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This paper presents policy-based motion planning for robotic systems. Themotion planning literature has been mostly focused on open-loop trajectoryplanning which is followed by tracking online. In contrast, we solve theproblem of path planning and controller synthesis simultaneously by solving therelated feedback control problem. We present a novel incremental policy(iPolicy) algorithm for motion planning, which integrates sampling-basedmethods and set-valued optimal control methods to compute feedback controllersfor the robotic system. In particular, we use sampling to incrementallyconstruct the state space of the system. Asynchronous value iterations areperformed on the sampled state space to synthesize the incremental policyfeedback controller. We show the convergence of the estimates to the optimalvalue function in continuous state space. Numerical results with variousdifferent dynamical systems (including nonholonomic systems) verify theoptimality and effectiveness of iPolicy.

iPolicy: Incremental Policy Algorithms for Feedback Motion Planning