Fast and Safe Trajectory Optimization for Autonomous Mobile Robots using Reachability Analysis

Abstract

Autonomous mobile robots (AMRs) can transform a wide variety of industries including transportation, shipping and goods delivery, and defense. AMRs must match or exceed human performance in metrics for task completion and safety. Motion plans for AMRs are generated by solving an optimization program where collision avoidance and the trajectory obeying a dynamic model of the robot are enforced as constraints.

This dissertation focuses on three main challenges associated with trajectory planning. First, collision checks are typically performed at discrete time steps. Second, there can be a nontrivial gap between the planning model used and the actual system. Finally, there is inherent uncertainty in the motion of other agents or robots.

This dissertation first proposes a receding-horizon planning methodology called Reachability-based Trajectory Design (RTD) to address the first and second challenges, where uncertainty is dealt with robustly. Sums-of-Squares (SOS) programming is used to represent the forward reachable set for a dynamic system plus uncertainty, over an interval of time, as a polynomial level set. The trajectory optimization is a polynomial optimization program over a space of trajectory parameters. Hardware demonstrations are implemented on a Segway, rover, and electric vehicle.

In a simulation of 1,000 trials with static obstacles, RTD is compared to Rapidly-exploring Random Tree (RRT) and Nonlinear Model Predictive Control (NMPC) planners. RTD has success rates of 95.4% and 96.3% for the Segway and rover respectively, compared to 97.6% and 78.2% for RRT and 0% for NMPC planners. RTD is the only successful planner with no collisions. In 10 simulations with a CarSim model, RTD navigates a test track on all trials. In 1,000 simulations with random dynamic obstacles RTD has success rates of 96.8% and 100% respectively for the electric vehicle and Segway, compared to 77.3% and 92.4% for a State Lattice planner. In 100 simulations performing left turns, RTD has a success rate of 99% compared to 80% for an MPC controller tracking the lane centerline.

The latter half of the dissertation treats uncertainty with the second and/or third challenges probabilistically. The Chance-constrained Parallel Bernstein Algorithm (CCPBA) allows one to solve the trajectory optimization program from RTD when obstacle states are given as probability functions. A comparison for an autonomous vehicle planning a lane change with one obstacle shows an MPC algorithm using Cantelli's inequality is unable to find a solution when the obstacle's predictions are generated with process noise three orders of magnitude less than CCPBA. In environments with 1-6 obstacles, CCPBA finds solutions in 1e-3 to 1.2 s compared to 1 to 16 s for an NMPC algorithm using the Chernoff bound. A hardware demonstration is implemented on the Segway.

The final portion of the dissertation presents a chance-constrained NMPC method where uncertain components of the robot model are estimated online. The application is an autonomous vehicle with varying road surfaces. In the first study, the controller uses a linear tire force model. Over 200 trials of lane changes at 17 m/s, the chance-constrained controller has a cost 86% less than a controller using fixed coefficients for snow, and only 29% more than an oracle controller using the simulation model. The chance-constrained controller also has 0 lateral position constraint violations, while an adaptive-only controller has minor violations. The second study uses nonlinear tire models on a more aggressive maneuver and provides similar results.