Parameter Sensitivity and Boundedness of Robotic Hybrid Periodic Orbits

Model-based nonlinear controllers like feedback linearization and control Lyapunov functions are highly sensitive to the model parameters of the robot. This paper addresses the problem of realizing these controllers in a particular class of hybrid models–systems with impulse effects–through a parameter sensitivity measure. This measure quantifies the sensitivity of a given model-based controller to parameter uncertainty along a particular trajectory. By using this measure, output boundedness of the controller (computed torque+PD) will be analyzed. Given outputs that characterize the control objectives, i.e., the goal is to drive these outputs to zero, we consider Lyapunov functions obtained from these outputs. The main result of this paper establishes the ultimate boundedness of the output dynamics in terms of this measure via these Lyapunov functions under the assumption of stable hybrid zero dynamics. This is demonstrated in simulation on a 5-DOF underactuated bipedal robot.