Feedback control for compass-like biped robot with underactuated ankles using transverse coordinate transformation

Robotica ◽  
2014 ◽  
Vol 33 (3) ◽  
pp. 563-577 ◽  
Author(s):  
Gangfeng Yan ◽  
Chong Tang ◽  
Zhiyun Lin ◽  
Ivan Malloci
Keyword(s):  
Feedback Control ◽  
Limit Cycle ◽  
Coordinate Transformation ◽  
Hybrid Control ◽  
Linear Time ◽  
Biped Robot ◽  
Impulsive System ◽  
Transverse Coordinate ◽  
Walking Gait ◽  
Linear Time Invariant

SUMMARYThis paper deals with the walking control problem of a compass-like biped robot with underactuated ankles in the framework of hybrid control systems. The compass-like biped robot is equipped with a constraint mechanism to lock the hip angle when the swing leg retracts. First, based on the Poincare return map, a limit cycle gait is obtained, and the stability of the gait is also checked. Then, a method based on transverse coordinate transformation is introduced to transform the problem of tracking a desired limit cycle into the stabilization problem of a linear time-invariant impulsive system. A feedback control design for stabilizing the walking gait is then presented. Finally, comparisons to several existing approaches for the similar model are provided to demonstrate the advantages of our proposed approach.

scholarly journals Design of active disturbance rejection controller for compass-like biped walking

2018 ◽  
Vol 15 (3) ◽  
pp. 172988141877684 ◽  
Author(s):  
Sumian Song ◽  
Chong Tang ◽  
Zidong Wang ◽  
Yinan Wang ◽  
Gangfeng Yan
Keyword(s):  
Limit Cycle ◽  
Disturbance Rejection ◽  
Controller Design ◽  
Linear Time ◽  
Biped Robot ◽  
Transverse Coordinate ◽  
Linear Time Invariant ◽  
Active Disturbance Rejection ◽  
Unstable Limit Cycle ◽  
Coordinate Control

This article proposes an active disturbance rejection controller design scheme to stabilize the unstable limit cycle of a compass-like biped robot. The idea of transverse coordinate transformation is applied to form the control system based on angular momentum. With the linearization approximation, the limit cycle stabilization problem is simplified into the stabilization of an linear time-invariant system, which is known as transverse coordinate control. In order to solve the problem of poor adaptability caused by linearization approximation, we design an active disturbance rejection controller in the form of a serial system. With the active disturbance rejection controller, the system error can be estimated by extended state observer and compensated by nonlinear state error feedback, and the unstable limit cycle can be stabilized. The numerical simulations show that the control law enhances the performance of transverse coordinate control.

scholarly journals The Best Achievableℋ2Tracking Performances for SIMO Feedback Control Systems

2007 ◽  
Vol 2007 ◽  
pp. 1-12 ◽  
Author(s):  
Shinji Hara ◽  
Toni Bakhtiar ◽  
Masaaki Kanno
Keyword(s):  
Feedback Control ◽  
Control Systems ◽  
Linear Time ◽  
Tracking Error ◽  
Control Input ◽  
Discrete Time System ◽  
Time System ◽  
Linear Time Invariant ◽  
Augmentation Strategy ◽  
Feedback Control Systems

This paper is concerned with the inherentℋ2tracking performance limitation of single-input and multiple-output (SIMO) linear time-invariant (LTI) feedback control systems. The performance is measured by the tracking error between a step reference input and the plant output with additional penalty on control input. We employ the plant augmentation strategy, which enables us to derive analytical closed-form expressions of the best achievable performance not only for discrete-time system, but also for continuous-time system by exploiting the delta domain version of the expressions.

Robust Observer Based Control for Stability of Linear Systems: Application to Polytopic Systems

2013 ◽  
Vol 136 (1) ◽  
Author(s):  
Mouna Belguith ◽  
Amel Benabdallah
Keyword(s):  
Feedback Control ◽  
Output Feedback ◽  
State Feedback ◽  
Linear Time ◽  
Sufficient Conditions ◽  
State Feedback Control ◽  
Robust Observer ◽  
Linear Time Invariant ◽  
Polytopic Systems ◽  
Linear Time Invariant Systems

This paper investigates the problem of global stabilization by output feedback for linear time-invariant systems. We give first a procedure to design a robust observer for the linear system. Then using this robust observer with the robust state feedback control law developed by Molander and Willems (1980, “Synthesis of State Feedback Control Laws With a Specified Gain and Phase Margin,” IEEE Trans. Autom. Control, 25(5), pp. 928–931), we construct an output feedback which yields a closed loop system with robustness characteristics. That is, we establish a separation principle. Finally, we give sufficient conditions to establish a robust output feedback for linear polytopic systems.

Nonsmooth Optimization Method for H∞ Output Feedback Control

2019 ◽  
Vol 36 (03) ◽  
pp. 1950015
Author(s):  
Qiong Wu ◽  
Jin-He Wang ◽  
Hong-Wei Zhang ◽  
Shuang Wang ◽  
Li-Ping Pang
Keyword(s):  
Feedback Control ◽  
Nonsmooth Optimization ◽  
Output Feedback ◽  
Closed Loop ◽  
Linear Time ◽  
Output Feedback Control ◽  
Initial Point ◽  
Optimization Method ◽  
Linear Time Invariant ◽  
Loop Transfer Function

This paper proposes a nonsmooth optimization method for [Formula: see text] output feedback control problem of linear time-invariant(LTI) systems based on bundle technique. We formulate this problem as a nonconvex and nonsmooth semi-infinite constrained optimization problem by quantifying both internal stability of closed-loop system and measurement of system performance, where [Formula: see text] norm of closed-loop transfer function and a stabilization channel is used. Our method uses progress function and bundle technique to solve the resulting problem which has a composite structure. We prove the convergence to a critical point from a feasible initial point and test some benchmarks to demonstrate the effectiveness of this method.

Biped Robot Control System Based on Adaptive Gain Energy Control with Angle Invariant

2011 ◽  
Vol 225-226 ◽  
pp. 540-545
Author(s):  
De Jun Liu ◽  
Yan Tao Tian ◽  
Hong Jiang
Keyword(s):  
Limit Cycle ◽  
Control Method ◽  
Nonlinear Function ◽  
Biped Robot ◽  
Convergence Domain ◽  
Energy Control ◽  
Walking Gait ◽  
Control Gain ◽  
Gain Energy ◽  
Invariant Control

The walking motion state of biped robot with knee is analyzed, the system model is established based on the walking phase; for the stability of passive walking gait is poor, The limit cycle convergence domain is smaller and sensitive to interference. Energy control and angle invariant control is merged, A steady gait is produced at different angles on the ground by the angle invariant control, the gait limit cycle convergence domain is expanded by the energy control method, the energy control gain is adjusted by nonlinear function. The simulation result shows that the method can expand the limit cycle convergence domain and increase the robustness.

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