Robust Cascade Controller for Nonlinearly Actuated Biped Robots: Experimental Evaluation

In this paper we consider the postural stability problem for nonlinearly actuated quasi-static biped robots, both with respect to the joint angular positions and also with reference to the gripping effect between the foot/feet against the ground during robot locomotion. Zero moment point based mathematical models are developed to establish a relationship between the robot state variables and the stability margin of the foot (feet) contact surface and the supporting ground. Then, in correspondence with the developed dynamical model and its associated uncertainty, and in the presence of non-modeled robot mechanical structure vibration modes, we propose a robust control architecture that uses two cascade regulators. The overall robust control system consists of a nonlinear robust variable structure controller in an inner feedback loop for joint trajectory tracking, and an H∞ linear robust regulator in an outer, direct zero moment point feedback loop to ensure the foot–ground contact stability. The effectiveness of this cascade controller is evaluated using a simplified prototype of a nonlinearly actuated biped robot in double support placed on top of a one-degree-of-freedom mobile platform and subjected to external disturbances. The achieved experimental results have revealed that the simplified prototype is successfully stabilized. KEY WORDS—biped robots, stability, zero moment point, robust control, nonlinear control, nonlinear actuators 1. Nomenclature 1.1. General Notation q = Joint angular position vector q̇ = Joint angular velocity vector q̈ = Joint angular acceleration vector The International Journal of Robotics Research Vol. 23, No. 10–11, October–November 2004, pp. 1075-1095, DOI: 10.1177/0278364904047394 ©2004 Sage Publications θi = Angle of linki against vertical qi = Relative angle between linki and linki–1 1.2. Actuator Dynamic Modeling γi = Motor axis angle (input angle for jointi ) γ̇i = Motor axis speed (input speed for jointi ) γ̈i = Motor axis acceleration (input acceleration for jointi ) Avi = Nonlinear transmission ratio for jointi U = Feeding voltage in motor terminals = Nonlinear matrix accounting for inertial effects = Nonlinear matrix accounting for damping and Coriolis effects Υ = Nonlinear matrix accounting for quadratic speed effects caused by the nonlinear transmission = Nonlinear vector accounting for gravity and other nonlinear effects 1.3. Control s = Laplace transform ω = Frequency (rad s−1) φ(t) = Sliding surface function P(s) = Plant transfer function (s) = Plant uncertainty transfer function Sp = Sensitivity function Tp = Complementary sensitivity function Gi = Nominal transfer function (i) Ci = Controller transfer function (i) Fi = Feedforward compensator transfer function (i) 2. Introduction The biped robot stabilization problem is an active field of investigation. Researchers such as Vukobratovic and Juricic