Unconstrained Model Predictive Control for Robot Navigation under Uncertainty

In this paper, we present a probabilistic and unconstrained model predictive control formulation for robot navigation under uncertainty. We present (1) a closed-form approximation of the probability of collision that naturally models the propagation of uncertainty over the planning horizon and is computationally cheap to evaluate, and (2) a collision-cost formulation which provably preserves forward invariance (i.e., keeps the robot away from obstacles) when combined with the probability formulation. Notably, our formulation avoids hard constraints by construction, which in turn avoids abrupt transitions in robot behavior around the constraint boundaries ensuring graceful navigation. Further, we present proof for the forward invariance and the stability of the approach. We compare the efficacy of our method with the baseline [1], which the proposed approach builds on. We demonstrate that the approach results in confident and safe robot navigation in tight spaces by smoothly slowing down the robot in low survivability environments (e.g., tight corridors), but also allows it to move away from obstacles safely when needed.