Robot Motion Planning Under Acceleration and Jerk Constraints
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Existing motion planning techniques for robots are computationally intensive and prone to getting stuck in non-optimal local minima when optimizing velocity while maintaining limits on acceleration and jerk, making them inefficient and unreliable.
Innovation Solution
Transforming the non-linear optimization problem into a quasi-convex linear optimization problem by using a linear approach to determine feasible ranges of velocity and acceleration, allowing for efficient computation and avoidance of local minima.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If non-linear optimization methods are used to optimize velocity while maintaining acceleration and jerk limits, then the solution can satisfy all constraints, but the computational complexity increases and the solution time becomes excessively long
Solution Approach 1:
The patent transforms the non-linear optimization problem into a linear optimization problem by changing the mathematical formulation parameters. Specifically, it reformulates the velocity optimization problem with jerk constraints as a linear program that can be solved efficiently using standard linear optimization algorithms, avoiding the computational burden and local minima issues of non-linear methods while maintaining constraint satisfaction
Solution Approach 2:
The patent replaces the complex non-linear optimization mechanism with a simpler linear optimization mechanism. By substituting the non-linear mathematical framework with a linear one, the system achieves the same constraint satisfaction goals but with dramatically reduced computational complexity and faster solution times suitable for real-time robot control
2Reliability
If conventional motion planning methods are used, then the robot can operate safely within constraints, but the computational efficiency is too low for real-time applications
Solution Approach 1:
The patent transforms the optimization parameters to convert a computationally intensive non-linear problem into an efficient linear problem. This parameter transformation maintains all safety constraints (velocity, acceleration, jerk limits) while reducing computational complexity to levels suitable for real-time robot control applications
Solution Approach 2:
The patent substitutes the conventional non-linear optimization approach with a linear optimization system. This replacement maintains safe operation within all constraints while achieving the computational efficiency required for real-time control, as linear optimization problems can be solved much faster and more reliably
Data Source
Figure 1A~1E
Figure 2
Figure 3
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.