientation controller has shown promising ability to simultaneously control a three-degrees-of-freedom robot manipulator’s end-effector pose. However, this controller does not perform optimally with robots of higher degrees-of-freedom nor does it resolve redundancies. The research presented in this paper extends the state-of-the-art kinematic-model-free controller to perform pose control of hyper-redundant robot manipulators and resolve redundancies by tracking and controlling multiple points along the robot’s serial chain. The results show that with more control points, the controller is able to reach desired poses in fewer steps, yielding an improvement of up to 66%, and capable of achieving complex configurations. The algorithm was validated by running the simulation 100 times, and it was found that, in 82% of the times, the robot successfully reached the desired target pose within 150 steps.

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Essomba, Terence, Juan Sandoval, Med Amine Laribi, Chieh-Tsai Wu, Cyril Breque, Saïd Zeghloul, and Jean-pierre Richer. "Torque Reduction of a Reconfigurable Spherical Parallel Mechanism Based on Craniotomy Experimental Data." Applied Sciences 11, no. 14 (July 16, 2021): 6534. http://dx.doi.org/10.3390/app11146534.

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This paper deals with a robotic manipulator dedicated to craniotomy with a remote center of motion based on a Spherical Parallel Manipulator (SPM) architecture. The SPM is proposed to handle the drilling tool through the requested craniotomy Degrees of Freedom (DoF) with two rotations. The proposed architecture allows one degree of redundancy according to the total DoF. Thus, a first contribution of this work focuses on the experimental analysis of craniotomy surgery tasks. Secondly, its behavior is improved, taking advantage of the redundancy of the SPM using the spinning motion as a reconfiguration variable. The spinning angle modulation allows the reconfigurable manipulator to minimize its motor torques. A series of motion capture and force experimentations is performed for the analysis of the kinematic and force interaction characterizing Burr hole craniotomy procedures. Experimentations were carried out by a neurosurgeon on a human cadaver, ensuring highly realistic conditions.

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41

Jiang, Yao, Tiemin Li, and Liping Wang. "The dynamic modeling, redundant-force optimization, and dynamic performance analyses of a parallel kinematic machine with actuation redundancy." Robotica 33, no. 2 (February 27, 2014): 241–63. http://dx.doi.org/10.1017/s0263574714000265.

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SUMMARYThis paper discusses a planar 2-DOF (degrees of freedom) parallel kinematic machine with actuation redundancy. Its inverse dynamic model is constructed by utilizing the Newton–Euler method based on the kinematic analysis. However, the dynamic model cannot be solved directly because the number of equations is less than the number of unknowns, which is due to the redundant force. In order to solve this problem, the relationship between the deformations of the links and the position errors of the moving platform are further explored. Then a novel method, which aims at minimizing the position errors of the machine, is proposed to optimize the redundant force. It also enables to solve the dynamic model. Finally, the dynamic performance analyses of this machine and its non-redundant counterpart are provided by numerical examples. Besides, another optimization method proposed for minimizing the constraint forces is also applied for comparison. The results show the effectiveness of the novel methods in improving the position precision of the machine.

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42

Schappler, Moritz, Svenja Tappe, and Tobias Ortmaier. "Modeling Parallel Robot Kinematics for 3T2R and 3T3R Tasks Using Reciprocal Sets of Euler Angles." Robotics 8, no. 3 (August 6, 2019): 68. http://dx.doi.org/10.3390/robotics8030068.

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Industrial manipulators and parallel robots are often used for tasks, such as drilling or milling, that require three translational, but only two rotational degrees of freedom (“3T2R”). While kinematic models for specific mechanisms for these tasks exist, a general kinematic model for parallel robots is still missing. This paper presents the definition of the rotational component of kinematic constraints equations for parallel robots based on two reciprocal sets of Euler angles for the end-effector orientation and the orientation residual. The method allows completely removing the redundant coordinate in 3T2R tasks and to solve the inverse kinematics for general serial and parallel robots with the gradient descent algorithm. The functional redundancy of robots with full mobility is exploited using nullspace projection.

