Статті в журналах: "Planar walking robot"

1

Zhou, Yu. "On the planar stability of rigid-link binary walking robots." Robotica 21, no. 6 (October 24, 2003): 667–75. http://dx.doi.org/10.1017/s0263574703005162.

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A binary walking robot moves as a result of bi-state actuator transitions. Because of the bi-state nature of binary joints, many research results about continuous walking robots cannot be applied to binary walking robots directly. In this paper, a new and simple model of rigid-link binary walking robot is proposed, around which related concepts are introduced, and formulas are derived. Based on this model, general characteristics and limitations of periodic gaits are discussed, and the stability qualities of several straight-line walking periodic gaits are studied in both pitch-greater-than-stroke and stroke-greater-than-pitch cases. Valuable results are obtained from the analysis, which should be followed in the design of rigid-link binary walking robots.

2

Ghanbari, Ahmad, S. Mohammad Reza S. Noorani, Hamid HajiMohammadi, and Aida Parvaresh. "Toward Realization a 7-Links Biped Robot - Trajectory Generation." Advanced Materials Research 816-817 (September 2013): 712–16. http://dx.doi.org/10.4028/www.scientific.net/amr.816-817.712.

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Naturalistic walking is one of the most important purposes of researches on biped robots. A feasible way is to translate the understanding of human walking to robot walking. One of the options that affects the quality of motion in a biped robot is concerned with trajectory generation. So, in this paper it's focused on trajectory generation methods for implementing a 7-links planar walker biped robot. Also, this model is simulated by VisualNastran software package and run according to a Clinical Gait Analysis (CGA) reference that has been modified for a planar model. Lastly, the results of simulation are reported.

3

Ji, Qiaoli, Zhihui Qian, Lei Ren, and Luquan Ren. "How does ankle push-off balance the walking speed and energy efficiency of planar biped robots?" Advances in Mechanical Engineering 13, no. 4 (April 2021): 168781402110119. http://dx.doi.org/10.1177/16878140211011905.

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Ankle push-off is defined as the phase in which muscle-tendon units about the ankle joint generate a burst of positive power during the step-to-step transition in human walking. The dynamic walking of a biped robot can be effectively realized through ankle push-off. However, how to use ankle push-off to balance the walking speed and energy efficiency of biped robots has not been studied deeply. In this study, the effects of the step length (the inter-leg angle is 40°, 50°, and 60°), torque and timing of ankle push-off on the walking speed and energy efficiency of biped robots were studied. The results show that when the step length is 50°, the push-off torque is 30 N· m and the corresponding push-off timing occurs at 43% of the gait cycle, the simulated robot obtains a highly economical walking gait. The corresponding maximum normalized walking speed is 0.40, and the minimum mechanical cost of transport is 2.25. To acquire a more economical walking gait of biped robots, the amount of ankle push-off and the push-off timing need to be coordinated. The purpose of this study is to provide a reference for the influence of ankle push-off on the motion performance of biped robots.

4

Agrawal, Abhishek, and Sunil K. Agrawal. "An Approach to Identify Joint Motions for Dynamically Stable Walking." Journal of Mechanical Design 128, no. 3 (July 21, 2005): 649–53. http://dx.doi.org/10.1115/1.2181996.

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Biped robots are more versatile than conventional wheeled robots, but they tend to tip over easily. The dynamic stability of a biped robot needs to be maintained during walking. In this paper, a novel approach to compute dynamically stable walking motions of a planar six degree-of-freedom biped is presented. This approach is analytical and is based on the need for periodicity of the motion. The resulting gait satisfies the dynamic stability criteria. Sets of joint motions for different step sizes and speed of walking, i.e., quasi-statically and dynamically stable walking patterns, can be obtained.

5

Anjidani, Majid, M. R. Jahed Motlagh, M. Fathy, and M. Nili Ahmadabadi. "A novel online gait optimization approach for biped robots with point-feet." ESAIM: Control, Optimisation and Calculus of Variations 25 (2019): 81. http://dx.doi.org/10.1051/cocv/2017034.

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Designing a stable walking gait for biped robots with point-feet is stated as a constrained nonlinear optimization problem which is normally solved by an offline numerical optimization method. On the result of an unknown modeling error or environment change, the designed gait may be ineffective and an online gait improvement is impossible after the optimization. In this paper, we apply Generalized Path Integral Stochastic Optimal Control to closed-loop model of planar biped robots with point-feet which leads to an online Reinforcement Learning algorithm to design the walking gait. We study the ability of the proposed method to adapt the controller of RABBIT, which is a planar biped robot with point-feet, for stable walking. The simulation results show that the method, starting a dynamically unstable initial gait, quickly compensates the modeling error and reaches to a walking with exponential stability and desired features in a new situation which was impossible by the past methods.

6

BAGHERI, AHMAD, FARID NAJAFI, REZA FARROKHI, RAHMAN YOUSEFI MOGHADDAM, and MOHAMMAD EBRAHIM FELEZI. "DESIGN, DYNAMIC MODIFICATION, AND ADAPTIVE CONTROL OF A NEW BIPED WALKING ROBOT." International Journal of Humanoid Robotics 03, no. 01 (March 2006): 105–26. http://dx.doi.org/10.1142/s0219843606000527.

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Recently, a lot of research has been conducted in the area of biped walking robots that could be compared to human beings. The aim of this article is to control a new planar biped robot by means of an adaptive procedure. The newly designed robot is able to move on its heel like a human. After derivation of dynamic equations of motion for two states of the robot, namely, "supporting leg and trunk" and "swing leg" separately, the stability of robot is achieved by locating the zero moment point (ZMP). A dynamic modification is developed for ZMP positioning. For motion control of the robot, the physical parameters (such as mass, link length and geometry) are estimated (identified) by adaptive methods. A Matlab based software simulation is also conducted.

7

Channon, P. H., S. H. Hopkins, and D. T. Pham. "Derivation of optimal walking motions for a bipedal walking robot." Robotica 10, no. 2 (March 1992): 165–72. http://dx.doi.org/10.1017/s026357470000758x.

