Multi-Agent Feedback Motion Planning using Probably Approximately Correct Nonlinear Model Predictive Control

For many tasks, multi-robot teams often provide greater efficiency, robustness, and resiliency. However, multi-robot collaboration in real-world scenarios poses a number of major challenges, especially when dynamic robots must balance competing objectives like formation control and obstacle avoidance in the presence of stochastic dynamics and sensor uncertainty. In this paper, we propose a distributed, multi-agent receding-horizon feedback motion planning approach using Probably Approximately Correct Nonlinear Model Predictive Control (PAC-NMPC) that is able to reason about both model and measurement uncertainty to achieve robust multi-agent formation control while navigating cluttered obstacle fields and avoiding inter-robot collisions. Our approach relies not only on the underlying PAC-NMPC algorithm but also on a terminal cost-function derived from gyroscopic obstacle avoidance. Through numerical simulation, we show that our distributed approach performs on par with a centralized formulation, that it offers improved performance in the case of significant measurement noise, and that it can scale to more complex dynamical systems.

PAC-NMPC with Learned Perception-Informed Value Function

Nonlinear model predictive control (NMPC) is typically restricted to short, finite horizons to limit the computational burden of online optimization. This makes a global planner necessary to avoid local minima when using NMPC for navigation in complex environments. For this reason, the performance of NMPC approaches are often limited by that of the global planner. While control policies trained with reinforcement learning (RL) can theoretically learn to avoid such local minima, they are usually unable to guarantee enforcement of general state constraints. In this paper, we augment a sampling-based stochastic NMPC (SNMPC) approach with an RL trained perception-informed value function. This allows the system to avoid observable local minima in the environment by reasoning about perception information beyond the finite planning horizon. By using Probably Approximately Correct NMPC (PAC-NMPC) as our base controller, we are also able to generate statistical guarantees of performance and safety. We demonstrate our approach in simulation and on hardware using a 1/10th scale rally car with lidar.