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Quan, Yuan, Chong Zhao, Congmin Lv, Ke Wang, and Yanlin Zhou. "The Dexterity Capability Map for a Seven-Degree-of-Freedom Manipulator." Machines 10, no. 11 (November 7, 2022): 1038. http://dx.doi.org/10.3390/machines10111038.

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For a grasping task planner, the pre-planning of the reachable tip pose in a manipulator’s workspace is important. On this basis, for a seven-degree-of-freedom (7-DOF) redundant manipulator, it is very meaningful to study how to give full play to its redundant characteristics to achieve more dexterous grasping. In this paper, through the improved shape primitive method, the reachability spheres of the 7-DOF manipulator studied were more accurately captured, and a more accurate reachability capability map was generated. Then, based on the idea of redundancy angle discretization, the concept of the obstacle avoidance ability (OAA) index is innovatively proposed to measure the dexterity of the grasping task of the manipulator in a certain tip pose. Based on the OAA index axis, the distribution of the OAA index in each reachability sphere was analyzed. The prediction models of the OAA index of all reachability spheres in the workspace of the manipulator were obtained by the Levenberg–Marquardt algorithm and finally formed a dexterity capability map of the manipulator, which provides a new idea for the pre-planning of the dexterous grasping task of the redundant manipulator. Finally, we give the general frameworks of different grasping pre-planning by combining two kinds of capability maps and verify the effect.

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Crenganis, Mihai, Radu Breaz, Gabriel Racz, and Octavian Bologa. "Kinematic Solutions of a 7 DOF Robotic Arm Using Redundancy Circle and Fuzzy Models." Applied Mechanics and Materials 555 (June 2014): 320–26. http://dx.doi.org/10.4028/www.scientific.net/amm.555.320.

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In this paper we have presented a method to solve the inverse kinematics problem of a redundant robotic arm with seven degrees of freedom and a human like workspace based on mathematical equations, Fuzzy Logic implementation and Simulink models. For better visualization of the kinematics simulation a CAD model that mimics the real robotic arm was created into SolidWorks® and then the CAD parts were converted into SimMechanics model.

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45

Su, Hang, Nima Enayati, Luca Vantadori, Andrea Spinoglio, Giancarlo Ferrigno, and Elena De Momi. "Online human-like redundancy optimization for tele-operated anthropomorphic manipulators." International Journal of Advanced Robotic Systems 15, no. 6 (November 1, 2018): 172988141881469. http://dx.doi.org/10.1177/1729881418814695.

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Robot human-like behavior can enhance the performance of human–robot cooperation with prominently improved natural interaction. This also holds for redundant robots with an anthropomorphic kinematics. In this article, we translated human ability of managing redundancy to control a seven degrees of freedom anthropomorphic robot arm (LWR4+, KUKA, Germany) during tele-operated tasks. We implemented a nonlinear regression method—based on neural networks—between the human arm elbow swivel angle and the hand target pose to achieve an anthropomorphic arm posture during tele-operation tasks. The method was assessed in simulation and experiments were performed with virtual reality tracking tasks in a lab environment. The results showed that the robot achieves a human-like arm posture during tele-operation, and the subjects prefer to work with the biologically inspired robot. The proposed method can be applied in control of anthropomorphic robot manipulators for tele-operated collaborative tasks, such as in factories or in operating rooms.

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Ghosal, Ashitava, and Bernard Roth. "Instantaneous Properties of Multi-Degrees-of-Freedom Motions—Point Trajectories." Journal of Mechanisms, Transmissions, and Automation in Design 109, no. 1 (March 1, 1987): 107–15. http://dx.doi.org/10.1115/1.3258773.

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A general framework is presented for the study of the properties of trajectories generated by points embedded in rigid bodies undergoing multi-degrees-of-freedom motions. Quantities are developed to characterize point trajectories generated by different mechanisms and to distinguish between different positions along the same trajectory. Point trajectories are classified into three types according to whether the number of degrees of freedom is less than, equal to, or greater than the dimension of the space in which the motion takes place. Local and global motion properties are developed for each of these three cases. A new way of using the redundant degrees of freedom in (redundant) mechanisms is presented. These analysis techniques are applied to two- and three-degrees-of-freedom mechanisms containing rotary and prismatic joints.

