Cable Joint Simulation for Robot Dynamics
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Solution Overview
Problem
Simulating cable-driven systems, such as robots and machines, is challenging due to the difficulty in enforcing inextensibility constraints and handling large mass ratios between small cable segments and larger objects, leading to inefficiencies in existing simulation methods.
Innovation Solution
The approach simulates cable-driven systems by grouping cable segments into portions that directly connect objects, modeling each portion as a 'cable joint' with dynamic attachment points and length limits, reducing complexity and improving robustness and speed by focusing on the effect of cables on connected objects rather than simulating each segment individually.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If cables are modeled as a large number of small segments connected via joints, then the simulation can capture detailed cable behavior, but the computational complexity and difficulty of handling large mass ratios increase significantly
Solution Approach 1:
The patent applies segmentation by dividing the cable into a finite number of segments that are connected via joints. Each segment is modeled with specific properties (mass, length, damping) allowing the cable to be represented as a discrete chain of elements rather than a continuous structure, balancing detail with computational feasibility
Solution Approach 2:
The patent merges the simulation of cable segments with the simulation of connected objects by using a unified constraint-based approach. The cable segments and object dynamics are solved together through constraint satisfaction, reducing the need for separate simulation loops and improving computational efficiency
2Measurement precision
If cables are modeled as a large number of small segments, then detailed cable dynamics can be captured, but the inextensibility constraint becomes difficult to satisfy
Solution Approach 1:
The patent applies preliminary action by pre-calculating constraint violations and applying corrective forces at each simulation step. The inextensibility constraint is enforced by detecting potential violations before they occur and applying preemptive correction forces to maintain cable length constraints
Solution Approach 2:
The patent implements feedback through an iterative constraint satisfaction process where constraint violations are detected, correction forces are applied, and the system state is updated. This closed-loop approach continuously monitors and corrects cable segment lengths to maintain inextensibility
3Measurement precision
If each cable segment is simulated individually, then detailed cable behavior is achieved, but the simulation speed decreases
Solution Approach 1:
The patent segments the cable into a finite number of manageable elements with defined properties, allowing parallel computation of segment dynamics while maintaining overall cable behavior accuracy
Solution Approach 2:
The patent uses partial action by selectively simulating only the cable segments that are currently under tension or actively contributing to the system dynamics. Inactive or slack segments are simplified or excluded from detailed computation, reducing overall computational load
Data Source
AI summary
A cable driving a large system such as cable driven machines, cable cars or tendons in a human or robot is typically modeled as a large number of small segments that are connected via joints. The two main difficulties with this model are satisfying the inextensibility constraint and handling the typically large mass ratio between the segments and the objects they connect. This disclosure introduces an effective approach to solving these problems. The introduced approach simulates the effect of a cable using a new type of distance constraint called ‘cable joint’ that changes both its attachment points and its rest length dynamically. The introduced approach models a cable connecting a series of objects, e.g., components of a robot, as a sequence of cable joints, reducing the complexity of the simulation from the order of the number of segments in the cable to the number of connected objects.