Academic literature on the topic 'Planar Hyper-redundant Robot'

Redundancy resolution in a hyper-redundant space robots is a big challenge due to its extra degrees of freedom. This article presents a methodology to control motion planning of a planar space robot with multiple links, that is, hyper-redundant space robot. For control purpose, first a curve-constrained link trajectory tracking control has been developed. Then, the developed control approach has been extended for a collision-free trajectory tracking. For curve-constrained link trajectory tracking control, the backbone reference set (curve fitting) has been applied to exploit the redundancy of two-dimensional space robot of multiple links. For kinematic control purpose, a limited number of joints are actuated. The hyper-redundant space robot has the advantage that manipulator can be configured differently through actuation of different joints. The concept of a limited number of joint actuation has further been extended for collision-free trajectory tracking in the workspace in the presence of obstacles. Collision avoidance is based on the configuration transformation approach where the joints are made active or fixed joint position to facilitate collision-free tip trajectory. Before configuration transformation, collision detection has been performed based on the pseudo-distance criterion. The bond graph technique has been used for the dynamic model of the system and to formulate system equations. The simulation and the animation results validated the successful execution of the proposed approaches for the curve-constrained collision-free trajectory planning.

Serial robot manipulators have their servo motors with reduction gears on the link joints. When it comes to hyper-redundant robots, this kind of joint actuation mechanism cannot be implemented since this makes hyper-redundant robots too heavy. Instead, cable driven mechanisms are preferred. However, the positioning accuracy is negatively affected by the cables. This paper addresses the positioning accuracy problem of cable driven hyper-redundant robots by employing a 2-DOF robotic arm whose modules are counter-balanced. While the actuators connected to the base actively do most of the work using cables and springs, light and compact actuators connected to the links produce precise motion. The method will result in compact, light and precise hyper-redundant robotic arms. The above-mentioned procedure governed by a control software including a 2D simulator developed is experimentally proved to be a feasible method to compensate the gravitational torque successfully.

Hyper-redundant snakelike serial robots are of great interest due to their application in search and rescue during disaster relief in highly cluttered environments and recently in the field of medical robotics. A key feature of these robots is the presence of a large number of redundant actuated joints and the associated well-known challenge of motion planning. This problem is even more acute in the presence of obstacles. Obstacle avoidance for point bodies, nonredundant serial robots with a few links and joints, and wheeled mobile robots has been extensively studied, and several mature implementations are available. However, obstacle avoidance for hyper-redundant snakelike robots and other extended articulated bodies is less studied and is still evolving. This paper presents a novel optimization algorithm, derived using calculus of variation, for the motion planning of a hyper-redundant robot where the motion of one end (head) is an arbitrary desired path. The algorithm computes the motion of all the joints in the hyper-redundant robot in a way such that all its links avoid all obstacles present in the environment. The algorithm is purely geometric in nature, and it is shown that the motion in free space and in the vicinity of obstacles appears to be more natural. The paper presents the general theoretical development and numerical simulations results. It also presents validating results from experiments with a 12-degree-of-freedom (DOF) planar hyper-redundant robot moving in a known obstacle field.

Hyper-redundant robots are characterized by the presence of a large number of actuated joints, a lot more than the number required to perform a given task. These robots have been proposed and used for many applications involving avoiding obstacles or, in general, to provide enhanced dexterity in performing tasks. Making effective use of the extra degrees-of-freedom or resolution of redundancy has been an extensive topic of research and several methods have been proposed in literature. In this paper, we compare three known methods and show that an algorithm based on a classical curve, called the tractrix, leads to a more “natural” motion of the hyper-redundant robot with the displacements diminishing from the end-effector to the fixed base. In addition, since the actuators nearer the base “see” a greater inertia due to the links farther away, smaller motion of the actuators nearer the base results in better motion of the end-effector as compared with other two approaches. We present simulation and experimental results performed on a prototype eight-link planar hyper-redundant manipulator.