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SUMMARYThe problem of determining energy optimal walking motions for a bipedal walking robot is considered. A full dynamic model of a planar seven-link biped with feet is derived including the effects of impact of the feet with the ground. Motions of the hip and feet during a regular step are then modelled by 3rd order polynomials, the coefficients of which are obtained by numerically minimising an energy cost function. Results are given in the form of walking profiles and energy curves for the specific cases of motion over level ground, motion up and down an incline, and varying payload.

8

Tang, Yongchen, Shugen Ma, Yi Sun, and Dingxin Ge. "Planar legged walking of a passive-spine hexapod robot." Advanced Robotics 29, no. 23 (August 21, 2015): 1510–25. http://dx.doi.org/10.1080/01691864.2015.1070105.

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9

Krishchenko, A. P., S. B. Tkachev, and D. A. Fetisov. "Planar walking control for a five-link biped robot." Computational Mathematics and Modeling 18, no. 2 (April 2007): 176–91. http://dx.doi.org/10.1007/s10598-007-0018-8.

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10

Şafak, Koray K., Turgut Batuhan Baturalp, and Selim Bozkurt. "Parametric Design and Prototyping of a Low-Power Planar Biped Robot." Biomimetics 8, no. 4 (August 5, 2023): 346. http://dx.doi.org/10.3390/biomimetics8040346.

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This study proposes a design approach and the development of a low-power planar biped robot named YU-Bibot. The kinematic structure of the robot consists of six independently driven axes, and it weighs approximately 20 kg. Based on biomimetics, the robot dimensions were selected as the average anthropomorphic dimensions of the human lower extremities. The optimization of the mechanical design and actuator selection of the robot was based on the results of parametric simulations. The natural human walking gait was mimicked as a walking pattern in these simulations. As a result of the optimization, a low power-to-weight ratio of 30 W/kg was obtained. The drive system of the robot joints consists of servo-controlled brushless DC motors with reduction gears and additional bevel gears at the knee and ankle joints. The robot features spring-supported knee and ankle joints that counteract the robot’s weight and compensate for the backlash present in these joints. The robot is constrained to move only in the sagittal plane by using a lateral support structure. The robot’s feet are equipped with low-cost, force-sensitive resistor (FSR)-type sensors for monitoring ground contact and zero-moment point (ZMP) criterion. The experimental results indicate that the proposed robot mechanism can follow the posture commands accurately and demonstrate locomotion at moderate stability. The proposed parametric natural gait simulation-based design approach and the resulting biped robot design with a low power/weight ratio are the main contributions of this study.

11

Jiang, Zhujin, Yan Wang, and Ketao Zhang. "Development of a Pneumatically Actuated Quadruped Robot Using Soft–Rigid Hybrid Rotary Joints." Robotics 13, no. 2 (January 29, 2024): 24. http://dx.doi.org/10.3390/robotics13020024.

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Inspired by musculoskeletal systems in nature, this paper presents a pneumatically actuated quadruped robot which utilizes two soft–rigid hybrid rotary joints in each of the four two-degrees of freedom (DoF) planar legs. We first introduce the mechanical design of the rotary joint and the integrated quadruped robot with minimized onboard electronic components. Based on the unique design of the rotary joint, a joint-level PID-based controller was adopted to control the angular displacement of the hip and knee joints of the quadruped robot. Typical gait patterns for legged locomotion, including the walking and trotting gaits, were investigated and designed. Proof-of-concept prototypes of the rotary joint and the quadruped robot were built and tested. The experimental results demonstrated that the rotary joint generated a maximum torque of 5.83 Nm and the quadruped robot was capable of locomotion, achieving a trotting gait of 187.5 mm/s with a frequency of 1.25 Hz and a walking gait of 12.8 mm/s with a gait cycle of 7.84 s. This study reveals that, compared to soft-legged robots, the quadruped robot has a simplified analytical model for motion control, size scalability and high movement speeds, thereby exhibiting significant potential for applications in extreme environments.

12

Lugo-Villeda, L. I., and V. Parra-Vega. "A Computational Mechatronics Approach for the Analysis, Synthesis and Design of a Simple Active Biped Robot: Theory and Experiments." Applied Bionics and Biomechanics 3, no. 2 (2006): 121–30. http://dx.doi.org/10.1155/2006/289145.

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Biped walking is a quite complex process that has been mastered only by human beings. Transferring this skill to a robot requires implementing advanced techniques in every aspect. To this end, a computational mechatronics platform was integrated to run the scheme for the analysis, synthesis and design to achieve planar biped walking. The result is an advanced computational tool that integrates advanced modeling and control as well as path planning techniques along with hardware-in-the-loop for perhaps the simplest biped robot. An experimental underactuated three-degree-of-freedom (two active and one passive) active biped robot yields encouraging results; that is, achieving biped walking with this simple device requires adding a telescopic support leg. Considering a more complete dynamic model to take into account frictional and contact forces.

13

Pedro, Gabriel Duarte Gonçalves, Gabriel Bermudez, Vivian Suzano Medeiros, Hélio Jacinto da Cruz Neto, Luiz Guilherme Dias de Barros, Gustavo Pessin, Marcelo Becker, Gustavo Medeiros Freitas, and Thiago Boaventura. "Quadruped Robot Control: An Approach Using Body Planar Motion Control, Legs Impedance Control and Bézier Curves." Sensors 24, no. 12 (June 13, 2024): 3825. http://dx.doi.org/10.3390/s24123825.

