A Minimum Jerk-Impedance Controller for Planning Stable and Safe Walking Patterns of Biped Robots

Abstract

Minimum Jerk based control is part of optimal control laws. Its main contribution resides in the generation of smooth trajectories allowing the avoidance of sudden and abrupt motion. This chapter proposes the elaboration of appropriate control laws, with controller parameters computed offline, able to produce stable smooth and safe walking cycles for bipedal robots evolving in the three dimensional space. To alternate footsteps, Minimum Jerk and Impedance control principles are used to switch successively between single support, impact and double support phases. A new methodology of Minimum Jerk control is proposed to produce human like trajectories. Its originality mostly relies on the generation of Cartesian three-dimensional reference trajectories that do combine benefits of trigonometric and polynomial functions. When considering the impact and double support phases, an appropriate impedance control law is proposed to ensure the robot stability and safe balance during the contact with the ground. Simulation results performed on a 15 link/26 degrees of freedom Humanoid robot with a weight of 70 kg and a height of 1.73 m walking at a velocity of 0.6 m s\(^{-1}\), show that the dynamics of the robot during the swing phase are very attractive since smooth trajectories without dynamic vibrations are observed and a stable and safe elastic contact takes place while achieving the constrained phases even in presence of sensory noise and uncertainties on the environment stiffness.