Deformable Robot Control Using Reduced Compliance Matrices
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Solution Overview
Problem
Controlling multi-actuated flexible or deformable robots is challenging due to their high number of degrees of freedom, which leads to prohibitive computing times for real-time control, especially when trying to achieve desired deformations using finite element methods.
Innovation Solution
An optimized inversion method for the finite element model is developed, reducing computational load by using an iterative Gauss-Seidel algorithm to determine actuation values, incorporating constraints and actuation directions, and employing a reduced compliance matrix to simplify the control of deformable robots.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If finite element methods are used to model flexible robots for real-time control, then the ability to determine robot behavior from applied forces is improved, but the computing time becomes prohibitive
Solution Approach 1:
The patent pre-calculates and stores the compliance matrix and its inverse during an offline phase, so that during real-time control only simple matrix-vector multiplications are needed. This preliminary preparation eliminates the need for time-consuming iterative solving during operation.
Solution Approach 2:
The control approach separates the complex FEM model into two distinct phases: an offline phase where the compliance matrix is pre-computed, and an online phase where only simple calculations are performed. This segmentation allows the heavy computational work to be done in advance when time is not critical.
2Manufacturing precision
If the inverse problem is solved using FEM to determine actuation values for desired deformation, then the control precision is improved, but the computational complexity increases
Solution Approach 1:
The compliance matrix and its inverse are pre-computed offline, transforming the complex inverse problem into simple matrix-vector multiplications during real-time control. This eliminates the need for iterative solving during operation while maintaining precision.
Solution Approach 2:
The patent replaces the complex iterative mechanical solving process with a pre-computed algebraic approach. By using the pre-calculated compliance matrix, the system substitutes time-consuming iterative numerical methods with simple linear algebra operations.
3Adaptability or versatility
If a large number of actuators are used to control deformation at multiple points, then the robot's ability to achieve desired trajectories is improved, but the number of degrees of freedom increases making control more difficult
Solution Approach 1:
The compliance matrix serves as a universal tool that simultaneously handles all actuator-effector relationships. A single pre-computed matrix encapsulates the mechanical coupling between all actuators and all effector points, allowing coordinated control of multiple degrees of freedom through unified linear algebra operations.
Data Source
Figure 1~2
Figure 3~4b
AI summary
The invention relates to a method for controlling a robot (1) defined by a node model and deformable by means of actuators (2). Effector points of the robot must follow a predetermined path. A matrix K defines a change in the inner forces of the robot in each node, on the basis of the change in position of the nodes. Said method includes: updating the K values on the basis of the current position of the nodes of the robot; determining the Jacobian matrix J of the vector δ (χ), x being a vector of the position of the nodes and the vector δ (χ) comprising respective lines which indicate the coordinates of the gaps between the position of each effector point and the predetermined path thereof, and the movement of each actuator; calculating the values of the matrix W = J. K-1 . JT; and solving the equation δ = W. λ + δ0 and controlling the robot on the basis of said resolution.