Robotic Arm Controller Singularity Mitigation

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Solution Overview

Problem

Robotic arm control systems face challenges in accurately positioning the end effector in task space due to singularities in the Jacobian matrix, leading to sudden changes in control torques that can excite vibrational modes and damage actuators.

Innovation Solution

A robotic arm controller that generates control parameters by perturbing joint angles to create distributed joint angles, minimizing an error function to smooth out control torque changes and maintain accurate positioning near singular configurations.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Reliability

If traditional Jacobian-based control is used near singular configurations, then the control system can compute control torques, but the control torques change sharply and suddenly causing vibrational modes and potential actuator damage

Engineering Contradiction:

Improvecontrol system stabilityVSAvoidsudden control torque changes

Core Design Contradiction:

ReliabilityVSObject-affected harmful factors

Solution Approach 1:

The method performs preliminary action by detecting potential singularities in advance and proactively adjusting the control parameters before the system reaches the singular configuration. By predicting the approach to singularity and pre-modifying the control torque computation, the system avoids the abrupt changes that would otherwise occur at the singularity boundary.

Inventive Principle:

Principle #10Preliminary action

Solution Approach 2:

The invention changes the control parameters by introducing a regularization term or modifying the Jacobian matrix computation to account for proximity to singular configurations. This parameter modification smooths the control torque transitions by adjusting the mathematical representation of the control law, preventing sharp changes while maintaining control accuracy.

Inventive Principle:

Principle #35Parameter changes

2Measurement precision

If the manipulator operates near singular configurations to achieve task space positioning, then the end effector can reach desired positions, but the control parameters change sharply causing vibrational modes

Engineering Contradiction:

Improveend effector positioning accuracyVSAvoidcontrol parameter smoothness

Core Design Contradiction:

Measurement precisionVSStability of the object's composition

Solution Approach 1:

The method implements feedback by continuously monitoring the manipulator's configuration and detecting proximity to singular configurations. This feedback mechanism triggers adaptive adjustments to the control parameters, creating a closed-loop system that maintains both positioning accuracy and control smoothness by responding to the system's real-time state.

Inventive Principle:

Principle #23Feedback

Solution Approach 2:

The invention applies dynamics by making the control parameters adaptive rather than static. The control law dynamically adjusts based on the manipulator's current configuration and velocity, allowing the system to maintain precision near singularities while smoothing out control torques through configuration-dependent parameter modification.

Inventive Principle:

Principle #15Dynamics

3Productivity

If conventional control methods are used to pass through singular configurations, then the manipulator can complete the task, but sudden control torque changes may damage joint actuators

Engineering Contradiction:

Improvetask completion capabilityVSAvoidactuator durability

Core Design Contradiction:

ProductivityVSStrength

Solution Approach 1:

The system performs preliminary action by detecting potential singularities in advance and proactively adjusting the control parameters before the system reaches the singular configuration. By predicting the approach to singularity and pre-modifying the control torque computation, the system avoids the abrupt changes that would otherwise occur at the singularity boundary.

Inventive Principle:

Principle #10Preliminary action

Solution Approach 2:

The method applies beforehand cushioning by introducing smoothing terms or regularization in the control law that act as a buffer against the abrupt torque changes at singularities. This cushioning effect protects the actuators from sudden load variations while allowing the manipulator to pass through singular configurations safely.

Inventive Principle:

Principle #11Beforehand cushioning (Prior cushioning)

Data Source

PatentUS10065312B1Unscented optimization and control allocation

Publication Date: 2018.09.04 THE GOVERNMENT OF THE UNITED STATES OF AMERICA AS REPRESENTED BY THE SECRETARY DEPARTMENT OF HEALTH & HUMAN SERVICES

AI summary

The disclosure provides a robotic arm controller which determines a control parameter for at least one actuator comprising the robotic arm using a control equation having the general form Ax=b, where A is a transformation matrix A based on the geometry and Jacobian of the robotic arm, x is the control parameter x such as a torque vector at a specific joint, and b is the end effector parameter b which specifies a desired corrective state of the end effector. The methodology, by way of constructing and solving an unscented optimization problem, provides a solution to the Ax=b problem by perturbing at least one joint angle appearing in the Jacobian to generate a plurality of distributed joint angles, determining a control parameter x which minimizes an error function. In a particular embodiment, the error function is sum of residual squares, and the appropriate control parameter x is determined by minimizing the error function subject to a series of constraints Aix−b−zi=0, where each constraint arises by virtue of the error generated through use of a given joint angle in the plurality of distributed joint angles selected.