Robot Impedance Control Through Kinematic Singularities
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Solution Overview
Problem
Conventional robots face challenges in performing complex dynamic interactions and tasks involving kinematic singularities due to numerical instability, limiting their ability to operate like humans who seamlessly transition through such configurations with ease.
Innovation Solution
The implementation of compositional impedance control methods that allow for the superposition of mechanical impedances, enabling robots to operate stably at singular configurations by managing redundancy and controlling closed kinematic chains, thereby reducing actuator effort and improving efficiency.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If conventional kinematic inversion methods are used to manage redundancy, then robot control is straightforward in normal configurations, but numerical instability occurs at or near singular configurations
Solution Approach 1:
The patent transforms the control approach by changing the mathematical parameters from kinematic inversion to impedance control in task space. Instead of inverting the Jacobian matrix to resolve redundancy, the system uses impedance parameters (stiffness, damping, mass) that can be directly applied without inversion, eliminating numerical instability at singularities while maintaining control authority throughout the full operational range
Solution Approach 2:
The patent replaces the conventional kinematic control system with an impedance-based control system. Rather than using kinematic inversion to manage redundant degrees of freedom, the system substitutes a dynamic model that operates in task space, allowing robots to pass through singular configurations smoothly while maintaining desired mechanical behavior through impedance shaping
2Ease of operation
If superposition of impedance controllers is used for redundancy management, then smooth operation at singular configurations is achieved, but interference between different impedance components may occur
Solution Approach 1:
The patent segments the impedance control into distinct task-specific components, each addressing a specific aspect of the manipulation task. By decomposing the overall impedance into separate controllable elements (position stiffness, orientation stiffness, damping terms), the system allows independent tuning of each component to prevent interference while maintaining smooth operation through singularities
Solution Approach 2:
The patent introduces task-space impedance as an intermediary layer between the robot's redundant degrees of freedom and the desired task execution. This intermediary impedance model mediates between multiple control objectives, allowing smooth transitions through singularities while preventing interference between different impedance components through proper task-space formulation
3Reliability
If conventional robots avoid singular configurations, then numerical stability is maintained, but task versatility and human-like performance are limited
Solution Approach 1:
The patent fundamentally changes the control parameters from joint-space kinematic inversion to task-space impedance control. This parameter transformation allows the robot to operate stably at singular configurations by using impedance parameters that do not require Jacobian inversion, thereby expanding the operational range to include previously avoided singular regions while maintaining control stability
Solution Approach 2:
The patent introduces dynamic impedance control that adapts the robot's mechanical properties (stiffness, damping, mass) in real-time based on task requirements. This dynamic approach allows the robot to exploit singular configurations for beneficial effects such as reduced actuator effort while maintaining stability and versatility across the full workspace, including previously avoided singular regions
Data Source
AI summary
According to some embodiments, a method includes: receiving an endpoint impedance matrix representing a desired stiffness or damping at the robot endpoint; reflecting the endpoint impedance matrix to an equivalent joint-space matrix associated with one or more of the robot joints, the equivalent joint-space matrix having a nullspace corresponding to near-zero-valued eigenvalues; generating a nullspace-filled impedance matrix from the equivalent joint-space matrix based in part on replacing the near-zero-valued eigenvalues with selected finite positive real values; generating a robot control law using the nullspace-filled impedance matrix; and using the robot control law to control the robot.