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MPPI-DBaS: Safe Trajectory Optimization with Adaptive Exploration

Fanxin Wang, Yikun Cheng, Chuyuan Tao

TL;DR

The paper addresses safety and exploration challenges in nonlinear trajectory optimization by integrating discrete barrier states (DBaS) into Model Predictive Path Integral (MPPI) control. It introduces MPPI-DBaS, which embeds safety directly into the system dynamics and cost through barrier-state augmentation and adds an adaptive exploration mechanism that scales sampling breadth based on barrier costs. Key contributions include the barrier-state safety-embedded model, a barrier-cost augmented running cost, and an adaptive trajectory sampling strategy that improves performance in tight, obstacle-rich environments. The proposed approach yields higher success rates and lower tracking errors in simulations of obstacle navigation, highlighting its potential for safer, real-time trajectory optimization on platforms with limited planning horizons. The work also suggests avenues for further enhancement, such as richer barrier formulations, multi-agent planning, and GPU-accelerated sampling to scale exploration.

Abstract

In trajectory optimization, Model Predictive Path Integral (MPPI) control is a sampling-based Model Predictive Control (MPC) framework that generates optimal inputs by efficiently simulating numerous trajectories. In practice, however, MPPI often struggles to guarantee safety assurance and balance efficient sampling in open spaces with the need for more extensive exploration under tight constraints. To address this challenge, we incorporate discrete barrier states (DBaS) into MPPI and propose a novel MPPI-DBaS algorithm that ensures system safety and enables adaptive exploration across diverse scenarios. We evaluate our method in simulation experiments where the vehicle navigates through closely placed obstacles. The results demonstrate that the proposed algorithm significantly outperforms standard MPPI, achieving a higher success rate and lower tracking errors.

MPPI-DBaS: Safe Trajectory Optimization with Adaptive Exploration

TL;DR

The paper addresses safety and exploration challenges in nonlinear trajectory optimization by integrating discrete barrier states (DBaS) into Model Predictive Path Integral (MPPI) control. It introduces MPPI-DBaS, which embeds safety directly into the system dynamics and cost through barrier-state augmentation and adds an adaptive exploration mechanism that scales sampling breadth based on barrier costs. Key contributions include the barrier-state safety-embedded model, a barrier-cost augmented running cost, and an adaptive trajectory sampling strategy that improves performance in tight, obstacle-rich environments. The proposed approach yields higher success rates and lower tracking errors in simulations of obstacle navigation, highlighting its potential for safer, real-time trajectory optimization on platforms with limited planning horizons. The work also suggests avenues for further enhancement, such as richer barrier formulations, multi-agent planning, and GPU-accelerated sampling to scale exploration.

Abstract

In trajectory optimization, Model Predictive Path Integral (MPPI) control is a sampling-based Model Predictive Control (MPC) framework that generates optimal inputs by efficiently simulating numerous trajectories. In practice, however, MPPI often struggles to guarantee safety assurance and balance efficient sampling in open spaces with the need for more extensive exploration under tight constraints. To address this challenge, we incorporate discrete barrier states (DBaS) into MPPI and propose a novel MPPI-DBaS algorithm that ensures system safety and enables adaptive exploration across diverse scenarios. We evaluate our method in simulation experiments where the vehicle navigates through closely placed obstacles. The results demonstrate that the proposed algorithm significantly outperforms standard MPPI, achieving a higher success rate and lower tracking errors.

Paper Structure

This paper contains 10 sections, 1 theorem, 15 equations, 5 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. MPPI-based Control Problem with Constraints
  4. Discrete Barrier States (DBaS)
  5. MPPI-DBaS with adaptive exploration
  6. DBaS augmentation with the running cost
  7. Adaptive trajectory sampling
  8. MPPI-DBaS with adaptive exploration algorithm
  9. Applications
  10. Conclusion

Key Result

Theorem 1

For the safety embedded system eq:safety_embedded_dyn, given $x(0)\in\mathcal{S}$, a continuous feedback controller $u=K(x)$ is safe, i.e. satisfies the safety condition $h(x_k) \geq 0$ and the safe set $\mathcal{S}$ is controlled invariant, if and only if $\beta(x_k)<\infty,\forall k\in \{0,1,\cdot

Figures (5)

  • Figure 1: Demonstration of MPPI trajectory sampling. The slashed yellow curves cover the sampled trajectories. The red curve illustrates a sub-optimal trajectory resulting from extensive, high variance exploration. The green curve denotes a near-optimal, refined trajectory.
  • Figure 2: Proposed MPPI-DBaS control scheme.
  • Figure 3: MPPI fail cases. The sampled trajectories are depicted as grey curves, with the near-optimal trajectories highlighted in purple. The red curves indicate the actual trajectory that has been executed.
  • Figure 4: MPPI-DBaS successful tracking. The sampled trajectories are depicted as grey curves, with the near-optimal trajectories highlighted in purple. The red curves indicate the actual trajectory that has been executed.
  • Figure 5: State and control result from 20 simulations. The mean is traced with solid line in each figure, with the variation is depicted by a shaded area.

Theorems & Definitions (3)

  • Definition 1
  • Definition 2
  • Theorem 1