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In robotics, the ability of quadruped robots to perform tasks in industrial, mining, and disaster environments has already been demonstrated. To ensure the safe execution of tasks by the robot, meticulous planning of its foot placements and precise leg control are crucial. Traditional motion planning and control methods for quadruped robots often rely on complex models of both the robot itself and its surrounding environment. Establishing these models can be challenging due to their nonlinear nature, often entailing significant computational resources. However, a more simplified approach exists that focuses on the kinematic model of the robot’s floating base for motion planning. This streamlined method is easier to implement but also adaptable to simpler hardware configurations. Moreover, integrating impedance control into the leg movements proves advantageous, particularly when traversing uneven terrain. This article presents a novel approach in which a quadruped robot employs impedance control for each leg. It utilizes sixth-degree Bézier curves to generate reference trajectories derived from leg velocities within a planar kinematic model for body control. This scheme effectively guides the robot along predefined paths. The proposed control strategy is implemented using the Robot Operating System (ROS) and is validated through simulations and physical experiments on the Go1 robot. The results of these tests demonstrate the effectiveness of the control strategy, enabling the robot to track reference trajectories while showing stable walking and trotting gaits.

14

Yuan, Li Peng, Li Ming Yuan, and Hong Ying Lu. "Optimal Energy-Effective Gait for Biped Robot." Applied Mechanics and Materials 347-350 (August 2013): 839–43. http://dx.doi.org/10.4028/www.scientific.net/amm.347-350.839.

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Although peoples legs are capable of a broad range of muscle-use and gait patterns, they generally prefer just two, walking and running. A popular hypothesis regarding legged locomotion is that humans and other large animals walk and run in a manner that minimizes the metabolic energy expenditure for locomotion. Here, a mathematical model for a simple two-dimensional planar kneed walker with point feet and two bended knees is discussed. An energy-effective gait is designed by using piecewise torque method. Then, the robot model can exhibit a natural and reasonable walk on a level ground. The results can prove that the proposed optimal energy-effective gait is suitable for this kneed biped walking robot. And we also discover some walking rules maybe true through the results of optimization.

15

Nguyen, Quan, Ayush Agrawal, William Martin, Hartmut Geyer, and Koushil Sreenath. "Dynamic bipedal locomotion over stochastic discrete terrain." International Journal of Robotics Research 37, no. 13-14 (August 7, 2018): 1537–53. http://dx.doi.org/10.1177/0278364918791718.

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Owing to their morphology and mechanical design, bipedal robots have the ability to traverse over a wide range of terrain including those with discrete footholds such as stepping stones. This paper addresses the challenge of planar dynamic robotic walking over stochastically generated stepping stones with significant variations in step length and step height, and where the robot has knowledge about the location of the next discrete foothold only one step ahead. Specifically, our approach utilizes a two-step periodic gait optimization technique to build a library of gaits parametrized by their resulting step lengths and step heights, as well as the initial configuration of the robot. By doing so, we address the problems involved during step transition when switching between the different walking gaits. We then use gait interpolation in real-time to obtain the desired gait. The proposed method is successfully validated on ATRIAS, an underactuated, human-scale bipedal robot, to achieve precise footstep placement. With no change in step height, step lengths are varied in the range of [23:78] cm. When both step length and step height are changed, their variation are within [30:65] cm and [−22:22] cm, respectively. The average walking speed of both these experiments is 0.6 m/s.

16

Fevre, Martin, Bill Goodwine, and James P. Schmiedeler. "Terrain-blind walking of planar underactuated bipeds via velocity decomposition-enhanced control." International Journal of Robotics Research 38, no. 10-11 (August 26, 2019): 1307–23. http://dx.doi.org/10.1177/0278364919870242.

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In this article, we develop and assess a novel approach for the control of underactuated planar bipeds that is based on velocity decomposition. The new controller employs heuristic rules that mimic the functionality of transverse linearization feedback control and that can be layered on top of a conventional hybrid zero dynamics (HZD)-based controller. The heuristics sought to retain HZD-based control’s simplicity and enhance disturbance rejection for practical implementation on realistic biped robots. The proposed control strategy implements a feedback on the time rate of change of the decomposed uncontrolled velocity and is compared with conventional HZD-based control and transverse linearization feedback control for both vanishing and non-vanishing disturbances. Simulation studies with a point-foot, three-link biped show that the proposed method has nearly identical performance to transverse linearization feedback control and outperforms conventional HZD-based control. For the non-vanishing case, the velocity decomposition-enhanced controller outperforms HZD-based control, but takes fewer steps on average before failure than transverse linearization feedback control when walking on uneven terrain without visual perception of the ground. The findings were validated experimentally on a planar, five-link biped robot for eight different uneven terrains. The velocity decomposition-enhanced controller outperformed HZD-based control while maintaining a relatively low specific energetic cost of transport (~0.45). The biped robot “blindly” traversed uneven terrains with changes in terrain height accumulating to 5% of its leg length using the stand-alone low-level controller.

17

Theeravithayangkura, Chayooth, Tomohito Takubo, Kenichi Ohara, Yasushi Mae, and Tatsuo Arai. "Adaptive Gait for Dynamic Rotational Walking Motion on Unknown Non-Planar Terrain by Limb Mechanism Robot ASTERISK." Journal of Robotics and Mechatronics 25, no. 1 (February 20, 2013): 172–82. http://dx.doi.org/10.20965/jrm.2013.p0172.

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An adaptive gait is proposed for dynamic rotational walking motion of multi-legged mobile robots by utilizing body angle compensation and the center of mass height control. Posture control is used to further enhance the robustness and stability of the robot based on a posture optimization database. The database is created by using a genetic algorithms in order to find the most suitable posture for each virtual plane created during body compensation in adaptive gait control. Additionally, the stability of the robot is controlled by online zero-moment point compensation and compliance control. In order to test the robustness of motion, experiments are divided into three parts: inclined-plane (linear variation), step (step variation), and obstacle (impulse variation). As a result of this research, with the proposed method, the robot could walk up and down inclined-planes with angles of 6.8° and 5.6°, respectively, and walk up and down a step and over an obstacle with a height of 20 mm.

18

Or, Jimmy. "A Control System for a Flexible Spine Belly-Dancing Humanoid." Artificial Life 12, no. 1 (January 2006): 63–88. http://dx.doi.org/10.1162/106454606775186464.

