Risk-Sensitive Motion Planning using Entropic Value-at-Risk

TL;DR

This paper introduces a risk-sensitive motion planning approach using Entropic Value-at-Risk (EVaR) within a model predictive control framework, effectively handling obstacle avoidance under uncertainty and demonstrating its application on 2D and 3D systems.

Contribution

It proposes a novel EVaR-based constraint formulation for risk-sensitive motion planning and develops an algorithm for waypoint following with finite-time guarantees.

Findings

EVaR-based policies outperform CVaR in numerical experiments.

The waypoint following algorithm is feasible and completes in finite time.

Successful implementation on a 3D quadcopter simulation.

Abstract

We consider the problem of risk-sensitive motion planning in the presence of randomly moving obstacles. To this end, we adopt a model predictive control (MPC) scheme and pose the obstacle avoidance constraint in the MPC problem as a distributionally robust constraint with a KL divergence ambiguity set. This constraint is the dual representation of the Entropic Value-at-Risk (EVaR). Building upon this viewpoint, we propose an algorithm to follow waypoints and discuss its feasibility and completion in finite time. We compare the policies obtained using EVaR with those obtained using another common coherent risk measure, Conditional Value-at-Risk (CVaR), via numerical experiments for a 2D system. We also implement the waypoint following algorithm on a 3D quadcopter simulation.