Bridging the Gap Between Safety and Real-Time Performance in Receding-Horizon Trajectory Design for Mobile Robots

TL;DR

This paper introduces RTD, a trajectory planning method for mobile robots that guarantees safety and dynamic feasibility in real-time by using reachability analysis and obstacle mapping, demonstrated through extensive simulations and hardware tests.

Contribution

The work presents a novel RTD approach combining offline reachability analysis with real-time obstacle mapping to ensure safe, feasible trajectories for mobile robots.

Findings

RTD guarantees safety and persistent feasibility in real-time planning.

RTD outperforms RRT and NMPC in simulations.

RTD successfully deployed on hardware platforms in diverse environments.

Abstract

To operate with limited sensor horizons in unpredictable environments, autonomous robots use a receding-horizon strategy to plan trajectories, wherein they execute a short plan while creating the next plan. However, creating safe, dynamically-feasible trajectories in real time is challenging; and, planners must ensure persistent feasibility, meaning a new trajectory is always available before the previous one has finished executing. Existing approaches make a tradeoff between model complexity and planning speed, which can require sacrificing guarantees of safety and dynamic feasibility. This work presents the Reachability-based Trajectory Design (RTD) method for trajectory planning. RTD begins with an offline Forward Reachable Set (FRS) computation of a robot's motion when tracking parameterized trajectories; the FRS provably bounds tracking error. At runtime, the FRS is used to map obstacles to parameterized trajectories, allowing RTD to select a safe trajectory at every planning iteration. RTD prescribes an obstacle representation to ensure that obstacle constraints can be created and evaluated in real time while maintaining safety. Persistent feasibility is achieved by prescribing a minimum sensor horizon and a minimum duration for the planned trajectories. A system decomposition approach is used to improve the tractability of computing the FRS, allowing RTD to create more complex plans at runtime. RTD is compared in simulation with Rapidly-Exploring Random Trees and Nonlinear Model-Predictive Control. RTD is also demonstrated in randomly-crafted environments on two hardware platforms: a differential-drive Segway, and a car-like Rover. The proposed method is safe and persistently feasible across thousands of simulations and dozens of real-world hardware demos.