Orbital stabilization of an underactuated bipedal gait via nonlinear $${{\mathcal H}}_{\infty }$$ H ∞ -control using measurement feedback

Abstract

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Trajectory planning and tracking control for 6‐DOF Stanford manipulator based on adaptive sliding mode multi‐stage switching control

“…Consider that robots have to face dynamic parameter uncertainties and external disturbances in the execution of a task, various of adaptive tracking controllers have been proposed, such as passivity‐based adaptive controllers, 11‐13 neural‐network‐based adaptive controllers, 14‐17 adaptive sliding mode controllers 18‐21 . Recently, nonlinear control synthesis developed for hybrid systems in References 22 and 23 has been successfully applied to the orbital stabilization of an underactuated bipedal robot 24 by introducing virtual constraint approach and transverse coordinates. The proposed output feedback tracking control strategy can guarantee the good performance of the closed‐loop system in the simultaneous presence of measurement noise, external disturbances, and uncertainties in the collision phase.…”

“…By means of inverse kinematics and algebraic method, 34 the planned trajectory in the task space can generate a smooth joint trajectory in the joint space. Finally, a state‐dependent switching control strategy is presented for tracking the generated joint trajectory so as to control the Stanford manipulator to perform a task. Compared with the nonlinear control synthesis developed for hybrid mechanical systems in References 22 and 24, the proposed control strategy circumvents the difficulty of solving Riccati equation or Hamilton–Jacobi–Isaacs inequality.…”

A Comparative Study on the L 1 Optimal Event-Based Method for Biped Walking on Rough Terrains

“…There have been a number of studies on stable walking of bipedal robots in structured environments (such as labs and indoors), which have shown successful demonstrations through simulations and experiments [1]- [3]. Consequently, stable and robust walking of bipedal robots on unstructured terrains has recently attracted much attention of robotics community, and various control methods for biped walking have been developed in [4]- [9].…”

Hybrid disturbance rejection control of dynamic bipedal robots

“…Conditions to achieve aperiodic gait patterns in the presence of persistent disturbances have been proposed in [18]. A recent development reported in [19] makes use of a robust nonlinear H ∞ -controller that ensures internal asymptotic stability. Despite the effectiveness and conservative nature of this controller, their approach does not allow to bound the control signals and the resulting peak torques may be unattainable in a physical implementation.…”