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Model Predictive Path Integral Methods with Reach-Avoid Tasks and Control Barrier Functions

Hardik Parwana, Mitchell Black, Georgios Fainekos, Bardh Hoxha, Hideki Okamoto, Danil Prokhorov

TL;DR

Robotics safety in dynamic and uncertain environments requires planning methods with formal guarantees. This work extends the CBFkit toolbox by integrating Model Predictive Path Integral (MPPI) planning with timed reach-avoid specifications and a Control Barrier Function (CBF) safety filter, enabling safe, robust task execution under uncertainty. It delivers a full autonomy stack with an MPPI-based high-level planner, multiple low-level controllers, JAX-based auto-differentiation for CBFs, and auto-generated sensors and estimators, backed by a versatile library of implementations. Through simulation studies in autonomous navigation scenarios, the approach demonstrates improved safety and performance and showcases rapid prototyping capabilities for complex autonomy stacks.

Abstract

The rapid advancement of robotics necessitates robust tools for developing and testing safe control architectures in dynamic and uncertain environments. Ensuring safety and reliability in robotics, especially in safety-critical applications, is crucial, driving substantial industrial and academic efforts. In this context, we extend CBFkit, a Python/ROS2 toolbox, which now incorporates a planner using reach-avoid specifications as a cost function. This integration with the Model Predictive Path Integral (MPPI) controllers enables the toolbox to satisfy complex tasks while ensuring formal safety guarantees under various sources of uncertainty using Control Barrier Functions (CBFs). CBFkit is optimized for speed using JAX for automatic differentiation and jaxopt for quadratic program solving. The toolbox supports various robotic applications, including autonomous navigation, human-robot interaction, and multi-robot coordination. The toolbox also offers a comprehensive library of planner, controller, sensor, and estimator implementations. Through a series of examples, we demonstrate the enhanced capabilities of CBFkit in different robotic scenarios.

Model Predictive Path Integral Methods with Reach-Avoid Tasks and Control Barrier Functions

TL;DR

Robotics safety in dynamic and uncertain environments requires planning methods with formal guarantees. This work extends the CBFkit toolbox by integrating Model Predictive Path Integral (MPPI) planning with timed reach-avoid specifications and a Control Barrier Function (CBF) safety filter, enabling safe, robust task execution under uncertainty. It delivers a full autonomy stack with an MPPI-based high-level planner, multiple low-level controllers, JAX-based auto-differentiation for CBFs, and auto-generated sensors and estimators, backed by a versatile library of implementations. Through simulation studies in autonomous navigation scenarios, the approach demonstrates improved safety and performance and showcases rapid prototyping capabilities for complex autonomy stacks.

Abstract

The rapid advancement of robotics necessitates robust tools for developing and testing safe control architectures in dynamic and uncertain environments. Ensuring safety and reliability in robotics, especially in safety-critical applications, is crucial, driving substantial industrial and academic efforts. In this context, we extend CBFkit, a Python/ROS2 toolbox, which now incorporates a planner using reach-avoid specifications as a cost function. This integration with the Model Predictive Path Integral (MPPI) controllers enables the toolbox to satisfy complex tasks while ensuring formal safety guarantees under various sources of uncertainty using Control Barrier Functions (CBFs). CBFkit is optimized for speed using JAX for automatic differentiation and jaxopt for quadratic program solving. The toolbox supports various robotic applications, including autonomous navigation, human-robot interaction, and multi-robot coordination. The toolbox also offers a comprehensive library of planner, controller, sensor, and estimator implementations. Through a series of examples, we demonstrate the enhanced capabilities of CBFkit in different robotic scenarios.
Paper Structure (12 sections, 11 equations, 4 figures, 1 table)

This paper contains 12 sections, 11 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. Supported Models and Control Design Problems
  3. Autonomy Stack
  4. High-Level Planner
  5. Nominal Controller
  6. Feedback Controller
  7. Auto-Differentiation for CBF Implementations
  8. Closing the Loop with Sensors and Estimators
  9. Simulation Examples
  10. MPPI with Timed Reach-Avoid Tasks
  11. MPPI-CBF controller
  12. Conclusion

Figures (4)

  • Figure 1: Closed-Loop Simulator in CBFkit.
  • Figure 2: A single integrator robot completes the timed-reach-avoid task 'reach $g_1$ between $0-3.5s$, $g_2$ between $3.6-5s$, and $g_3$ between $5.1-10s$ while avoiding obstacles'. For animation, see here: https://youtu.be/Iie4pq_zVfA.
  • Figure 3: Comparison of three controller setups for navigating from the initial location to the goal location. The stochastic CBF controller (orange) becomes infeasible due to the number of obstacles. The MPPI controller (red) alone violates safety constraints. Finally, the MPPI and stochastic CBF (blue) successfully navigate from the initial to the goal location.
  • Figure 4: Visualizing MPPI sampled and output trajectories for comparison.