Robotic Motion Model Control Under Uncertain Dynamics Constraints
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Existing model-based control methods for robotic systems face challenges due to uncertain motion models and changing dynamics, leading to suboptimal performance or instability, particularly when structural constraints are not incorporated into the learning process.
Innovation Solution
A probabilistic control approach using a Gaussian process modelled as a weighted combination of basis functions, with structural constraints applied to select basis functions, allowing for real-time estimation of the motion model and state distribution, incorporating process and measurement noise uncertainties.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If adaptive or learning-based MPC is used to estimate unknown parameters, then control performance is improved, but the method becomes insufficient when system dynamics are changing
Solution Approach 1:
The patent applies dynamics by making the basis functions time-varying, allowing them to adapt to changing system dynamics. The Gaussian process model uses time-varying basis functions that can capture non-stationary behavior, enabling the controller to adapt to changing dynamics rather than assuming static parameters.
Solution Approach 2:
The patent changes the parameter representation from fixed unknown parameters to time-varying Gaussian process parameters. By modeling parameters as Gaussian processes with time-varying basis functions, the system can continuously adapt to parameter changes while maintaining probabilistic constraints.
2Productivity
If structural constraints are not incorporated into the learning process, then learning efficiency is maintained, but the learned model may not satisfy physical constraints leading to instability
Solution Approach 1:
The patent applies preliminary action by pre-selecting basis functions that inherently satisfy structural constraints. By choosing basis functions with appropriate properties (e.g., positivity, monotonicity) before the learning process, the resulting model automatically satisfies physical constraints while maintaining learning efficiency.
Solution Approach 2:
The patent uses basis functions as an intermediary between the learning process and structural constraints. The basis functions act as a mediator that translates unconstrained Gaussian process learning into a constrained model that satisfies physical requirements, avoiding direct constraint enforcement during optimization.
3Measurement precision
If a probabilistic filter with Gaussian process is used to estimate motion model, then control accuracy under uncertainty is improved, but computational complexity increases
Solution Approach 1:
The patent applies segmentation by decomposing the Gaussian process into a weighted combination of time-varying basis functions. This segmentation transforms the complex infinite-dimensional GP estimation into a manageable finite-dimensional problem with a specific number of basis functions and weights, reducing computational burden while maintaining accuracy.
Solution Approach 2:
The patent changes the parameterization from general Gaussian process parameters to specific basis function weights. By representing the GP as a sum of predefined basis functions with time-varying weights, the computational complexity is reduced to estimating a finite number of weight parameters rather than full GP hyperparameters.
Data Source
AI summary
A probabilistic feedback controller for controlling an operation of a robotic system using a probabilistic filter subject to a structural constraint on an operation of the robotic system is configured to execute a probabilistic filter estimates a distribution of a current state of the robotic system given a previous state of the robotic system based on a motion model of the robotic system perturbed by stochastic process noise and a measurement model of the robotic system perturbed by stochastic measurement noise having an uncertainty modeled as a time-varying Gaussian process represented as a weighted combination of time-varying basis functions with weights defined by corresponding Gaussian distributions. The probabilistic filter recursively updates both the distribution of the current state of the robotic system and the Gaussian distributions of the weights of the basis functions selected to satisfy the structural constraint indicated by measurements of the state of a robotic system.