RDA: An Accelerated Collision Free Motion Planner for Autonomous Navigation in Cluttered Environments (2210.00192v4)

Abstract: Autonomous motion planning is challenging in multi-obstacle environments due to nonconvex collision avoidance constraints. Directly applying numerical solvers to these nonconvex formulations fails to exploit the constraint structures, resulting in excessive computation time. In this paper, we present an accelerated collision-free motion planner, namely regularized dual alternating direction method of multipliers (RDADMM or RDA for short), for the model predictive control (MPC) based motion planning problem. The proposed RDA addresses nonconvex motion planning via solving a smooth biconvex reformulation via duality and allows the collision avoidance constraints to be computed in parallel for each obstacle to reduce computation time significantly. We validate the performance of the RDA planner through path-tracking experiments with car-like robots in both simulation and real-world settings. Experimental results show that the proposed method generates smooth collision-free trajectories with less computation time compared with other benchmarks and performs robustly in cluttered environments. The source code is available at https://github.com/hanruihua/RDA_planner.

An Overview of "RDA: An Accelerated Collision Free Motion Planner for Autonomous Navigation in Cluttered Environments"

The paper presents a novel accelerated collision-free motion planner for autonomous navigation in cluttered environments, termed the Regularized Dual Alternating Direction Method of Multipliers (RDA). This approach aims to address the challenges in autonomous motion planning, particularly within multi-obstacle environments where nonconvex collision avoidance constraints pose significant computational demands. The authors propose leveraging a smooth biconvex reformulation via duality, which facilitates substantial computation time reduction by enabling parallel computation of collision avoidance constraints.

Key Contributions and Methodology

The RDA offers several innovative contributions:

1. Non-Point-Mass Obstacle Modeling: The authors propose an optimization-based navigation problem that accommodates non-point-mass representations of obstacles. They reformulate the nonconvex constraints into bi-convex counterparts using joint linearization and strong duality, where the collision avoidance constraints are automatically tuned through $l_1$ regularization.
2. Parallel Local Planning: The paper introduces a parallel local planner using the RDA, which efficiently solves the redefined bi-convex problem in parallel. This approach significantly enhances robustness concerning algorithm convergence.
3. Empirical Validation: The proposed RDA algorithm is evaluated through experiments involving path-tracking with car-like robots both in high-fidelity Gazebo simulations and real-world settings. The results demonstrate that RDA outperforms existing benchmarks in computation time while maintaining robust performance in cluttered environments.

The authors adeptly utilize parallel computation facilitated by ADMM, significantly mitigating the complexity typically associated with such optimization problems. This approach enables a reduction in computation time, providing a viable pathway towards real-time obstacle avoidance in dynamic environments.

Results and Evaluation

Experimental validation highlights RDA's capability to find smooth collision-free trajectories effectively and efficiently. The impact on practical scenarios is underscored by significant reductions in path-tracking execution times compared to other methodologies. Notably, the computation time remains relatively stable with an increasing number of obstacles, a highlight in autonomous navigation settings prone to dense clutter.

Implications and Future Work

The adoption of RDA could reshape the potential applications of autonomous navigation in dense, cluttered environments by providing a more efficient solution to collision avoidance problems. Future work could explore the scalability of RDA to other vehicle models with complex dynamics. Moreover, integrating RDA within a multi-agent framework could extend its applicability to scenarios requiring coordinated navigational strategies.

In conclusion, this paper furnishes a highly efficient computational framework to address the challenges of autonomous motion planning in dense environments, paving the way for further research and development in adaptive and robust autonomous systems. Future exploration could incorporate considerations for extended environments and dynamic adaptability, ensuring continued advancement in autonomous navigation technologies.