Funnel Libraries for Real-Time Robust Feedback Motion Planning

TL;DR

This paper introduces a method for real-time, robust motion planning for robots using precomputed funnels that guarantee safety despite uncertainties and disturbances, validated through hardware and simulation experiments.

Contribution

It presents a novel approach to real-time robust motion planning by precomputing funnel libraries using convex optimization, enabling safe navigation in uncertain environments.

Findings

Successfully demonstrated on a fixed-wing airplane avoiding obstacles at high speed

Validated with extensive simulation on ground vehicles and quadrotors in cluttered environments

First to show provably safe, robust control for complex nonlinear robotic systems in real-time

Abstract

We consider the problem of generating motion plans for a robot that are guaranteed to succeed despite uncertainty in the environment, parametric model uncertainty, and disturbances. Furthermore, we consider scenarios where these plans must be generated in real-time, because constraints such as obstacles in the environment may not be known until they are perceived (with a noisy sensor) at runtime. Our approach is to pre-compute a library of "funnels" along different maneuvers of the system that the state is guaranteed to remain within (despite bounded disturbances) when the feedback controller corresponding to the maneuver is executed. We leverage powerful computational machinery from convex optimization (sums-of-squares programming in particular) to compute these funnels. The resulting funnel library is then used to sequentially compose motion plans at runtime while ensuring the safety of the robot. A major advantage of the work presented here is that by explicitly taking into account the effect of uncertainty, the robot can evaluate motion plans based on how vulnerable they are to disturbances. We demonstrate and validate our method using extensive hardware experiments on a small fixed-wing airplane avoiding obstacles at high speed (~12 mph), along with thorough simulation experiments of ground vehicle and quadrotor models navigating through cluttered environments. To our knowledge, these demonstrations constitute one of the first examples of provably safe and robust control for robotic systems with complex nonlinear dynamics that need to plan in real-time in environments with complex geometric constraints.