Computing Feedback Plans from Dynamical System Composition

Computing plans for systems with differential constraints is a fundamental component in numerous robotic applications. Most previous approaches are based on creating motion plans between an initial and a goal location. However, a more robust approach is to compute feedback plans over the entire configuration space to account for uncertainty in the robot's motions. In this paper, we therefore propose a new method that constructs a feedback plan by incrementally composing the long-term behavior of the robot's motions for a set of actions. Our method takes advantage of dynamical system analysis techniques and efficient combinatorial algorithms. We implement our method in simulations considering a robot under a simple bouncing behavior. A feedback plan for the robot to reach the goal region starting from any location of an environment is successfully constructed using the implementation of our method. Our method is also applicable to non-linear systems with uncertainty.