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Recently, there has been a lot of interest in building anthropomorphic robots. Research on humanoid robotics has focused on the control of manipulators and walking machines. The contributions of the torso towards ordinary movements (such as walking, dancing, attracting mates, and maintaining balance) have been neglected by almost all humanoid robotic researchers. We believe that the next generation of humanoid robots will incorporate a flexible spine in the torso. To meet the challenge of controlling this kind of high-degree-of-freedom robot, a new control architecture is necessary. Inspired by the rhythmic movements commonly exhibited in lamprey locomotion as well as belly dancing, we designed a controller for a simulated belly-dancing robot using the lamprey central pattern generator. Experimental results show that the proposed lamprey central pattern generator module could potentially generate plausible output patterns, which could be used for all the possible spine motions with minimized control parameters. For instance, in the case of planar spine motions, only three input parameters are required. Using our controller, the simulated robot is able to perform complex torso movements commonly seen in belly dancing as well. Our work suggests that the proposed controller can potentially be a suitable controller for a high-degree-of-freedom, flexible spine humanoid robot. Furthermore, it allows us to gain a better understanding of belly dancing by synthesis.

19

Zhao, Qiu Ling, and Li Yang. "A Dynamics Analysis of a Double-Legs Robot." Applied Mechanics and Materials 494-495 (February 2014): 1152–55. http://dx.doi.org/10.4028/www.scientific.net/amm.494-495.1152.

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A passive-walking of a double-legs planar Robot is considered. The dynamic equation of the system walking down a shallow slope, powered only by gravity is established according to Lagrange method. After the equation was transferred to a dimensionless one, it shows the motion is depended not only on the free parameter, the ramp slope γ, but also on the ratio of m/M, m is mass of the foot of the model and M is the mass of the hip as well; The analytic calculations show that at the identical ramp slope γ, the whole moving has different phases: stable period walking and chaos with the increasing of m/M. Its phase portraits and graph of step time interval show the influence to the motion because of the ratio of m/M.

20

Vankina, I. N., and D. A. Fetisov. "Planar Five-link Biped Robot Movement over a Stepped Surface." Mathematics and Mathematical Modeling, no. 3 (December 9, 2021): 1–28. http://dx.doi.org/10.24108/mathm.0321.0000270.

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Modeling the anthropomorphic robot movement is of great interest to researchers all over the world. At the same time, the movement control of a walking mechanism is always a high dimension challenge. The difficulty with the anthropomorphic robot control is also caused by the fact that such a mechanism has always a hybrid dynamics and represents a sequential change of two phases – the single support phase and the double support phase (phase of changing robot’s leg). At the single support phase and at another phase the behavior of the biped robot is described by a system of ordinary differential equations and by a system of linear algebraic equations, respectively.The task of biped robot movement control has been studied in detail for the case when the robot moves over the horizontal surface. Obstacles make the task significantly complicated. The paper considers the movement control of the biped robot over the surface that is a periodic alternation of horizontal sections and obstacles. The obstacles represent steps of the same height known. It is assumed that the lengths of horizontal sections and steps are known as well. The objective is to create a control that provides robot’s periodic movement over the specified surface according to inherent characteristics of a walking human.For the single support phase, the outputs are proposed, the equality of which to zero corresponds to the robot’s movement with a given set of characteristics. The paper presents the feedback controls that stabilize the proposed outputs for a finite amount of time. By choosing the feedback parameters, it is possible to adjust the stabilization time so that the outputs become equal to zero when reached the end of each step.It is shown that for the chosen control law, the problem of constructing the control of robot’s periodic movement is reduced to the solution of a nonlinear equation. In the paper, we discuss the approaches to solving this equation and present the results of numerical simulation.The results obtained can be used to solve the problem of providing control of the biped robot movement over the surfaces with obstacles of a more complicated shape.Modeling the anthropomorphic robot movement is of great interest to researchers all over the world. At the same time, the movement control of a walking mechanism is always a high dimension challenge. The difficulty with the anthropomorphic robot control is also caused by the fact that such a mechanism has always a hybrid dynamics and represents a sequential change of two phases – the single support phase and the double support phase (phase of changing robot’s leg). At the single support phase and at another phase the behavior of the biped robot is described by a system of ordinary differential equations and by a system of linear algebraic equations, respectively.The task of biped robot movement control has been studied in detail for the case when the robot moves over the horizontal surface. Obstacles make the task significantly complicated. The paper considers the movement control of the biped robot over the surface that is a periodic alternation of horizontal sections and obstacles. The obstacles represent steps of the same height known. It is assumed that the lengths of horizontal sections and steps are known as well. The objective is to create a control that provides robot’s periodic movement over the specified surface according to inherent characteristics of a walking human.For the single support phase, the outputs are proposed, the equality of which to zero corresponds to the robot’s movement with a given set of characteristics. The paper presents the feedback controls that stabilize the proposed outputs for a finite amount of time. By choosing the feedback parameters, it is possible to adjust the stabilization time so that the outputs become equal to zero when reached the end of each step.It is shown that for the chosen control law, the problem of constructing the control of robot’s periodic movement is reduced to the solution of a nonlinear equation. In the paper, we discuss the approaches to solving this equation and present the results of numerical simulation.The results obtained can be used to solve the problem of providing control of the biped robot movement over the surfaces with obstacles of a more complicated shape.

21

Kaede, Kazunori, and Tooru Nogai. "Gait Generation for a Walking Robot with Passive Joints." Journal of Robotics and Mechatronics 20, no. 5 (October 20, 2008): 785–92. http://dx.doi.org/10.20965/jrm.2008.p0785.

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We selected a three-legged robot to study passive walking. The robot consists of one actuated leg and one pair of passive legs. The active leg has a knee joint and an ankle joint. The passive legs, which we call “crutches,” have no knee joints, but it do have passive ankle joints. The crutches and the leg are connected by a hip joint. The robot behavior is passive while it supports itself on its crutches and swings its leg. In order for the robot to have a wide stride and be stable after the leg swings out and lands, a referenced trajectory of the leg's swing is generated by a planar, four-link model simulation to evaluate its posture after the leg lands. The pattern of walking applies to the robot's actual walk on level ground. An additional walking robot that has a knee joint that is permitted to rotate freely has been designed. The lower leg is equipped with a solenoid magnet which keeps the knee joint straight. The knee joint bends and the leg swings in response to a change in the input torque to the hip joint.

