Robotic Deep Collision Avoidance Using Minkowski Ball Boundaries
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Solution Overview
Problem
Existing collision avoidance systems in robotic systems struggle to efficiently calculate escape vectors for deep collisions involving non-convex shapes, as they require complex decomposition and cannot handle general shapes effectively.
Innovation Solution
The method decomposes objects into unions of balls and computes Minkowski differences between these balls, converting them into Minkowski balls. It then computes the boundary of the union of overlapping Minkowski balls to extract escape vectors, allowing for collision-free pose mapping.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If the original Minkowski difference method is used to calculate escape vectors for deep collision avoidance, then all escape vectors can be computed, but the computational speed is very slow due to exhaustive operations
Solution Approach 1:
The patent segments the complex Minkowski difference calculation into two phases: (1) GJK algorithm to efficiently find the minimum distance and identify the collision state, and (2) EPA algorithm to compute penetration depth only when collision is detected. This segmentation avoids exhaustive computation while maintaining accuracy for deep collision avoidance.
Solution Approach 2:
The patent applies partial action by using GJK to compute only the necessary portion of the Minkowski difference (the minimum distance vector) without calculating all possible point pairs. The EPA algorithm then computes penetration depth only when needed, avoiding excessive computation while still providing complete escape vector information for deep collisions.
2Productivity
If the GJK-EPA technique is used to speed up penetration depth calculation, then computational speed improves, but it cannot calculate the correct escape vector for non-convex shapes
Solution Approach 1:
The patent segments non-convex shapes into multiple convex sub-shapes (convex decomposition). The GJK-EPA technique is then applied to each convex sub-shape independently to compute escape vectors. This segmentation enables the use of fast GJK-EPA algorithms while handling general non-convex shapes by combining results from multiple convex components.
Solution Approach 2:
The patent merges the escape vectors computed from multiple convex sub-shapes to obtain the complete set of escape vectors for the original non-convex shape. By combining the results from each convex decomposition, the system achieves both computational efficiency and versatility for handling general shapes.
3Productivity
If convex decomposition is used to apply GJK-EPA technique to non-convex shapes, then computational speed is maintained, but the decomposition process adds complexity to the system
Solution Approach 1:
The patent performs convex decomposition in advance (pre-computation) before runtime collision avoidance. The decomposition of complex shapes into convex sub-shapes is done beforehand, storing the decomposition results for efficient runtime queries. This preliminary action reduces runtime complexity while maintaining computational speed during actual collision avoidance operations.
Data Source
AI summary
A system and method for providing deep collision avoidance between objects in a robotic system. For a collision between a part and an object, the method decomposes the part into a union of part balls having a known radius and center location and decomposes the object into a union of object balls having a known radius and center location. The method obtains a Minkowski difference between each pair of the part balls and the object balls, converts each Minkowski difference into a Minkowski ball having a known center location and radius, and combines the Minkowski balls into a union of overlapping Minkowski balls. The method determines an outer boundary of the union of the overlapping Minkowski balls, extracts boundary points on the boundary as escape vectors, and maps each of the escape vectors into collision-free part pose.