Robot Trajectory Safety Control Using Circle-Based Reachable Sets
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Solution Overview
Problem
Existing methods for verifying the safety of robot trajectories, such as those described by Liu et al. (2017), are not real-time capable due to high computational demands, particularly for mobile robots with limited computing capacities.
Innovation Solution
A method that evaluates the safety of a robot's trajectory by comparing the sum of the distance between the robot and the robot's trajectory using circles to determine potential collisions, reducing computational requirements by avoiding polygon intersections and using distance calculations between circles.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If polygonal hull intersection methods are used to verify robot trajectory safety, then measurement precision is improved, but computing time increases significantly
Solution Approach 1:
The patent segments the continuous reachable set verification problem into discrete time point checks. Instead of computing polygonal hulls over the entire time horizon, the method divides the verification into individual time points and uses circle-based reachable sets at each discrete moment, significantly reducing computational complexity while maintaining safety verification accuracy.
Solution Approach 2:
The patent replaces the complex geometric computation of polygonal hull intersections with simpler circle-based distance calculations. By substituting the mechanical/geometric system of polygon operations with a mathematical system based on circle equations and distance formulas, the computation becomes tractable for real-time embedded systems.
2Device complexity
If embedded computing systems are used in mobile robots, then device complexity is reduced, but computing capacity is limited
Solution Approach 1:
The patent changes the mathematical parameters from complex polygonal hull representations to simple circular representations characterized by center positions and radii. This parameter transformation reduces the computational burden from O(n²) polygon operations to O(1) circle distance calculations, making the system suitable for embedded computing with limited power resources.
3Productivity
If real-time trajectory evaluation is implemented, then productivity is improved, but measurement precision may be reduced
Solution Approach 1:
The patent performs preliminary computation of circle-based reachable sets at discrete time points before actual trajectory execution. By pre-calculating the safety zones and collision boundaries using the simplified circle model, the system enables real-time trajectory evaluation without sacrificing collision detection accuracy, as the critical safety margins are established in advance.
Data Source
AI summary
A computer-implemented method for ascertaining a control signal of a robot. The method includes: obtaining a position and movement direction of an object; ascertaining a first set of reachable positions of the object with respect to at least one physical model of the movement of the object and a set of time points, wherein the reachable positions of the first set are characterized by a set of first circles which are each assigned to a time point; ascertaining a trajectory of the robot, which is characterized by positions of the robot at time points, wherein each position is characterized by at least one second circle, which corresponds to the time point of the position; ascertaining the control signal depending on whether at a given time point the second circle corresponding to the time point intersects with the first circle corresponding to the time point or touches the first circle.