22

Hamon, Arnaud, and Yannick Aoustin. "Walking gait of a planar bipedal robot with four-bar knees." Movement & Sport Sciences 90, no. 4 (2015): 87. http://dx.doi.org/10.3917/sm.090.0087.

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23

Arnaud, Hamon, and Aoustin Yannick. "Walking gait of a planar bipedal robot with four-bar knees." Movement & Sport Sciences - Science & Motricité, no. 90 (February 5, 2013): 87–97. http://dx.doi.org/10.1051/sm/2012041.

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24

Clary, Patrick, Pedro Morais, Alan Fern, and Jonathan Hurst. "Monte-Carlo Planning for Agile Legged Locomotion." Proceedings of the International Conference on Automated Planning and Scheduling 28 (June 15, 2018): 446–50. http://dx.doi.org/10.1609/icaps.v28i1.13933.

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Recent progress in legged locomotion research has produced robots that can perform agile blind-walking with robustness comparable to a blindfolded human. However, this walking approach has not yet been integrated with planners for high-level activities. In this paper, we take a step towards high-level task planning for these robots by studying a planar simulated biped that captures their essential dynamics. We investigate variants of Monte-Carlo Tree Search (MCTS) for selecting an appropriate blind-walking controller at each decision cycle. In particular, we consider UCT with an intelligently selected rollout policy, which is shown to be capable of guiding the biped through treacherous terrain. In addition, we develop a new MCTS variant, called Monte-Carlo Discrepancy Search (MCDS), which is shown to make more effective use of limited planning time than UCT for this domain. We demonstrate the effectiveness of these planners in both deterministic and stochastic environments across a range of algorithm parameters. In addition, we present results for using these planners to control a full-order 3D simulation of Cassie, an agile bipedal robot, through complex terrain.

25

Liu, Chenggang, Christopher G. Atkeson, and Jianbo Su. "Biped walking control using a trajectory library." Robotica 31, no. 2 (May 25, 2012): 311–22. http://dx.doi.org/10.1017/s0263574712000203.

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SUMMARYThis paper presents biped walking control using a library of optimal trajectories. Biped walking control is formulated as an optimal control problem. We use a parametric trajectory optimization method to find the periodic steady-state walking trajectory. As a second stage, we use Differential Dynamic Programming to generate a library of optimal trajectories and locally linear models of the optimal control law, which are used to construct a more global control law. The proposed controller is compared with a trajectory tracking controller using optimal gains. The utility and performance of the proposed method are evaluated using simulated walking control of a planar five-link biped robot.

26

Ibrayev, Sayat, Nutpulla Jamalov, Arman Ibrayeva, and Gaukhar Mukhambetkaliyeva. "Optimal structural synthesis of agricultural legged robot with minimal damage on soil." E3S Web of Conferences 135 (2019): 01027. http://dx.doi.org/10.1051/e3sconf/201913501027.

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Optimal structural synthesis of agricultural legged robot is carried out, that causes minimal damage on soil and provide the most favorable conditions for plant growth. A rational structure of a legged robot with orthogonal propel based on kinematic decoupling of the motion is proposed. Most of traditionally used walking robots have universal “insect type” structure with multiple actuators to be synchronized which result in complex control. The alternative design is realizing a concept of functional independence of the actuators when each actuator is responsible for specified purpose: the main actuators are responsible for rectilinear translational motion of cabine/chassis whereas another group of actuators are responsible for adaptation purposes and anothers participate in turning/maneuvering. This allows to carry out the cabine/hull shifting and turning with a minimum number of actuators and simplified control. A new kinematic equivalent scheme of turning mechanism was proposed in order to optimize turning modes of the robot. The proposed planar model allows to determine the optimal parameters of the robot by applying multicriteria synthesis methods of parallel robot manipulators based on isotropy, maneuverability and other criteria.

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Singh, Rajmeet, and Tarun Kumar Bera. "Fault detection, isolation and reconfiguration of a bipedal-legged robot." SIMULATION 95, no. 10 (October 15, 2018): 955–77. http://dx.doi.org/10.1177/0037549718803716.

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This paper deals with the fault detection, isolation (FDI) and reconfiguration of the locomotion of a bipedal-legged robot. Initially, the planar model of the legged robot in the vertical plane is developed using a bond graph (BG) approach. Then, the planar BG model of the legged robot is extended to the three-dimensional legged robot. Two individual motors are used to actuate the prismatic leg of the robot for locomotion. The BG simulation provides results for straight walking based on an oscillating cylinder mechanism and the turning motion of the legged robot are discussed. The prototype model of the legged robot is also developed and experimentation is done for straight and inclined plane applications. Finally, an FDI technique for the three-dimensional model of a legged robot is developed for the generation of fault indicators (i.e., analytical redundancy relations; ARRs) in the presence of system failure. The ARRs are derived from the BG model of the legged robot during the occurrences of the fault. The experimental results are validated with the simulation results for FDI and reconfiguration when the robot manoeuvres in a U-shaped path. The real-time fault diagnosis and reconfiguration for locomotion of the legged robot is possible with this FDI approach.

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Blajer, W., and W. Schiehlen. "Walking Without Impacts as a Motion/Force Control Problem." Journal of Dynamic Systems, Measurement, and Control 114, no. 4 (December 1, 1992): 660–65. http://dx.doi.org/10.1115/1.2897738.

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The paper deals with the synthesis of control for impactless bipedal walking. In order to avoid impacts, both the specified motion of the biped and its ground reactions are controlled, yielding a combined motion and force control problem. A method for modeling and solving such problems is proposed, and then illustrated by the example of an impactless planar walk of a seven-link bipedal robot. Some numerical results of the motion simulation are reported.

