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Guaranteed Reach-Avoid for Black-Box Systems through Narrow Gaps via Neural Network Reachability

Long Kiu Chung, Wonsuhk Jung, Srivatsank Pullabhotla, Parth Shinde, Yadu Sunil, Saihari Kota, Luis Felipe Wolf Batista, Cédric Pradalier, Shreyas Kousik

TL;DR

NeuralPARC addresses the problem of providing reach-avoid guarantees for black-box mobile robots in narrow-gap scenarios. It learns a trajectory model with ReLU neural networks from data and uses Reachable Polyhedral Marching ($\text{RPM}$) to certify all affine dynamics implied by the network, while accounting for modeling error via explicit bounds. Online, NeuralPARC computes aBackward Reachable Set ($\text{BRAS}$) and aBackward Avoid Set ($\text{BAS}$) to guarantee that the system reaches a goal while avoiding obstacles, even under disturbances and with deep RL controllers. Hardware and simulation experiments on extreme drift parking and a disturbed ASV demonstrate improved safety guarantees and practical viability, validating the approach against the prior PARC method.

Abstract

In the classical reach-avoid problem, autonomous mobile robots are tasked to reach a goal while avoiding obstacles. However, it is difficult to provide guarantees on the robot's performance when the obstacles form a narrow gap and the robot is a black-box (i.e. the dynamics are not known analytically, but interacting with the system is cheap). To address this challenge, this paper presents NeuralPARC. The method extends the authors' prior Piecewise Affine Reach-avoid Computation (PARC) method to systems modeled by rectified linear unit (ReLU) neural networks, which are trained to represent parameterized trajectory data demonstrated by the robot. NeuralPARC computes the reachable set of the network while accounting for modeling error, and returns a set of states and parameters with which the black-box system is guaranteed to reach the goal and avoid obstacles. NeuralPARC is shown to outperform PARC, generating provably-safe extreme vehicle drift parking maneuvers in simulations and in real life on a model car, as well as enabling safety on an autonomous surface vehicle (ASV) subjected to large disturbances and controlled by a deep reinforcement learning (RL) policy.

Guaranteed Reach-Avoid for Black-Box Systems through Narrow Gaps via Neural Network Reachability

TL;DR

NeuralPARC addresses the problem of providing reach-avoid guarantees for black-box mobile robots in narrow-gap scenarios. It learns a trajectory model with ReLU neural networks from data and uses Reachable Polyhedral Marching () to certify all affine dynamics implied by the network, while accounting for modeling error via explicit bounds. Online, NeuralPARC computes aBackward Reachable Set () and aBackward Avoid Set () to guarantee that the system reaches a goal while avoiding obstacles, even under disturbances and with deep RL controllers. Hardware and simulation experiments on extreme drift parking and a disturbed ASV demonstrate improved safety guarantees and practical viability, validating the approach against the prior PARC method.

Abstract

In the classical reach-avoid problem, autonomous mobile robots are tasked to reach a goal while avoiding obstacles. However, it is difficult to provide guarantees on the robot's performance when the obstacles form a narrow gap and the robot is a black-box (i.e. the dynamics are not known analytically, but interacting with the system is cheap). To address this challenge, this paper presents NeuralPARC. The method extends the authors' prior Piecewise Affine Reach-avoid Computation (PARC) method to systems modeled by rectified linear unit (ReLU) neural networks, which are trained to represent parameterized trajectory data demonstrated by the robot. NeuralPARC computes the reachable set of the network while accounting for modeling error, and returns a set of states and parameters with which the black-box system is guaranteed to reach the goal and avoid obstacles. NeuralPARC is shown to outperform PARC, generating provably-safe extreme vehicle drift parking maneuvers in simulations and in real life on a model car, as well as enabling safety on an autonomous surface vehicle (ASV) subjected to large disturbances and controlled by a deep reinforcement learning (RL) policy.
Paper Structure (26 sections, 3 theorems, 31 equations, 4 figures, 1 table)

This paper contains 26 sections, 3 theorems, 31 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. Related Work
  3. Contributions
  4. Preliminaries
  5. Set Representations
  6. H-Polytopes
  7. AH-Polytopes
  8. PWA Systems
  9. ReLU Neural Networks and RPM
  10. Problem Formulation
  11. Proposed Method
  12. Learning the Trajectory Model (Offline)
  13. Estimating Modeling Error (Offline)
  14. NeuralPARC: Reach Set (Online)
  15. NeuralPARC: Avoid Set (Online)
  16. ...and 11 more sections

Key Result

Lemma 3

If eq:max_final_error and eq:max_int_error provides an upper bound to the modeling error, then the BRAS $\hat{\Xi}$ of the trajectory model: fulfills eq:true_bras, which is defined on the black-box system eq:blackboxsys.

Figures (4)

  • Figure 1: (Top) A flowchart of our Neural Piecewise Affine Reach-avoid Computation (NeuralPARC) method labelled with relevant paper sections and symbols. We test NeuralPARC on (bottom left) extreme vehicle drift parking and (bottom right) an autonomous surface vehicle (ASV) controlled by deep reinforcement learning (RL) and subject to large disturbances. In each example, a timelapse of the realized motion of the agents are shown. The blue tube is the overapproximation of the agent's body as a circle swept across NeuralPARC's predicted trajectory (dashed line), and the yellow tube represents NeuralPARC's modeling error bounds. We denote the actual trajectory of the ASV with a solid line, and show two timelapses (orange and purple) of the drifting vehicle following the same motion plan. Despite the large variance in the robots' tracking performance, NeuralPARC always guarantees the agents to reach the green goal and avoid the red obstacles.
  • Figure 2: 100 samples of (left) the drift parking vehicle and (right) the ASV from NeuralPARC using a network of depth 5 and width 8 for each hidden layer. The yellow tubes are the modeling error bounds buffered onto NeuralPARC's predicted trajectories (dashed lines). All actual trajectories (solid lines) reach the green goal and avoid the red obstacles buffered with the agent's circular volume.
  • Figure 3: PWA regions in $K$ for different network sizes in NeuralPARC, visualized with (a)-(c) BRAS computation time, where color indicates time elapsed, and (d)-(f) success of finding a safe sample, where red indicates failure, green indicates success, and yellow indicates an empty BRS. The green regions for (d) and (e), highlighted by purple squares, are zoomed in for clarity.
  • Figure 4: Maximum interval error of $p_x$ for PARC and NeuralPARC with different network sizes.

Theorems & Definitions (6)

  • Lemma 3: Translating Guarantees from Trajectory Model to Black-Box System
  • proof
  • Proposition 4: BRS of an Affine Map
  • proof
  • Theorem 5: BAS of an Affine Map
  • proof