Towards Efficient MPPI Trajectory Generation with Unscented Guidance: U-MPPI Control Strategy (2306.12369v3)

Abstract: The classical Model Predictive Path Integral (MPPI) control framework, while effective in many applications, lacks reliable safety features due to its reliance on a risk-neutral trajectory evaluation technique, which can present challenges for safety-critical applications such as autonomous driving. Furthermore, when the majority of MPPI sampled trajectories concentrate in high-cost regions, it may generate an infeasible control sequence. To address this challenge, we propose the U-MPPI control strategy, a novel methodology that can effectively manage system uncertainties while integrating a more efficient trajectory sampling strategy. The core concept is to leverage the Unscented Transform (UT) to propagate not only the mean but also the covariance of the system dynamics, going beyond the traditional MPPI method. As a result, it introduces a novel and more efficient trajectory sampling strategy, significantly enhancing state-space exploration and ultimately reducing the risk of being trapped in local minima. Furthermore, by leveraging the uncertainty information provided by UT, we incorporate a risk-sensitive cost function that explicitly accounts for risk or uncertainty throughout the trajectory evaluation process, resulting in a more resilient control system capable of handling uncertain conditions. By conducting extensive simulations of 2D aggressive autonomous navigation in both known and unknown cluttered environments, we verify the efficiency and robustness of our proposed U-MPPI control strategy compared to the baseline MPPI. We further validate the practicality of U-MPPI through real-world demonstrations in unknown cluttered environments, showcasing its superior ability to incorporate both the UT and local costmap into the optimization problem without introducing additional complexity.

• The paper presents a novel U-MPPI strategy that integrates the Unscented Transform to propagate both mean and covariance, improving trajectory exploration.
• The approach incorporates a risk-sensitive cost function that dynamically adjusts penalties based on uncertainty, balancing performance and safety.
• Extensive simulations and real-world tests demonstrate higher task completion and more collision-free trajectories in complex, cluttered navigation scenarios.

Overview of U-MPPI Control Strategy

The paper presents the U-MPPI control strategy, an enhancement of the Model Predictive Path Integral (MPPI) framework aimed at improving system safety and trajectory efficiency in dynamic environments. By integrating the Unscented Transform (UT) into MPPI, the proposed U-MPPI strategy addresses some inherent limitations of classical MPPI, particularly its risk-neutral stance and tendency to sample trajectories within high-cost regions, which can compromise safety in autonomous navigation tasks.

Core Innovations:

1. Unscented-Based Trajectory Sampling:
   • Classical MPPI samples trajectories based on the mean control sequence disturbed by Gaussian noise, focusing solely on the mean of system dynamics. U-MPPI, however, leverages UT to propagate both the mean and covariance of system states. This propagation is achieved through a novel sampling strategy that covers a broader state space, enhancing the algorithm's exploration capabilities and reducing the risk of local minima trapping.
2. Risk-Sensitive Cost Function:
   • The U-MPPI strategy incorporates a risk-sensitive cost function that explicitly considers system uncertainties during trajectory evaluation. This function is designed to account for the covariance information provided by UT, effectively balancing performance and safety by adjusting the penalty matrix based on the level of uncertainty. The cost function is effectively integrated into the MPPI framework, enhancing resilience against variability in dynamic environments.

Simulation and Experimental Validation:

The effectiveness of the U-MPPI control strategy has been validated through extensive simulations and real-world demonstrations using autonomous ground vehicle scenarios in cluttered environments. Key performance metrics compared between U-MPPI and traditional MPPI include task completion rates, success rates, and the number of collision-free trajectories generated.

• Simulation Results:
  • In simulated forest environments with varying obstacle densities, U-MPPI demonstrated superior performance, achieving higher task completion rates and exhibiting reduced instances of local minima trapping compared to MPPI. In denser environments, U-MPPI maintained robustness and safety, illustrating its advantage in complex navigation tasks.
• Real-World Demonstration:
  • In real-world corridor navigation tasks, U-MPPI showcased effective real-time performance and improved smoothness in robot motion. The comprehensive incorporation of the local costmap into the U-MPPI framework underscores its practicality and adaptability in unpredictable environments, resulting in more accurate localization and fewer collisions.

Implications and Future Directions:

The introduction of U-MPPI represents a significant advancement in trajectory optimization frameworks for autonomous systems. By explicitly incorporating risk considerations and improving state-space exploration with UT, the proposed strategy enhances both theoretical control frameworks and practical applications in safety-critical domains such as autonomous driving.

Future work may explore further integration of advanced risk measures, such as chance constraints, to refine the trade-off between exploration and exploitation in uncertain environments. Additionally, extending the framework to handle dynamic obstacles with real-time adaptability could broaden its applicability in autonomous robotics and navigation systems.