Multi-robot Motion Planning with Circular Holding Patterns
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Solution Overview
Problem
Existing multi-robot systems face challenges in generating scalable and complete safe motion plans, particularly for labeled robots operating in two-dimensional spaces with limited altitudes, as existing algorithms are either not complete or not scalable for large teams.
Innovation Solution
The proposed system designs optimal motion plans for each robot, which includes a circular holding pattern to resolve imminent collisions, ensuring collision-free trajectories and scalability to hundreds of robots, using a method that combines optimal motion plans and circular holding patterns.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If coupled planners search for optimal paths in joint configuration space, then optimality and completeness are guaranteed, but computational complexity grows exponentially with the number of robots
Solution Approach 1:
The patent segments the joint configuration space into individual robot configuration spaces, allowing each robot to be planned independently. This decomposition transforms the exponentially complex joint planning problem into multiple simpler individual planning problems, maintaining completeness guarantees while dramatically reducing computational complexity.
Solution Approach 2:
The patent introduces a temporal dimension by planning paths and velocity profiles separately in space and time. This dimensional separation allows the system to guarantee safety and completeness without searching the full joint configuration space, as time-based velocity adjustments resolve potential collisions without requiring exponential computational resources.
2Productivity
If decoupled planners plan for each robot separately in priority order, then computational speed improves, but completeness is lost
Solution Approach 1:
The patent implements feedback mechanisms where each robot's planned trajectory is continuously checked for potential collisions with other robots. When conflicts are detected, the system adjusts velocity profiles or triggers replanning, ensuring that the final solution is complete and collision-free while maintaining the computational efficiency of decoupled planning.
Solution Approach 2:
The patent performs preliminary path planning for each robot independently to establish collision-free geometric paths. This preliminary action separates the path generation phase from the velocity coordination phase, allowing fast individual planning while subsequently ensuring completeness through centralized velocity profile coordination that resolves all potential collisions.
3Reliability
If algorithms compute solutions to Hamilton-Jacobi-Isaacs PDE equation for reciprocal collision avoidance, then safety is guaranteed, but computational difficulty increases for large teams
Solution Approach 1:
The patent replaces the computationally expensive Hamilton-Jacobi-Isaacs PDE solutions with simpler, analytically constructed velocity profiles and holding patterns. These lightweight computational objects provide sufficient safety guarantees for large teams without the prohibitive computational cost of solving complex partial differential equations, making the system scalable to hundreds of robots.
Data Source
AI summary
The present subject matter relates to systems and methods for generating trajectories for a plurality of vehicles in a multi-vehicle system. An optimal motion plan is determined for moving each of the plurality of vehicles between a respective starting position and an assigned goal position, possible collisions are identified among the optimal motion plans of the plurality of vehicles, and, for a subset of the plurality of vehicles identified as being associated with a possible collision, the optimal motion plan of each vehicle in the subset is modified to define modified trajectories that each include a common circular holding pattern such that the possible collision is avoided.