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This paper addresses planning and control of robot motion under uncertaintythat is formulated as a continuous-time, continuous-space stochastic optimalcontrol problem, by developing a topology-guided path integral control method.The path integral control framework, which forms the backbone of the proposedmethod, re-writes the Hamilton-Jacobi-Bellman equation as a statisticalinference problem; the resulting inference problem is solved by a samplingprocedure that computes the distribution of controlled trajectories around thetrajectory by the passive dynamics. For motion control of robots in a highlycluttered environment, however, this sampling can easily be trapped in a localminimum unless the sample size is very large, since the global optimality oflocal minima depends on the degree of uncertainty. Thus, a homology-embeddedsampling-based planner that identifies many (potentially) local-minimumtrajectories in different homology classes is developed to aid the samplingprocess. In combination with a receding-horizon fashion of the optimal controlthe proposed method produces a dynamically feasible and collision-free motionplans without being trapped in a local minimum. Numerical examples on asynthetic toy problem and on quadrotor control in a complex obstacle fielddemonstrate the validity of the proposed method.

Topology-Guided Path Integral Approach for Stochastic Optimal Control in Cluttered Environment