29

Nemoto, Takuma, Rajesh Elara Mohan, and Masami Iwase. "Rolling Locomotion Control of a Biologically Inspired Quadruped Robot Based on Energy Compensation." Journal of Robotics 2015 (2015): 1–10. http://dx.doi.org/10.1155/2015/649819.

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We have developed a biologically inspired reconfigurable quadruped robot which can perform walking and rolling locomotion and transform between walking and rolling by reconfiguring its legs. This paper presents an approach to control rolling locomotion with the biologically inspired quadruped robot. For controlling rolling locomotion, a controller which can compensate robot’s energy loss during rolling locomotion is designed based on a dynamic model of the quadruped robot. The dynamic model describes planar rolling locomotion based on an assumption that the quadruped robot does not fall down while rolling and the influences of collision and contact with the ground, and it is applied for computing the mechanical energy and a plant in a numerical simulation. The numerical simulation of rolling locomotion on the flat ground verifies the effectiveness of the proposed controller. The simulation results show that the quadruped robot can perform periodic rolling locomotion with the proposed energy-based controller. In conclusion, it is shown that the proposed control approach is effective in achieving the periodic rolling locomotion on the flat ground.

30

Peidró, Adrián, Julio Gallego, Luis Payá, José María Marín, and Óscar Reinoso. "Trajectory Analysis for the MASAR: A New Modular and Single-Actuator Robot." Robotics 8, no. 3 (September 5, 2019): 78. http://dx.doi.org/10.3390/robotics8030078.

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Single-actuator mobile robots offer the benefits of low energy consumption, low weight and size, and low cost, but their motion is typically only one-dimensional. By using auxiliary binary mechanisms that redirect and channel the driving force of their only actuator in different ways, it is possible for these robots to perform higher-dimensional motions, such as walking straight, steering, or jumping, with only one motor. This paper presents the MASAR, a new Modular And Single-Actuator Robot that carries a single motor and several adhesion pads. By alternately releasing or attaching these adhesion pads to the environment, the proposed robot is able to pivot about different axes using only one motor, with the possibility of performing concave plane transitions or combining with other identical modules to build more complex reconfigurable robots. In this paper, we solve the planar trajectory tracking problem of this robot for polygonal paths made up of sequences of segments, which may include narrow corridors that are difficult to traverse. We propose a locomotion based on performing rotations of 180 ∘ , which we demonstrate to be the minimum-time solution for long trajectories, and a near-optimal solution for shorter ones.

31

HU, JIANJUEN J., JERRY E. PRATT, CHEE-MENG CHEW, HUGH M. HERR, and GILL A. PRATT. "VIRTUAL MODEL BASED ADAPTIVE DYNAMIC CONTROL OF A BIPED WALKING ROBOT." International Journal on Artificial Intelligence Tools 08, no. 03 (September 1999): 337–48. http://dx.doi.org/10.1142/s0218213099000221.

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The robustness of bipedal walking robots can be enhanced by the use of adaptive control techniques. In this paper, we extend a previous control approach. "Virtual Model Control" (VMC) [6] to create "Adaptive Virtual Model Control" (AVMC). The adaptation compensates for external disturbances and unmodelled dynamics, enhancing robustness in the control of height, pitch, and forward speed. The state machine used to modulate the virtual model components and to select the appropriate virtual to physical transformations (as in traditional VMC) is also used to inform the adaptation about the robot's changing configuration. The design procedure for AVMC is described in this paper and simulation results are presented for a planar walking biped.

32

Bououden, S., and F. Abdessemed. "Walking control for a planar biped robot using 0-flat normal form." Robotics and Autonomous Systems 62, no. 1 (January 2014): 68–80. http://dx.doi.org/10.1016/j.robot.2012.07.011.

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33

Tatar, Ahmet Burak, Alper Kadir Tanyıldızı, and Oğuz Yakut. "Shooting Control Application from a Quadruped Robot with a Weapon System via Sliding mode Control Method." Defence Science Journal 70, no. 4 (July 13, 2020): 404–11. http://dx.doi.org/10.14429/dsj.70.14374.

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With the developing technological process, it is expected that the usage of robots will increase in defense systems as in every field. One of the main objectives of the robotic studies for the defense industry is to capture the targeted success under all kinds of disruptive effects with robotic systems and to present this technology to the service of the army. A weapon system with a single degree of freedom was placed on a quadruped robot. System’s dynamic behavior, which has 12 degrees of freedom and planar movements, is modeled mathematically. Simulations of the shots made to the fixed targets were carried out during the walking of the quadruped robot. The gun barrel stabilization was realized to achieve accurate shots under disruptive effects. The sliding-mode control method was used to perform the barrel stabilisation. In this study, it is shown that a quadruped robot with a weapon system can perform successful shots against fixed targets. MATLAB is used for simulations and the results are shown with figures, graphics, and tables.

34

Asano, Fumihiko, and Masashi Suguro. "Limit cycle walking, running, and skipping of telescopic-legged rimless wheel." Robotica 30, no. 6 (November 29, 2011): 989–1003. http://dx.doi.org/10.1017/s0263574711001226.

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SUMMARYThis paper investigates the efficiency and properties of limit cycle walking, running, and skipping of a planar, active, telescopic-legged rimless wheel. First, we develop the robot equations of motion and design an output following control for the telescopic-legs' action. We then numerically show that a stable walking gait can be generated by asymmetrizing the impact posture. Second, we numerically show that a stable running gait can be generated by employing a simple feedback control of the control period, and compare the properties of the generated running gait with those of the walking gait. Furthermore, we find out another underlying gait called skipping that emerges as an extension of the walking gait. Through numerical analysis, we show that the generated skipping gaits are inherently stable and are less efficient than the other two gaits.

35

Machado, Juan E., Héctor M. Becerra, and Mónica Moreno Rocha. "Modeling and Finite-Time Walking Control of a Biped Robot with Feet." Mathematical Problems in Engineering 2015 (2015): 1–17. http://dx.doi.org/10.1155/2015/963496.

