Robot Motion Planning Under Acceleration and Jerk Limits
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Solution Overview
Problem
Current motion planning techniques for robots are computationally inefficient and prone to getting stuck in non-optimal local minima when optimizing velocity while maintaining limits on acceleration and jerk, making it difficult to achieve maximum velocity without violating constraints.
Innovation Solution
A processor-based method that linearly determines maximized velocity along a geometric path by applying acceleration and jerk limits, using a backward and forward pass approach to select optimal values of acceleration and jerk within defined limits, and iteratively refining the solution to ensure compliance with constraints.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If non-linear optimization methods are used to maximize robot velocity along a path, then velocity optimization capability is improved, but computational speed deteriorates and the system gets stuck in local minima
Solution Approach 1:
The patent transforms the non-linear optimization problem into a linear one by changing the mathematical parameters and formulation of the velocity optimization problem. This allows the use of efficient linear programming algorithms instead of slow non-linear methods, achieving both computational speed and optimization accuracy.
Solution Approach 2:
The patent replaces the conventional non-linear optimization approach with a linear programming-based method. This substitution of the optimization mechanism eliminates the problem of local minima and significantly improves computational efficiency while maintaining velocity optimization capability.
2Measurement precision
If non-linear optimization methods are used to maximize robot velocity, then velocity optimization capability is improved, but reliability deteriorates due to getting stuck in local minima
Solution Approach 1:
The patent replaces the non-linear optimization mechanism with a linear programming approach. Linear programming guarantees finding the global optimum and eliminates the reliability issue of getting stuck in local minima, while still achieving accurate velocity optimization.
Solution Approach 2:
By changing the mathematical formulation from non-linear to linear parameters, the patent ensures that the optimization problem has a unique global solution, thereby improving the reliability and consistency of the velocity optimization results.
3Reliability
If complex optimization algorithms are used to maintain acceleration and jerk limits, then constraint satisfaction is improved, but device complexity increases
Solution Approach 1:
The patent incorporates acceleration and jerk constraints directly into the linear programming formulation by defining appropriate decision variables and constraints. This integration maintains constraint satisfaction while keeping the algorithm structure simple and efficient.
Solution Approach 2:
The patent merges the velocity optimization objective with the acceleration and jerk constraints into a single linear programming problem. This unified approach ensures all constraints are satisfied simultaneously without requiring separate complex algorithms for each constraint.
Data Source
AI summary
Faster, less computational intense, and more robust techniques to optimize velocity of robots or portions thereof without violating constraints on acceleration and jerk (derivative of acceleration with respect to time) are described. A nonlinear problem of optimizing velocity without violating acceleration constraints is linearized, and produces acceleration constrained velocity estimates. A nonlinear problem of optimizing velocity without violating jerk constraints in linearized, and produces jerk constrained velocity estimates, and may be feed by the acceleration constrained velocity estimates. Configuration and timing may be generated and provided, e.g., as vectors, to control operation of a robot, robotic appendage or other structure.