PRIEST: Projection Guided Sampling-Based Optimization For Autonomous Navigation (2309.08235v1)

Abstract: Efficient navigation in unknown and dynamic environments is crucial for expanding the application domain of mobile robots. The core challenge stems from the nonavailability of a feasible global path for guiding optimization-based local planners. As a result, existing local planners often get trapped in poor local minima. In this paper, we present a novel optimizer that can explore multiple homotopies to plan high-quality trajectories over long horizons while still being fast enough for real-time applications. We build on the gradient-free paradigm by augmenting the trajectory sampling strategy with a projection optimization that guides the samples toward a feasible region. As a result, our approach can recover from the frequently encountered pathological cases wherein all the sampled trajectories lie in the high-cost region. Furthermore, we also show that our projection optimization has a highly parallelizable structure that can be easily accelerated over GPUs. We push the state-of-the-art in the following respects. Over the navigation stack of the Robot Operating System (ROS), we show an improvement of 7-13% in success rate and up to two times in total travel time metric. On the same benchmarks and metrics, our approach achieves up to 44% improvement over MPPI and its recent variants. On simple point-to-point navigation tasks, our optimizer is up to two times more reliable than SOTA gradient-based solvers, as well as sampling-based approaches such as the Cross-Entropy Method (CEM) and VPSTO. Codes: https://github.com/fatemeh-rastgar/PRIEST

• The paper introduces a novel projection-guided sampling optimizer that fuses gradient-free and gradient-based methods for generating feasible, collision-free trajectories.
• It leverages a GPU-accelerated projection method with fixed-point iterations to efficiently handle quadratic and affine constraints in dynamic and cluttered environments.
• Experimental results demonstrate a 90% success rate on benchmarks like the BARN dataset, outperforming established methods such as MPPI and TEB in real-time navigation.

Overview of PRIEST: Projection Guided Sampling-Based Optimization for Autonomous Navigation

The paper entitled "PRIEST: Projection Guided Sampling-Based Optimization For Autonomous Navigation" presents a novel optimization strategy that integrates projection methods into sampling-based approaches for trajectory planning in autonomous navigation. The primary aim is to address the challenges associated with non-differentiable cost functions and infeasible trajectory samplings which are common in dynamic and unknown environments. The methodology exploits the synergy between gradient-free and gradient-based methods to create an optimizer that can project solutions into feasible regions, ensuring collision-free navigation even in complex environments.

Algorithmic Insights

The core component of the proposed algorithm, PRIEST (Projection Guided Sampling-Based Optimization), lies in its projection optimizer. The optimizer functions by sampling trajectories and projecting them onto a feasible set that satisfies the problem's constraints. This is achieved through a series of fixed-point iterations designed to handle both quadratic and affine constraints efficiently. Furthermore, the projection optimizer is formulated to be GPU-accelerated, allowing the method to remain computationally efficient and suitable for real-time applications.

PRIEST incorporates a structure that allows it to be integrated into decentralized optimization frameworks. By maintaining multiple Gaussian distributions, the decentralized variant (D-PRIEST) enhances the search over multiple homotopies and improves the global exploration capability. The paper provides rigorous mathematical formulations and proofs showcasing the algorithm's robustness, grounded in the principles of convex optimization and differential flatness.

Performance Evaluation

The paper highlights PRIEST's strong performance across several benchmarks. Notably, it achieves a 90% success rate on the BARN dataset, with significant improvements over state-of-the-art methods such as MPPI and TEB, which achieve lower success rates of 58% and 83%, respectively. In dynamic and cluttered environments, PRIEST showed a success rate of 83%, outperforming other optimization methods systematically. The approach also maintains competitive computational efficiency, demonstrating its capability to solve real-time navigation tasks effectively.

For point-to-point navigation in both 2D and 3D contexts, PRIEST achieved higher success rates compared to conventional and sampling-based optimizers like ROCKIT, FATROP, CEM, and VPSTO. These results are quantified further by improved metrics in computational time while ensuring provably smoother trajectories.

Theoretical Contributions

The paper's theoretical contribution primarily resides in the development of a novel optimization framework that adeptly combines projection-guidance with sampling-based exploratory mechanisms. This combination enhances the local planner's ability to generate feasible trajectory plans, overcoming the limitations posed by standard sampling-based methods which often struggle in high-cost regions. Additionally, by leveraging differential flatness, the framework broadens its applicability across various robotic systems such as mobile robots and quadrotors.

Future Implications

The implications of this work are twofold: practical and theoretical. Practically, PRIEST offers a robust path for advancing autonomous navigation capabilities in mobile robots, particularly in environments characterized by unknown and dynamic obstacles. Theoretical implications involve contributions toward the integration of convex optimization techniques within sampling-based frameworks, suggesting new directions for optimizing complex, non-linear systems in real-time. Future research could explore the adaptability of PRIEST to even higher-dimensional control problems and its application in non-navigation tasks like robotic manipulation.

In conclusion, PRIEST addresses critical challenges in trajectory optimization for autonomous navigation, providing a significant methodological advancement by facilitating feasible, smooth, and computationally efficient trajectory planning—even under stringent constraints imposed by unknown and dynamic environments.