Redundant Drive Nonlinear Constraint Approximation for Control Allocation
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Solution Overview
Problem
Current methods are ineffective for determining the control attainable set of a redundant drive system with nonlinear constraint relationships between actuators, such as in a four-wheel independently driven vehicle.
Innovation Solution
A secant line approximation method is employed to transform nonlinear constraints into a combination of rectangles and elliptical triangles, allowing for the approximation of the region enclosed by the nonlinear constraint and enabling the calculation of the control attainable set.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If a nonlinear constraint relationship between actuators is present in a redundant drive system, then the system can achieve more complex control capabilities (e.g., four-wheel independent drive, brake, and steer), but the control attainable set cannot be determined using existing methods
Solution Approach 1:
The patent transforms the nonlinear constraint problem into a linear approximation problem by changing the mathematical representation parameters. It uses secant lines to approximate the nonlinear constraint boundaries, converting difficult nonlinear optimization into manageable linear segments that can be processed by existing control allocation methods
Solution Approach 2:
The patent introduces an intermediary approach by using control attainable set calculations as a bridge between the nonlinear physical constraints and the linear control allocation algorithms. By calculating the control attainable set through approximation, it mediates between the complex nonlinear system and simpler control methods
2Productivity
If the nonlinear constraint is approximated by transforming it into a combination of rectangles and elliptical triangles, then the control attainable set can be calculated, but the approximation introduces some error in representing the original nonlinear constraint
Solution Approach 1:
The patent divides the complex nonlinear constraint region into smaller geometric segments (rectangles and elliptical triangles). This segmentation allows each subset to be handled independently with simpler calculations, improving overall computational efficiency while maintaining reasonable accuracy through the combination of segments
Solution Approach 2:
The patent creates simplified geometric copies (rectangles and elliptical triangles) that approximate the original nonlinear constraint boundaries. These copied geometric forms are computationally easier to handle while preserving the essential characteristics of the original constraint region
Data Source
AI summary
Provided is a secant line approximation method for a nonlinear constraint of a redundant drive system, which relates to the technical field of dynamics control allocation of the redundant drive system. The method includes: first obtaining, based on a control input model for a redundant drive system with any pair of nonlinear constraint components, a closed region of the model that is formed by intersecting a rectangle and an ellipse on a geometric plane; and after dividing the closed region into a union set of rectangles and elliptical triangles, approximating the elliptical triangle based on a combination of rectangles and triangles to obtain an approximation result of the closed region, thereby achieving a linear approximation of the pair of nonlinear constraint components.