This paper presents a general discretization-based approach to the large deflection problems of spatial flexible links in compliant mechanisms. Based on the principal axes decomposition of structural compliance matrices, a particular type of elements, which relate to spatial six degrees-of-freedom (DOF) serial mechanisms with passive elastic joints, is developed to characterize the force-deflection behavior of the discretized small segments. Hence, the large deflection problems of spatial flexible rods can be transformed to the determination of static equilibrium configurations of their equivalent hyper-redundant mechanisms. The main advantage of the proposed method comes from the use of robot kinematics/statics, rather than structural mechanics. Thus, a closed-form solution to the system overall stiffness can be derived straightforwardly for efficient gradient-based searching algorithms. Two kinds of typical equilibrium problems are intensively discussed and the correctness has been verified by means of physical experiments. In addition, a 2DOF planar compliant parallel manipulator is provided as a case study to demonstrate the potential applications.

Recent years show an increasing interest in flexible robots due to their adaptability merits. This paper introduces a novel set of hyper-redundant flexible robots which we call actuated flexible manifold (AFM). The AFM is a two-dimensional hyper-redundant grid surface embedded in ℝ2 or ℝ3. Theoretically, such a mechanism can be manipulated into any continuous smooth function. We introduce the mathematical framework for the kinematics of an AFM. We prove that for a nonsingular configuration, the number of degrees of freedom (DOF) of an AFM is simply the number of its grid segments. We also show that for a planar rectangular grid, every nonsingular configuration that is also energetically stable is isolated. We show how to calculate the forward and inverse kinematics for such a mechanism. Our analysis is also applicable for three-dimensional hyper-redundant structures as well. Finally, we demonstrate our solution on some actuated flexible grid-shaped surfaces.

This thesis deals with motion planning of flexible one-dimensional objects and hyper-redundant serial robots moving in a plane or in three dimensional space. The flexible one-dimensional object is modeled as a continuous curve and a point on the curve is given a prescribed dis-placement. The key problem studied in the thesis is to obtain the motion of all points on the curve for the prescribed displacement subject to the condition of the length of the curve being preserved. Such motions are motivated by the need to model, analyze and realistically render of motion of hair, ropes and, more recently, flexible endoscopes where the assumption of constant axial length is realistic and reasonable. In this thesis, the discretized form of the flexible one-dimensional object is related to hyper-redundant robots and motion planning for such robots are obtained when the robot moves in free space and in a cluttered environment, avoiding obstacles. The motion planning of flexible one-dimensional objects is posed as an optimization problem with constraints and calculus of variation is employed to derive general analytical results. The first analytical result is that, for a given motion of a point on the curve and subject to the preservation of the length of the curve, the infinitesimal motion of any other point on the curve is minimized when the velocity vector at that point of the curve is along the tangent to the curve at that point. This leads to the second key result that when one end of a straight line segment is moved along a straight line, the velocity of the distal (far) end is minimized when it is along the straight line segment and the curve traced by the distal end is the well-known tractrix curve whose closed-form analytic expressions can be obtained using hyperbolic functions. If the flexible one-dimensional object is discretized by several piece-wise straight line segments, the magnitude of the velocity vector of the distal end of the segments attenuates as one goes away from the end where the input displacement is provided and if the direction of the input displacement is not changed, all the line segments eventually line up along the direction of the input displacement. It is shown that the attenuating and eventual aligning features lead to realistic and a more natural motion of the discretized segments and results in the establishment of a O(n) algorithm for motion planning. It is shown that the developed algorithm can be used for real-time simulation of the motion of discretized flexible one-dimensional objects and hyper-redundant serial robots. For realistic simulation and rendering of the motion, the flexible object must be discretized into a large number of straight segments. In the second part of the thesis, the flexible one-dimensional object is represented by a spline and motion planning algorithm is applied to the segments of the underlying control polygon of the spline. Since the number of segments in a control polygon can be significantly less, a significant increase in efficiency in simulation and rendering of the motion is obtained. However, it is known that as the control polygon is moved, the length of the spline curve changes. To overcome this problem, an innovative adaptive algorithm, involving sub-division and merging of the segments of the control polygon, is presented and this restricts the variation in the length of the curve to within a user prescribed tolerance. New analytical results related to the length of the curve and the angle between the adjacent segments of the control polygon are derived for quadratic and cubic splines and, depending on the prescribed tolerance, threshold values of the angle are obtained and used in the algorithm for approximate length preservation. The last part of the thesis deals with development of a planar hyper-redundant robot and implementation of motion planning algorithm on this robot. The hyper-redundant robot contains 12 links connected by actuated rotary joints which can change the angle between the links in a controlled manner. The links are on the wheels which provide support and allow it to move forward. The leading link also has a DC motor which can rotate the wheels so that it can move forward and pull the trailing links. Using the motion planning algorithm, for a prescribed motion of the leading link, the angle between two successive links are computed. These are given as input to the robot and the path traced by the 12 link robot is observed. It is seen that the motion of the hyper-redundant robot has the expected natural and realistic motion characteristics. It is furthermore demonstrated that the calculus of variation based approach for motion planning can be extended to include obstacle avoidance by adding additional constraints related to the location and size of the obstacles. It is shown that the entire robot optimally avoids the obstacles and moves in a more natural and realistic way.

