Shield Model Predictive Path Integral: A Computationally Efficient Robust MPC Approach Using Control Barrier Functions (2302.11719v1)

Abstract: Model Predictive Path Integral (MPPI) control is a type of sampling-based model predictive control that simulates thousands of trajectories and uses these trajectories to synthesize optimal controls on-the-fly. In practice, however, MPPI encounters problems limiting its application. For instance, it has been observed that MPPI tends to make poor decisions if unmodeled dynamics or environmental disturbances exist, preventing its use in safety-critical applications. Moreover, the multi-threaded simulations used by MPPI require significant onboard computational resources, making the algorithm inaccessible to robots without modern GPUs. To alleviate these issues, we propose a novel (Shield-MPPI) algorithm that provides robustness against unpredicted disturbances and achieves real-time planning using a much smaller number of parallel simulations on regular CPUs. The novel Shield-MPPI algorithm is tested on an aggressive autonomous racing platform both in simulation and using experiments. The results show that the proposed controller greatly reduces the number of constraint violations compared to state-of-the-art robust MPPI variants and stochastic MPC methods.

• The paper introduces Shield-MPPI, integrating discrete-time CBFs into MPPI to secure robust control under disturbances.
• It employs a double-layer safety mechanism with local repair optimization to reduce computational demand while ensuring safety.
• Extensive simulations and real-world tests on AutoRally confirm substantial crash rate reduction and improved operational efficiency.

Shield Model Predictive Path Integral: A Computationally Efficient Robust MPC Approach Using Control Barrier Functions

The paper presents Shield-MPPI, an advanced algorithm aimed at enhancing the robustness and efficiency of Model Predictive Path Integral (MPPI) Control using Control Barrier Functions (CBFs). This approach is designed to improve the adaptability and safety of autonomous systems subject to disturbances and limited computational resources.

Introduction to MPPI and Its Challenges

MPPI is a sampling-based model predictive control framework that generates optimal control strategies through trajectory simulation. Although effective, MPPI is limited by its sensitivity to unmodeled dynamics and environmental disturbances, as well as its substantial computational demands, particularly when deploying on systems without high-performance GPUs.

Existing Approaches

Various MPPI variants have been developed to mitigate these limitations:

• Risk-based Penalties: Introduce extra penalties for trajectories entering high-risk areas (Figure 1).
• Distribution Shaping: Adjusts trajectory distribution to improve sampling efficiency while potentially limiting exploration (Figure 1).
• Tracking-based Methods: Use robust tracking controllers to bridge simulation and reality (Figure 1).

  Figure 1: Comparison of different MPPI variants in the presence of unexpected disturbances.

Contributions of Shield-MPPI

Shield-MPPI integrates discrete-time CBFs to create a double-layer safety mechanism:

1. Safety Shield Using CBFs: Incorporates CBFs into the trajectory cost to penalize constraint violations, thus prioritizing safety during trajectory sampling.
2. Local Repair Optimization: Applies gradient-based optimization to locally adjust control actions for ensuring safety even when trajectory samples are limited.

   Figure 2: Shield-MPPI control architecture.

Advantages over Standard MPPI

• Safety Assurance: Provides guarantees of safety by making feasible control decisions that respect CBF constraints even under large disturbances (Figure 3).
• Reduced Computational Demand: Achieves robust planning with minimal use of trajectory samples, suitable for CPUs (Figure 4).

  Figure 3: Cost sensitivity comparison between Shield-MPPI and MPPI.

  

  Figure 4: Comparison of MPPI and Shield-MPPI using CPU implementation.

Comparative Analysis

Shield-MPPI was evaluated against standard MPPI and stochastic MPC variants such as RA-MPPI and CS-SMPC through extensive simulations. It demonstrated superior crash rate reduction and handling of disturbances while maintaining high velocities efficiently (Figure 5).

Figure 5: Collision rate reduction and absolute collision rate of Shield-MPPI controller.

Experimental Validation

Real-world tests on the AutoRally platform confirmed Shield-MPPI's capability to maintain safety and improve operational efficiency despite external disturbances, achieving notable speed enhancements with reduced computational resources (Figure 6).

Figure 6: AutoRally experiment.

Conclusion

The Shield-MPPI framework offers a significant advancement in robust MPC, particularly beneficial for autonomous systems that must operate efficiently under constraints. By effectively integrating CBFs, Shield-MPPI ensures safety while optimizing performance, facilitating broader adoption in fields like autonomous driving and drone navigation where computational power is limited.

Future efforts may involve expanding the Shield-MPPI's applicability using learned certificates and deploying it in more complex, multi-agent settings, enhancing its utility in diverse robotic applications.