GrAVITree: Graph-based Approximate Value Function In a Tree

Abstract: In this paper, we introduce GrAVITree, a tree- and sampling-based algorithm to compute a near-optimal value function and corresponding feedback policy for indefinite time-horizon, terminal state-constrained nonlinear optimal control problems. Our algorithm is suitable for arbitrary nonlinear control systems with both state and input constraints. The algorithm works by sampling feasible control inputs and branching backwards in time from the terminal state to build the tree, thereby associating each vertex in the tree with a feasible control sequence to reach the terminal state. Additionally, we embed this stochastic tree within a larger graph structure, rewiring of which enables rapid adaptation to changes in problem structure due to, e.g., newly detected obstacles. Because our method reasons about global problem structure without relying on (potentially imprecise) derivative information, it is particularly well suited to controlling a system based on an imperfect deep neural network model of its dynamics. We demonstrate this capability in the context of an inverted pendulum, where we use a learned model of the pendulum with actuator limits and achieve robust stabilization in settings where competing graph-based and derivative-based techniques fail.