Nonlinear Robot Impedance Control via Sigmoid Transformation
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Solution Overview
Problem
Existing impedance control methods for robots face challenges in stability verification and practical implementation, particularly when dealing with large forces and virtual displacements, leading to potential damage to workpieces and instability issues.
Innovation Solution
A robot controller system that performs nonlinear impedance control by using a force control unit with an impedance processor and a nonlinear converter, allowing for filter processing on output or input values to manage displacement changes and verify stability through digital filters.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Force
If large virtual displacement is specified in linear impedance control to generate large force, then large force can be produced, but the manipulator produces very large movement when external force disappears, causing safety problems
Solution Approach 1:
The patent applies parameter changes by transitioning from linear impedance control to nonlinear impedance control. Specifically, it uses a nonlinear function (sigmoid function) to transform the relationship between virtual displacement and force, changing the control parameters from linear to nonlinear characteristics. This allows the system to generate large forces when needed while limiting the manipulator's movement range, thus resolving the contradiction between force generation and safety.
2Force
If large virtual displacement is specified in linear impedance control, then large force can be produced, but the workpiece may be broken by the produced force
Solution Approach 1:
The patent uses parameter changes by implementing nonlinear impedance control through a sigmoid function transformation. This nonlinear transformation modifies the force-displacement relationship to produce large forces only when necessary, while automatically limiting the force magnitude to prevent workpiece damage. The parameter transformation ensures force is applied within safe boundaries for the workpiece.
3Adaptability or versatility
If nonlinear impedance control is implemented by using a nonlinear function, then force control capability is improved, but it becomes very difficult to determine whether the equation of motion is stable
Solution Approach 1:
The patent introduces an intermediary approach by using a sigmoid function as a transformation mediator. This function serves as a bridge between linear and fully nonlinear control, providing a smooth nonlinear transformation that maintains mathematical tractability. The sigmoid function's well-defined properties allow for stability analysis while still achieving the desired nonlinear force control characteristics, thus resolving the contradiction between control capability and stability verification.
4Reliability
If sliding mode control with multiple control mechanisms and switching is used to ensure stability, then control stability is improved, but the system becomes difficult to design and not suitable for practical use
Solution Approach 1:
The patent extracts the essential stability-guaranteeing feature from sliding mode control while removing its complexity. Instead of implementing multiple switching control mechanisms and hyperplane definitions, it uses a single nonlinear transformation (sigmoid function) that inherently provides stable behavior. This extraction approach maintains the stability benefit while eliminating the design complexity, making the system suitable for practical use.
Data Source
AI summary
A robot controller includes a force control unit that outputs a correction value of a target track of a robot based on a detected sensor value acquired from a force sensor, a target value output unit that obtains a target value by performing correction processing on the target track based on the correction value and outputs the obtained target value, and a robot control unit that performs feedback control of the robot based on the target value. The force control unit includes an impedance processor that obtains a solution of a differential equation in force control as the correction value before the conversion processing, and a nonlinear convertor that obtains the correction value after the conversion processing by performing nonlinear conversion processing on the correction value before the conversion processing acquired from the impedance processor and outputs the obtained correction value after the conversion processing.