(untitled) (Інформатика. Культура. Техніка, 2025)
Collision-free path planning for redundant robotic manipulators is a significant challenge in robotics, primarily due to the highdimensional joint spaces and the complexity of real-world environments. While foundational sampling-based planners have proven effective, they often struggle in scenarios with narrow passages or complex constraints. The Recursive Random Intermediate State (RRIS) method was recently introduced as a promising alternative that employs a "divide and conquer" strategy, recursively inserting intermediate states to simplify a complex planning problem into a series of more simple subproblems. However, the original RRIS implementation relies on a simplistic heuristic for evaluating intermediate states: it counts the number of discrete configurations in a state of collision. This binary metric lacks nuance, treating a path with a minor, grazing contact identically to one with severe interpenetration. In this paper, we propose an enhancement to the RRIS method by replacing this binary count with a more physically intuitive, continuous metric. Instead of merely counting collisions, we accumulate the penetration depth returned by the collision checker for each state along a path segment. This approach allows the planner to differentiate between the severity of different collisions and prioritize paths that are closer to being collision-free. Furthermore, we refine the method’s early-exit condition to make the recursive search more efficient. The new condition not only requires the cumulative collision depth of a path through an intermediate state to be lower than the direct path but also introduces an adaptive thresholding mechanism: if a new intermediate state reduces the number of unique pairs of objects that are in collision, then a more lenient depth-reduction threshold is applied for early termination. Conversely, if the set of colliding pairs remains unchanged, a much stricter improvement is required. The experimental validation was conducted on a test suite of 105 start–goal pairs with three distinct tool configurations. The results confirm the efficacy of the proposed enhancements. Switching from the original count-based heuristic to the depth-based comparison reduced the total planning time from 38.3 s to 29.6 s. The introduction of the adaptive distinct-pair check further decreased the total time to 22.9 s, achieving a total speedup of approximately 1.67x over the baseline while preserving a 100% success rate on this test suite. While these results are promising, we position them as preliminary and suggest that future work should involve validation across a broader and more diverse range of complex scenarios