Chance-Constrained Motion Planning using Modeled Distance-to-Collision Functions

This paper introduces Chance Constrained Gaussian Process-Motion Planning\n(CCGP-MP), a motion planning algorithm for robotic systems under motion and\nstate estimate uncertainties. The paper's key idea is to capture the variations\nin the distance-to-collision measurements caused by the uncertainty in state\nestimation techniques using a Gaussian Process (GP) model. We formulate the\nplanning problem as a chance constraint problem and propose a deterministic\nconstraint that uses the modeled distance function to verify the\nchance-constraints. We apply Simplicial Homology Global Optimization (SHGO)\napproach to find the global minimum of the deterministic constraint function\nalong the trajectory and use the minimum value to verify the\nchance-constraints. Under this formulation, we can show that the optimization\nfunction is smooth under certain conditions and that SHGO converges to the\nglobal minimum. Therefore, CCGP-MP will always guarantee that all points on a\nplanned trajectory satisfy the given chance-constraints. The experiments in\nthis paper show that CCGP-MP can generate paths that reduce collisions and meet\noptimality criteria under motion and state uncertainties. The implementation of\nour robot models and path planning algorithm can be found on GitHub.\n