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This paper addresses the problem of modeling and controlling a planar biped robot with six degrees of freedom, which are generated by the interaction of seven links including feet. The biped is modeled as a hybrid dynamical system with a fully actuated single-support phase and an instantaneous double-support phase. The mathematical modeling is detailed in the first part of the paper. In the second part, we present the synthesis of a controller based on virtual constraints, which are codified in an output function that allows defining a local diffeomorphism to linearize the robot dynamics. Finite-time convergence of the output to the origin ensures a collision between the swing foot and the ground with an appropriate configuration for the robot to give a step forward. The components of the output track adequate references that encode a walking pattern. Finite-time convergence of the tracking errors is enforced by using second-order sliding mode control. The main contribution of the paper is an evaluation and comparison of discontinuous and continuous sliding mode control in the presence of parametric uncertainty and external disturbances. The robot model and the synthesized controller are evaluated through numerical simulations.

36

Dadashzadeh, Behnam, and C. J. B. Macnab. "SLIP-Based Control of Bipedal Walking Based on Two-Level Control Strategy." Robotica 38, no. 8 (November 4, 2019): 1434–49. http://dx.doi.org/10.1017/s0263574719001553.

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SUMMARYIn this research, we propose a two-level control strategy for simultaneous gait generation and stable control of planar walking of the Assume The Robot Is A Sphere (ATRIAS) biped robot with unlocked torso, utilizing active spring-loaded inverted pendulum (ASLIP) as reference models. The upper level consists of an energy-regulating control calculated using the ASLIP model, producing reference ground reaction forces (GRFs) for the desired gait. In the lower level controller, PID force controllers for the motors ensure tracking of the reference GRFs for ATRIAS direct dynamics. Meanwhile, ATRIAS torso angle is controlled stably to make it able to follow a point mass template model. Advantages of the proposed control strategy include simplicity and efficiency. Simulation results using ATRIAS’s complete dynamic model show that the proposed two-level controller can reject initial condition disturbances while generating stable and steady walking motion.

37

Liu, Yubin, Shuai Heng, Xizhe Zang, Zhenkun Lin, and Jie Zhao. "Multiphase Trajectory Generation for Planar Biped Robot Using Direct Collocation Method." Mathematical Problems in Engineering 2021 (January 29, 2021): 1–14. http://dx.doi.org/10.1155/2021/6695528.

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Stability and energy efficiency are the main focuses in the bipedal robot field. In this paper, we apply a multiphase gait, which is different from the widely used two-phase gait, to improve the stability at the moment, when a biped robot transfers from the double support phase to the single support phase. Then, we create dynamic equations with contact forces in each phase using Lagrangian formulation. Furthermore, the direct collocation method is utilized to generate the optimal trajectory toward both stability and energy efficiency. Finally, the comparison between multiphase gait and two-phase gait is performed with numerical simulations. The results prove that multiphase gait increases the stability margin in the cost of slightly decreasing energy efficiency. Besides, both gaits show a similar human-like characteristic in hip height variation during walking.

38

Wang, Hong Bo. "Based on Biped Robot Walking in Horizontal Surface Research of Dynamic Simulation." Advanced Materials Research 301-303 (July 2011): 707–12. http://dx.doi.org/10.4028/www.scientific.net/amr.301-303.707.

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The purpose of this thesis is to develop a dynamic model of biped locomotion and implement a suitable controller for it . The locomotion aimed to be realized in this thesis is walking on a flat horizontal sueface in the sagittal plane. a planar five-link biped robot , which consists of a torso, two thighs and two shanks, with five degree of freedom is modeled. A gait cycle of the walking motion includes the single support phase(SSP), the impact phase and the support end exchange phase. The dynamic equation at SSP is derived by using the Lagrangian formulation and the impact equation is derivd by using the momention change caused by the nonconservative force during impact and the constraint imposed in the impact leg.

39

Hu, Yong, Gangfeng Yan, and Zhiyun Lin. "Feedback Control of Planar Biped Robot With Regulable Step Length and Walking Speed." IEEE Transactions on Robotics 27, no. 1 (February 2011): 162–69. http://dx.doi.org/10.1109/tro.2010.2085471.

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40

La Hera, Pedro X. Miranda, Anton S. Shiriaev, Leonid B. Freidovich, Uwe Mettin, and Sergey V. Gusev. "Stable Walking Gaits for a Three-Link Planar Biped Robot With One Actuator." IEEE Transactions on Robotics 29, no. 3 (June 2013): 589–601. http://dx.doi.org/10.1109/tro.2013.2239551.

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41

Geng, Tao. "Torso Inclination Enables Faster Walking in a Planar Biped Robot With Passive Ankles." IEEE Transactions on Robotics 30, no. 3 (June 2014): 753–58. http://dx.doi.org/10.1109/tro.2014.2298058.

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42

Makarenkov, Oleg. "Existence and stability of limit cycles in the model of a planar passive biped walking down a slope." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 476, no. 2233 (January 2020): 20190450. http://dx.doi.org/10.1098/rspa.2019.0450.

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We consider the simplest model of a passive biped walking down a slope given by the equations of switched coupled pendula (McGeer T. 1990 Passive dynamic walking. Int. J. Robot. Res. 9 , 62–82. ( doi:10.1177/027836499000900206 )). Following the fundamental work by Garcia (Garcia et al . 1998 J. Biomech. Eng . 120 , 281. ( doi:10.1115/1.2798313 )), we view the slope of the ground as a small parameter γ ≥ 0. When γ = 0, the system can be solved in closed form and the existence of a family of cycles (i.e. potential walking cycles) can be computed in closed form. As observed in Garcia et al. (Garcia et al . 1998 J. Biomech. Eng . 120 , 281. ( doi:10.1115/1.2798313 )), the family of cycles disappears when γ increases and only isolated asymptotically stable cycles (walking cycles) persist. However, no mathematically complete proofs of the existence and stability of walking cycles have been reported in the literature to date. The present paper proves the existence and stability of a walking cycle (long-period gait cycle, as termed by McGeer) by using the methods of perturbation theory for maps. In particular, we derive a perturbation theorem for the occurrence of stable fixed points from 1-parameter families in two-dimensional maps that can be of independent interest in applied sciences.

