Unifying Robot Trajectory Tracking with Control Contraction Metrics

Abstract

In this paper we present new results for nonlinear tracking control design based on the search for a “control contraction metric” (CCM). We show that for fully-actuated robots, CCMs can be found analytically that correspond to classical methods of robot control including sliding and energy-based designs. We also show that, for underactuated robots, the CCM approach extends more recent optimization-based methods such as LQR-Trees to tracking of arbitrary feasible trajectories. Therefore the CCM methodology represents a bridge between these methods. We illustrate our results with calculations and simulations on the single and double inverted pendulums and the underactuated cart-pole system.