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Crenganis, Mihai, Radu Eugen Breaz, Sever Gabriel Racz, and Octavian Bologa. "Inverse Kinematics for a 7 DOF Robotic Arm Using the Redundancy Circle and ANFIS Models." Applied Mechanics and Materials 657 (October 2014): 823–28. http://dx.doi.org/10.4028/www.scientific.net/amm.657.823.

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In this paper we have presented a method to solve the inverse kinematics problem of a redundant robotic arm with seven degrees of freedom and a human like workspace based on mathematical equations, ANFIS implementation and Simulink models. For better visualization of the kinematics simulation a CAD model that mimics the real robotic arm was created into SolidWorks® and then the CAD parts were converted into SimMechanics model.

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Gallardo-Alvarado, Jaime, Horacio Orozco-Mendoza, and José M. Rico-Martínez. "A novel five-degrees-of-freedom decoupled robot." Robotica 28, no. 6 (December 23, 2009): 909–17. http://dx.doi.org/10.1017/s0263574709990749.

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SUMMARYIn this work a new nonoverconstrained redundant decoupled robot, free of compound joints, formed from three parallel manipulators, with two moving platforms and provided with six active limbs connected to the fixed platform, called LinceJJP, is presented. Interesting applications such as multi-axis machine tools with parallel kinematic architectures, solar panels, radar antennas, and telescopes are available for this novel spatial mechanism.

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Okabe, Kousuke. "Elucidation of kinetics for use with redundant manipulators." Impact 2022, no. 1 (February 4, 2022): 15–17. http://dx.doi.org/10.21820/23987073.2022.1.15.

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Robotics have numerous applications in industry and rely on manipulators, which are devices that can manipulate materials without the need for direct human contact. Manipulators are able to perform tasks thanks to so-called 'degrees of freedom'. Researchers are working to elucidate kinetics for use with redundant manipulators with potential benefits for industries across the globe in terms of time, energy and cost savings. Dr Kousuke Okabe, Department of Electrical Engineering, National Institute of Technology, which forms part of Wakayama College, Japan, is exploring redundant manipulators and their algorithms and wants to fill some of the existing knowledge gaps in this area. Okabe has found the orthogonal complement of the space spanned by the column vector of the inverse matrix of a generalised manipulator with a degree of redundancy of two or more and is working to find the generalised vector of this orthogonal complement in the future. Okabe and his team are also interested in exploring the effects of kinetics based on the state of movement of the hands. The researchers believe that their research results will be relevant to research on energy conservation in the field of high-speed manipulation, as well as the industrial world.

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Guigon, Emmanuel, Pierre Baraduc, and Michel Desmurget. "Computational Motor Control: Redundancy and Invariance." Journal of Neurophysiology 97, no. 1 (January 2007): 331–47. http://dx.doi.org/10.1152/jn.00290.2006.

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The nervous system controls the behavior of complex kinematically redundant biomechanical systems. How it computes appropriate commands to generate movements is unknown. Here we propose a model based on the assumption that the nervous system: 1) processes static (e.g., gravitational) and dynamic (e.g., inertial) forces separately; 2) calculates appropriate dynamic controls to master the dynamic forces and progress toward the goal according to principles of optimal feedback control; 3) uses the size of the dynamic commands (effort) as an optimality criterion; and 4) can specify movement duration from a given level of effort. The model was used to control kinematic chains with 2, 4, and 7 degrees of freedom [planar shoulder/elbow, three-dimensional (3D) shoulder/elbow, 3D shoulder/elbow/wrist] actuated by pairs of antagonist muscles. The muscles were modeled as second-order nonlinear filters and received the dynamics commands as inputs. Simulations showed that the model can quantitatively reproduce characteristic features of pointing and grasping movements in 3D space, i.e., trajectory, velocity profile, and final posture. Furthermore, it accounted for amplitude/duration scaling and kinematic invariance for distance and load. These results suggest that motor control could be explained in terms of a limited set of computational principles.

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Journal articles on the topic 'Redundancy of Degrees of Freedom'

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