Simulation-based LQR-trees with input and state constraints

— We present an algorithm that probabilistically covers a bounded region of the state space of a nonlinear system with a sparse tree of feedback stabilized trajectories leading to a goal state. The generated tree serves as a lookup table control policy to get any reachable initial condition within that region to the goal. The approach combines motion planning with reasoning about the set of states around a trajectory for which the feedback policy of the trajectory is able to stabilize the system. The key idea is to use a random sample from the bounded region for both motion planning and approximation of the stabilizable sets by falsification; this keeps the number of samples and simulations needed to generate covering policies reasonably low. We simulate the nonlinear system to falsify the stabilizable sets, which allows enforcing input and state constraints. Compared to the algebraic verification using sums of squares optimization in our previous work, the simulationbased approxim...

• Type: Journal
• Year: 2010
• Where: ICRA
• Authors: Philipp Reist, Russ Tedrake
• Keywords: ICRA 2010, Nonlinear Systems, Reachable Initial Condition, Robotics, Stabilizable Sets