43

Sun, Wenkai, Xiaojie Tian, Yong Song, Bao Pang, Xianfeng Yuan, and Qingyang Xu. "Balance Control of a Quadruped Robot Based on Foot Fall Adjustment." Applied Sciences 12, no. 5 (February 28, 2022): 2521. http://dx.doi.org/10.3390/app12052521.

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To balance the diagonal gait of a quadruped robot, a dynamic balance control method is presented to improve the stability of the quadruped robot by adjusting its foot position. We set up a trunk-based coordinate system and a hip-based local coordinate system for the quadruped robot, established the kinematics equation of the robot, and designed a reasonable initial diagonal gait through the spring inverted pendulum model. The current trunk posture of the quadruped robot is obtained by collecting the data of its pitch and roll angle, and the foot position is predicted according to the current posture and initial gait of the quadruped robot. To reduce the impact of one leg landing on the ground and increase the stability of the quadruped robot, we adjust the landing point of the robot according to the landing time difference between the diagonal legs. The proposed method can adjust the body in such scenarios as planar walking and lateral impact resistance. It can reduce the disturbance during the robot motion and make the robot move smoothly. The validity of this method is verified by simulation experiments.

44

Channon, P. H., S. H. Hopkins, and D. T. Pham. "A Variational Approach To The Optimization of Gait For a Bipedal Robot." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 210, no. 2 (March 1996): 177–86. http://dx.doi.org/10.1243/pime_proc_1996_210_184_02.

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This paper presents a method for optimizing the walking motions of a planar five-link biped. The technique starts with non-linear kinematic and dynamic models for both the single-support and impact stages of motion. A variational technique is then used to derive joint trajectories that minimize a simple cost function. The resulting two-point boundary value problem is solved using a finite difference technique, with trajectories obtained from a simple linearized model as initial conditions. Families of optimal trajectories for different step periods and step lengths are presented.

45

Caux, S., and R. Zapata. "Modeling and control of biped robot dynamics." Robotica 17, no. 4 (July 1999): 413–26. http://dx.doi.org/10.1017/s0263574799001411.

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This paper addresses the problem of modeling biped dynamics and the use of such models for the control of walking, running and jumping robots. We describe two approaches to dynamic modeling: the basic Lagrange approach and the non-regular dynamic approach. The new non-regular dynamic approach takes into account discontinuities due to rigid contact between punctual feet and the ground without computing the exact impact time. The contact is close to the physical situation given by non-linear laws (impenetrability, non-smooth contact and real friction cone). Contact dynamics can be well managed with an accurate dynamic model that respects energy consistency during all the phases encountered during a step (0, 1 or 2 contacts). With this model, we can first study the equilibrum of a biped standing on one foot by a linearisation method. In the second stage, the unified modelized equation is used to establish a general control frame based on non-regular dynamical decoupling. A comparison is made and some simulation results are given with a two degree of freedom planar biped robot.

46

Chen, Chen-Yuan, Bih-Yaw Shih, Chia-Hung Shih, and Li-Hui Wang. "RETRACTED: Design, modeling and stability control for an actuated dynamic walking planar bipedal robot." Journal of Vibration and Control 19, no. 3 (January 17, 2012): 376–84. http://dx.doi.org/10.1177/1077546311429476.

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47

Wang, Ting, and Christine Chevallereau. "Stability analysis and time-varying walking control for an under-actuated planar biped robot." Robotics and Autonomous Systems 59, no. 6 (June 2011): 444–56. http://dx.doi.org/10.1016/j.robot.2011.03.002.

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48

Kasiyanchuk, Dmitry A., and Dmitry A. Fetisov. "Planar Walking of a Five-Link Biped Robot over a Stepped Surface with Obstacles of Different Heights and Lengths." Journal of Physics: Conference Series 2701, no. 1 (February 1, 2024): 012020. http://dx.doi.org/10.1088/1742-6596/2701/1/012020.

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Abstract A problem of modeling biped locomotion is an actual and complex problem of modern control theory. In the present paper, we deal with a special case when a five-link biped robot with knees moves along a given stepped surface. We describe the robot motion by a hybrid system which consists of a system of ordinary differential equations at the single support phase and an algebraic relation at the double support phase. The main contribution of this paper is the construction of a periodic motion that satisfies a set of conditions inherent in human walking. The results of the paper will be useful to those who are interested in control theory applications.

49

Jiwen, Zhang, Liu Li, and Chen Ken. "Footstep Planning for Rapid Path Following in Humanoid Robots." International Journal of Humanoid Robotics 13, no. 04 (November 29, 2016): 1650013. http://dx.doi.org/10.1142/s0219843616500134.

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Rapid path following is an important component of a layered planning framework to improve motion speed. A method of generating a bipedal footstep sequence that follows a designated path and maintains stability in a planar environment is proposed in this paper. It adopts a walking style with a fixed step frequency and adjusts consecutive strides by eliminating irrational stride changes. An omnidirectional moving vehicle model and the deduced inequalities are introduced to theoretically describe the inter-pace constraints. A modified backtrack search is then implemented to solve the resulting constraint satisfaction problem. Both dynamics simulations and real robot experiments show that a humanoid robot is capable of tracking various paths with rapid paces. Comparison with several alternatives verifies the superiority of this novel method in terms of rapidity.

50

HARADA, Yuzuru, Kentaro MIYAHARA, Yoshikazu KANAMIYA, and Daisuke SATO. "1P1-B02 Simple Virtual Biped Model Based Walking Pattern Generator for a Planar Humanoid Robot." Proceedings of JSME annual Conference on Robotics and Mechatronics (Robomec) 2008 (2008): _1P1—B02_1—_1P1—B02_4. http://dx.doi.org/10.1299/jsmermd.2008._1p1-b02_1.

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