University of Michigan, University of Pennsylvania, and Ford Motor Company.
Paper
</Code>
Supplimentary: Satisfaction of Linear Regimes of Tire Models
Supplimentary: Generalization to AWD and RWD
REFINE generates real-time, motion plans that guarantee robot safety using robust feedback lineariation and zonotopes.
Abstract
Performing real-time receding horizon motion planning for autonomous vehicles while providing safety guarantees remains difficult.
This is because existing methods to accurately predict ego vehicle behavior under a chosen controller use online numerical integration that requires a fine time discretization and thereby adversely affects real-time performance.
To address this limitation, several recent papers have proposed to apply offline reachability analysis to conservatively predict the behavior of the ego vehicle.
This reachable set can be constructed by utilizing a simplified model whose behavior is assumed a priori to conservatively bound the dynamics of a full-order model.
However, guaranteeing that one satisfies this assumption is challenging.
This paper proposes a framework named REFINE to overcome the limitations of these existing approaches.
REFINE utilizes a parameterized robust controller that partially linearizes the vehicle dynamics even in the presence of modeling error.
Zonotope-based reachability analysis is then performed on the closed-loop, full-order vehicle dynamics to compute the corresponding control-parameterized, over-approximate Forward Reachable Sets (FRS).
Because reachability analysis is applied to the full-order model, the potential conservativeness introduced by using a simplified model is avoided.
The pre-computed, control-parameterized FRS is then used online in an optimization framework to ensure safety.
The proposed method is compared to several state of the art methods during a simulation-based evaluation on a full-size vehicle model and is demonstrated on a 1/10-th race car robot in real hardware testing.
In contrast to existing methods, REFINE is shown to enable the vehicle to safely navigate itself through complex environments.
Method
REFINE first designs a robust controller to track parametrized desired reference trajectories by feedback linearizing a subset of vehicle states.
REFINE then performs offline reachability analysis using a closed-loop full-order vehicle dynamics to construct a control-parameterized, zonotope reachable sets (shown as grey boxes) that over-approximate all possible behaviors of the vehicle model over the planning horizon.
During online planning, REFINE computes a parameterized controller that can be safely applied to the vehicle by solving an optimization problem, which selects subsets of pre-computed zonotope reachable sets that are guaranteed to be collision-free.
In this figure, subsets of grey zonotope reachable sets corresponding to the control parameter shown in green ensures a collision-free path while the other two control parameters shown in pink might lead to collisions with white obstacles.
Simulation Results
In simulation we compare REFINE against state-of-the-art trajectory planning methods: a Sum-of-Squares-based RTD (SOS-RTD) method, and an NMPC method using GPOPS-II.
Legends of the visualization are illustrated below.
Case 1
Case 2
In both cases, REFINE safely nevigates the ego vehicle through the traffic without collisions.
In both cases, online plannng of SOS-RTD gets infeasible due to the conservatism of polynomial reachable sets, thus the ego vehicle brakes safely to a stop without collisions.
In Case 1, NMPC safely nevigates the ego vehicle through the traffic without collisions. In Case 2, online planning using NMPC is feasible, but crash happens because safety conditions are enforced at discrete time instances. Moreover, the average solving time of online planning using NMPC is longer than the planning horizon.
Hardware Demo
On hardware REFINE is illustrated using a 1/10-th ALL-Wheel-Drive car-like robot, Rover, based on a Traxxas.
Max speed of the car robot is 2.0 [m/s], and legends of the visualization are illustrated below.
Case 1: Pass Through the Gap
Case 2: Avoid the Obstacle
Case 3: Successive Turns
Case 4: Avoid Random Obstacles
Case 5: Stop Before the Wall
REFINE returns infeasible because it cannot pass through the wall.
@article{liu2022refine,
author={Jinsun Liu and Yifei Shao and Lucas Lymburner and Hansen Qin and Vishrut Kaushik and Lena Trang and Ruiyang Wang and Vladimir Ivanovic and H. Eric Tseng and Ram Vasudevan},
journal={arXiv preprint arXiv:2211.11997},
title={REFINE: Reachability-based Trajectory Design using Robust Feedback Linearization and Zonotopes},
year={2022},
doi={https://arxiv.org/abs/2211.11997}}
