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Data-Driven Sampling Based Stochastic MPC for Skid-Steer Mobile Robot Navigation

Ananya Trivedi, Sarvesh Prajapati, Anway Shirgaonkar, Mark Zolotas, Taskin Padir

TL;DR

This paper enhances a dynamic unicycle model with Gaussian Process regression outputs by enhancing a dynamic unicycle model with Gaussian Process (GP) regression outputs to solve the resultant stochastic optimal control problem using a chance-constrained Model Predictive Path Integral (MPPI) control method.

Abstract

Traditional approaches to motion modeling for skid-steer robots struggle with capturing nonlinear tire-terrain dynamics, especially during high-speed maneuvers. In this paper, we tackle such nonlinearities by enhancing a dynamic unicycle model with Gaussian Process (GP) regression outputs. This enables us to develop an adaptive, uncertainty-informed navigation formulation. We solve the resultant stochastic optimal control problem using a chance-constrained Model Predictive Path Integral (MPPI) control method. This approach formulates both obstacle avoidance and path-following as chance constraints, accounting for residual uncertainties from the GP to ensure safety and reliability in control. Leveraging GPU acceleration, we efficiently manage the non-convex nature of the problem, ensuring real-time performance. Our approach unifies path-following and obstacle avoidance across different terrains, unlike prior works which typically focus on one or the other. We compare our GP-MPPI method against unicycle and data-driven kinematic models within the MPPI framework. In simulations, our approach shows superior tracking accuracy and obstacle avoidance. We further validate our approach through hardware experiments on a skid-steer robot platform, demonstrating its effectiveness in high-speed navigation. The GPU implementation of the proposed method and supplementary video footage are available at https: //stochasticmppi.github.io.

Data-Driven Sampling Based Stochastic MPC for Skid-Steer Mobile Robot Navigation

TL;DR

This paper enhances a dynamic unicycle model with Gaussian Process regression outputs by enhancing a dynamic unicycle model with Gaussian Process (GP) regression outputs to solve the resultant stochastic optimal control problem using a chance-constrained Model Predictive Path Integral (MPPI) control method.

Abstract

Traditional approaches to motion modeling for skid-steer robots struggle with capturing nonlinear tire-terrain dynamics, especially during high-speed maneuvers. In this paper, we tackle such nonlinearities by enhancing a dynamic unicycle model with Gaussian Process (GP) regression outputs. This enables us to develop an adaptive, uncertainty-informed navigation formulation. We solve the resultant stochastic optimal control problem using a chance-constrained Model Predictive Path Integral (MPPI) control method. This approach formulates both obstacle avoidance and path-following as chance constraints, accounting for residual uncertainties from the GP to ensure safety and reliability in control. Leveraging GPU acceleration, we efficiently manage the non-convex nature of the problem, ensuring real-time performance. Our approach unifies path-following and obstacle avoidance across different terrains, unlike prior works which typically focus on one or the other. We compare our GP-MPPI method against unicycle and data-driven kinematic models within the MPPI framework. In simulations, our approach shows superior tracking accuracy and obstacle avoidance. We further validate our approach through hardware experiments on a skid-steer robot platform, demonstrating its effectiveness in high-speed navigation. The GPU implementation of the proposed method and supplementary video footage are available at https: //stochasticmppi.github.io.

Paper Structure

This paper contains 15 sections, 16 equations, 5 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Preliminaries
  4. Probabilistic Motion Modeling
  5. Stochastic Navigation Problem
  6. Chance-Constrained MPPI
  7. Robot Dynamics
  8. Navigation Cost Functions
  9. Inequality Constraints Reformulation
  10. Overall Stochastic MPPI Algorithm
  11. Experiments and Discussion
  12. Simulation Experiments
  13. Hardware Validation
  14. Discussion
  15. Conclusion

Figures (5)

  • Figure 1: Illustration of two MPPI trajectories (Traj 1 and Traj 2). The obstacle radii are adjusted based on propagated state variance (ellipses) and the safety threshold $p_x$ (Eq. \ref{['eq:generic_chance_constraint']}). Traj 1 is 'unsafe' due to a collision with an obstacle (Obs 1).
  • Figure 2: Visualization of the track half-width reduction along the MPC horizon as a function of propagated variance.
  • Figure 3: Visualization of the modified signed distance function, leading to a predicted collision at time step $k$.
  • Figure 4: Circular paths on tiles tracked by a skid-steer robot operating at a reference linear speed of 2 m/s (top speed of robot) and an angular speed of 1.25 rad/s.
  • Figure 5: (a) Navigating a beach terrain around virtual obstacles highlighted as stones. (b) Trajectories from all planners: Unicycle-MPPI (green) collides with obstacles, EDD5-MPPI (pink) takes longer and passes close to obstacles, while GP-MPPI (red) avoids obstacles and reaches the goal faster. (c) GP-MPPI based slaloming around trees on a bushy terrain.