Feedback motion planning with simulation based LQR-trees

Abstract

In autonomous and non-autonomous systems, a motion planner generates reference trajectories which are tracked by a low-level controller. In this report we consider the problem of generating a feedback motion planning algorithm for a nonlinear dynamical systems; the algorithm computes the stability regions to build a set of LQR-stabilized trajectories by generating a feedback control law from a set of initial conditions that are goal reachable. Furthermore, we consider the case where these plans must be generated offline, because the LQR trees lack the ability to handle events in which the goal and environments are unknown till run-time. Moreover, the algorithm approximates the funnel [2] of a trajectory using the one step Lyapunov method which is a sampling-based approach, generating a control law that stabilizes the bounded set to the goal is equivalent to adding trajectories to the tree until their funnels cover the design set. We further validate our approach by carefully evaluating the guarantees on invariance provided by funnels on nonlinear systems. We demonstrate and validate our method using simulation experiments of some nonlinear models. These demonstrations constitute examples of provably safe and robust control for robotic systems with complex nonlinear dynamics with Obstacles and dynamic constraints.