Abstract A new approach to solve the inverse kinematic problem for hyper-redundant planar manipulators following any desired path is presented. The method is singularity free and provides a robust solution even in the event of mechanical failure of some of the robot actuators. The approach is based on defining virtual layers and dividing them into virtual/real three-link or four-link sub-robots. It starts by solving the inverse kinematic problem for the sub-robot located in the lowest virtual layer, which is then used to solve the inverse kinematic equations for the sub-robots located in the upper virtual layers. An algorithm is developed which provides a singularity-free solution up to full extension through a configuration index. The configuration index can be interpreted as the average of the determinants of the Jacobians of the sub-robots. The equations for the velocities and accelerations of the manipulator are solved by extending the same approach where it is realized that the value of configuration index is critical in maintaining joint velocity continuity. The inverse dynamic problem of the robot is also solved to obtain the torques required for the robot actuators to accomplish its task. Computer simulations of several hyper-redundant manipulators using the proposed method are presented as numerical examples.

Hyper-redundant robots are characterized by the presence of a large number of actuated joints, many more than the number required to perform a given task. These robots have been proposed and used for many application involving avoiding obstacles or, in general, to provide enhanced dexterity in performing tasks. Making effective use of the extra degrees of freedom or resolution of redundancy have been an extensive topic of research and several methods have been proposed in literature. In this paper, we compare three known methods and show that an algorithm based on a classical curve called the tractrix leads to a more ‘natural’ motion of the hyper-redundant robot with the displacements diminishing from the end-effector to the fixed base. In addition, since the actuators at the base ‘see’ the inertia of all links, smaller motion of the actuators nearer to the base results in a smoother motion of the end-effector as compared to other two approaches. We present simulation and experimental results performed on a prototype eight link planar hyper-redundant manipulator.

The Cartesian workspace of an n-DOF parallel robot (n < 6) is generally divided by singularity hyper-surfaces of dimension n−1. A common approach to reducing the dimension of the singularity manifold is to use actuation redundancy. However, in all previously reported works, adding one redundant actuator reduces the dimension of the singularity manifold by only one. This paper is the first to demonstrate that a properly designed actuation redundancy can be much more effective than this. Specifically, a 3-RPR design is presented in which the mobile platform and the base are equilateral triangles and show that adding a single RPR leg connecting the centers of these two triangles completely eliminates the singularities of the robot, which are otherwise a surface in the Cartesian space.