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

Abstract

This paper introduces Chance Constrained Gaussian Process-Motion Planning (CCGP-MP), a motion planning algorithm for robotic systems under motion and state estimate uncertainties. The paper's key idea is to capture the variations in the distance-to-collision measurements caused by the uncertainty in state estimation techniques using a Gaussian Process (GP) model. We formulate the planning problem as a chance constraint problem and propose a deterministic constraint that uses the modeled distance function to verify the chance-constraints. We apply Simplicial Homology Global Optimization (SHGO) approach to find the global minimum of the deterministic constraint function along the trajectory and use the minimum value to verify the chance-constraints. Under this formulation, we can show that the optimization function is smooth under certain conditions and that SHGO converges to the global minimum. Therefore, CCGP-MP will always guarantee that all points on a planned trajectory satisfy the given chance-constraints. The experiments in this paper show that CCGP-MP can generate paths that reduce collisions and meet optimality criteria under motion and state uncertainties. The implementation of our robot models and path planning algorithm can be found on GitHub 1 .

UrbanFly: Uncertainty-Aware Planning for Navigation Amongst High-Rises with Monocular Visual-Inertial SLAM Maps

“…Thus, our approach is expected to scale better if the problem complexity demands an increase in the sample size of CEM. Our SCP-MMD planner is faster than [3] while unsuprisingly the deterministic planner [23] has the lowest run-time.…”

“…Unfortunately, existing algorithms for uncertaintyaware planning are not designed to work with systems that rely on monocular vision-based perception. For example, works like [3], [4], either assume that the obstacle geometries are precisely known or rely on depth sensors to obtain obstacle geometries during run-time.…”

CCO-VOXEL: Chance Constrained Optimization over Uncertain Voxel-Grid Representation for Safe Trajectory Planning

“…Specifically there appears no known methods that handle non parametric uncertainty of discretized volumetric voxel grids other than the proposed. While [19] provides for a chance constrained framework for nearest distance to obstacle it formulates over well defined obstacle shapes and not over voxel grids. Moreover, its computation of safe trajectories runs into minutes while the proposed method is in the order of tens of milliseconds.…”