Certifying Bimanual RRT Motion Plans in a Second (2310.16603v2)

Abstract: We present an efficient method for certifying non-collision for piecewise-polynomial motion plans in algebraic reparametrizations of configuration space. Such motion plans include those generated by popular randomized methods including RRTs and PRMs, as well as those generated by many methods in trajectory optimization. Based on Sums-of-Squares optimization, our method provides exact, rigorous certificates of non-collision; it can never falsely claim that a motion plan containing collisions is collision-free. We demonstrate that our formulation is practical for real world deployment, certifying the safety of a twelve degree of freedom motion plan in just over a second. Moreover, the method is capable of discriminating the safety or lack thereof of two motion plans which differ by only millimeters.

• The paper introduces a novel SOS optimization method to provide rigorous, collision-free certificates for bimanual RRT motion plans.
• It leverages algebraic reparametrizations and convex optimization to achieve precise non-collision guarantees with millimeter-level accuracy.
• Results validate the approach by certifying a 12-DOF motion plan in just over one second, enhancing robotic safety in dynamic environments.

Overview of "Certifying Bimanual RRT Motion Plans in a Second"

This paper introduces a novel method for certifying the safety of motion plans in robotics, specifically focusing on non-collision guarantees for piecewise-polynomial paths within configuration space reparametrizations. It addresses a key challenge in robotic motion planning: ensuring a motion plan is collision-free for all configurations along its path, not just at sampled points. The authors leverage Sums-of-Squares (SOS) optimization to provide rigorous non-collision certificates with strong correctness guarantees.

Methods

The proposed framework utilizes SOS programming to certify that robotic motion plans are free from collisions. This approach involves algebraic reparametrizations of the configuration space, enabling the use of polynomial motion paths within algorithms commonly used in trajectory optimization, such as Rapidly-exploring Random Trees (RRT) and Probabilistic Roadmaps (PRM).

The certification process involves formulating non-collision as a convex optimization problem, using the concept of separating hyperplanes in configuration space. The mathematics leverages the positive semidefinite properties of matrices and vector-matrix formulations to provide numerical certificates that are both efficient and exact.

Key Results

A primary contribution of the paper is demonstrating that the proposed certification method is viable for real-world deployment. The authors provide evidence by certifying the safety of a 12-DOF motion plan in just over a second. Notably, their method discriminates between motion plans with minor spatial differences, accurately identifying potential collisions with millimeter-level precision.

Practical and Theoretical Implications

The certification of non-collision has major implications for the safety and reliability of robotic systems, particularly in environments where precision and safety are paramount, such as in collaborative industrial settings or surgical robotics. By providing guarantees on safety, roboticists can better ensure that their systems are robust to motion planning errors or inaccuracies in modeling environmental interactions.

Speculation on Future Developments

As the field progresses, it is possible that advancements in both computational efficiency and SOS optimization techniques could allow for even faster certification across more complex and higher-dimensional robotic systems. Additionally, future work might explore integration of these certification methods with real-time motion planning algorithms to continually ensure safety as plans are generated and executed.

In conclusion, the paper presents a robust approach to certifying motion plans in robotic systems, addressing critical challenges in ensuring collision-free operation with precision and efficiency. The use of SOS programming in this context provides theoretically sound assurances that enhance the safety of robotic maneuvers within dynamic and potential collision-prone environments.