Neural Controller Synthesis for Underactuated Robotic Manipulators
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Solution Overview
Problem
Designing a stabilizing controller for underactuated robotic manipulators is challenging due to their nonlinear dynamics, as existing methods like IDA-PBC require tedious analytical solutions to partial differential equations, which are impracticable for some systems.
Innovation Solution
A machine learning-based model using neural networks approximates functions for underactuated controllers, learning parameters through a loss function that satisfies conditions for structure preservation, integrability, and equilibrium assignment, enabling the solution of complex PDEs for generic systems.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If IDA-PBC method is used to design controller, then stabilization of underactuated systems is achieved, but the design procedure becomes conceptually complex requiring solution of partial differential equations
Solution Approach 1:
The patent replaces the traditional analytical mathematical approach (solving partial differential equations) with a machine learning-based neural network system. The neural networks learn to approximate the controller parameters directly from system states, substituting the complex analytical mechanics-based IDA-PBC design procedure with a data-driven approach that achieves the same stabilization goal without requiring explicit PDE solutions.
Solution Approach 2:
The patent transforms the controller design from solving for fixed analytical expressions to learning parameterized functions through neural networks. By representing controller parameters as learnable functions of system states rather than fixed analytical solutions, the method changes the parameter representation from symbolic mathematics to numerical approximations that can be optimized through training.
2Measurement precision
If traditional analytical methods are used, then exact solutions can be obtained, but the method becomes impracticable for some underactuated systems
Solution Approach 1:
The patent substitutes the analytical solution method with a numerical learning-based approach. Instead of requiring closed-form mathematical solutions that may not exist for complex underactuated systems, neural networks provide numerical approximations that are computationally tractable and applicable to a broader range of systems, trading exact analytical precision for practical implementability.
Solution Approach 2:
The patent introduces neural networks as an intermediary between the system dynamics and the controller. Rather than directly solving the complex relationships between system states and control inputs through analytical methods, the neural network serves as a learned mediator that maps states to control actions, making the control design feasible for systems where direct analytical solutions are impracticable.
Data Source
AI summary
A computer-implemented system and method for synthesizing a controller for an under actuated robotic manipulator includes a machine learning based model having a plurality of neural network modules. Each module is configured to approximate a function related to an underactuated controller for a robotic manipulator. Parameters of each function are learned during training of the model using a loss function that satisfies one or more conditions including structure preservation, integrability and equilibrium assignment.