A Generalized Continuous Collision Detection Framework of Polynomial Trajectory for Mobile Robots in Cluttered Environments (2206.13175v1)

Abstract: In this paper, we introduce a generalized continuous collision detection (CCD) framework for the mobile robot along the polynomial trajectory in cluttered environments including various static obstacle models. Specifically, we find that the collision conditions between robots and obstacles could be transformed into a set of polynomial inequalities, whose roots can be efficiently solved by the proposed solver. In addition, we test different types of mobile robots with various kinematic and dynamic constraints in our generalized CCD framework and validate that it allows the provable collision checking and can compute the exact time of impact. Furthermore, we combine our architecture with the path planner in the navigation system. Benefiting from our CCD method, the mobile robot is able to work safely in some challenging scenarios.

• The paper introduces a generalized continuous collision detection framework for mobile robots that represents collision conditions as polynomial inequalities to efficiently detect potential collisions and calculate time of impact.
• The framework offers versatility across various robot types, including AGVs, quadrotors, and CDPRs, by modeling robots and obstacles using simple geometric shapes for efficient collision checking.
• Practical implications include enhanced safety in shared workspaces through accurate collision detection, improved computational efficiency compared to point-wise methods, and potential for integration into real-time navigation systems.

Overview of a Generalized Continuous Collision Detection Framework for Mobile Robots

The paper introduces a novel framework for continuous collision detection (CCD) to enhance the safety and efficiency of mobile robots navigating through cluttered environments. This framework emphasizes the polynomial trajectory planning, enabling precise collision checking against various static obstacles modeled as simple geometric shapes. The authors leverage polynomial inequalities to detect potential collisions, significantly enhancing computational efficiency and accuracy.

Technical Contributions and Methodology

1. Transformation of Collision Conditions: The research pivots around representing collision conditions as polynomial inequalities. This mathematical formulation allows for direct computation of collision intervals and the exact time of impact (ToI). By utilizing a polynomial solver, the framework calculates these intervals, offering the potential for real-time application.
2. Geometric Modeling: The framework models mobile robots and obstacles using simple geometric shapes such as ellipsoids, cylinders, spheres, and polyhedrons. This abstraction enables computationally efficient collision checking using set polynomial inequalities derived from geometric relationships.
3. Versatility and Generalization: One notable feature of the proposed method is its generalization capability across different types of mobile robots, including cable-driven parallel robots (CDPRs), aerial quadrotors, and ground automated guided vehicles (AGVs). This versatility stems from addressing the nonlinear kinematic and dynamic constraints specific to each robot type within the CCD framework.
4. Integration with Path Planning: The proposed CCD framework is integrable with existing path planning algorithms, such as dynamic window approach (DWA), in navigation systems. This synergy allows for a direct application in real-world scenarios, ensuring safe robot operation through efficient path planning and collision avoidance.

Practical Implications and Potential Impact

• Enhanced Safety in Shared Workspaces: The accurate detection of ToI and collision-free intervals ensures that mobile robots can safely navigate environments with static obstacles, optimizing operation in shared spaces.
• Computational Efficiency: By deriving collision conditions as polynomial inequalities, the framework performs efficiently compared to traditional point-wise collision detection methods, which often require intensive computation and risk collision oversight.
• Real-time Navigation Applications: The proposed approach is designed for integration into real-time navigation systems, providing rapid feedback on collision potential and enabling dynamic path adjustment.

Numerical Results and Validation

The framework has undergone extensive validation through numerous simulation scenarios involving different robot models and cluttered environments. Strong numerical results highlight the efficiency of the framework:

• Collision intervals and instances are precisely computed, with experiments showing a significant reduction in time compared to point-wise methods.
• Application scenarios demonstrate successful navigation of narrow passages with AGVs and complex environments with aerial and cable-driven robots, underlining the method's robustness and applicability.

Future Directions

This research paves the way for further exploration in several areas:

• Sensing and Environment Abstraction: Future work may delve into improving the abstraction from raw sensor data to generalized geometric models, enhancing practical deployment.
• Expanded Robotic Applications: Expanding the CCD framework's application to other robotic systems with more intricate dynamic models could provide broader system optimization.
• Optimization in Dynamic Environments: Further research could integrate dynamic obstacle avoidance, providing a holistic solution for environments where both stationary and moving obstacles exist.

In summary, the paper presents a methodologically sound and practically viable approach to polynomial-based CCD in mobile robotics, poised to significantly contribute to advancing autonomous navigation safety and efficiency.