Convex Optimization for Fast Contact Force Computation
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Solution Overview
Problem
Current methods for solving the force optimization problem in mechanisms with closed kinematic chains involving multiple frictional contacts are inefficient, particularly in real-time applications and when optimizing contact points for grasping objects, as they require solving numerous force optimization problems sequentially, which is time-consuming and computationally intensive.
Innovation Solution
The method formulates the force optimization problem as a convex optimization problem and introduces a primal barrier subproblem to rapidly determine feasible solutions, allowing for the rapid solution of multiple force optimization problems by retaining solution states as starting points for subsequent problems, thereby reducing computational time.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If current methods for solving force optimization problems are used, then feasibility and optimality can be determined, but computational time is excessive and the method is too slow for real-time applications
Solution Approach 1:
The patent segments the force optimization problem into two distinct phases: a feasibility phase that determines whether a valid solution exists, and an optimality phase that finds the best solution. This segmentation allows the computationally intensive optimality calculations to be performed only when necessary, significantly reducing overall computational time while maintaining accuracy.
Solution Approach 2:
The patent performs preliminary feasibility analysis before committing to full optimization computation. By first checking whether a feasible solution exists using a simplified test, the system avoids wasting computational resources on problems that have no solution, and prepares the groundwork for efficient optimization when feasible solutions do exist.
2Manufacturing precision
If multiple force optimization problems are solved sequentially to optimize contact points for grasping, then the optimal grasp configuration can be found, but the computational complexity and time consumption increase significantly
Solution Approach 1:
The patent applies segmentation by dividing the overall grasp optimization task into independent feasibility checks for each candidate configuration, followed by optimization only for feasible configurations. This reduces the computational complexity from solving full optimization problems for all configurations to solving simplified feasibility tests for all configurations plus full optimization only for the feasible subset.
Solution Approach 2:
The patent performs partial action by solving only the necessary portion of the optimization problem - first determining feasibility with a simplified test, then performing full optimization only when needed. This partial approach to problem-solving significantly reduces computational complexity while still achieving optimal grasp configurations.
Data Source
AI summary
A method for rapidly determining feasibility of a force optimization problem and for rapidly solving a feasible force optimization problem is disclosed. The method comprises formulating the force optimization problem or force feasibility problem as a convex optimization problem, formulating a primal barrier subproblem associated with the convex optimization problem, and solving the primal barrier subproblem. The method and related methods may also be used to solve each problem in a set of force optimization problems, determine the minimum or maximum force required to satisfy any of a set of force optimization problems, solve a force closure problem, compute a conservative contact force vector, or solve a feasible force optimization problem with bidirectional forces.