Robot Control Under Disturbance Mismatch Using KL-Robust Risk Sensitivity
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Solution Overview
Problem
Existing robot control methods face challenges in accurately modeling stochastic disturbances, leading to model mismatch issues, especially in real-time applications, where limited knowledge of the system and computational intensity hinder effective control and decision-making under uncertainty.
Innovation Solution
The implementation of a system that uses an iterative Linear-Exponential-Quadratic-Gaussian (iLEQG) algorithm and cross-entropy process to solve a bilevel optimization problem, adjusting the risk-sensitivity parameter dynamically based on the Kullback-Leibler divergence bound between modeled and actual probability distributions, enabling distributionally robust control for nonlinear systems.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If a complicated stochastic phenomenon is perfectly modeled, then measurement precision is improved, but device complexity increases
Solution Approach 1:
The patent transforms the complex stochastic control problem into a more tractable form by changing the parameter representation. Specifically, it uses a bilevel optimization framework where the inner level solves a stochastic optimal control problem with a simplified Gaussian model, while the outer level adjusts risk-sensitivity parameters to account for distributional uncertainty. This parameter transformation allows accurate representation of complex phenomena without requiring complex models at the operational level.
Solution Approach 2:
The patent introduces an intermediary bilevel optimization framework that mediates between the simplified Gaussian model and the unknown actual distribution. The risk-sensitivity parameters act as intermediaries that translate the effects of distributional uncertainty into adjustments of the control policy, avoiding the need to directly model the complex stochastic phenomenon while still accounting for its effects.
2Ease of operation
If model-based stochastic control methods use Gaussian noise assumption, then ease of operation is improved, but manufacturing precision deteriorates
Solution Approach 1:
The patent maintains computational tractability by assuming Gaussian noise in the inner optimization level, but compensates for the simplification by introducing risk-sensitivity parameters in the outer optimization level. These parameters adjust the control policy to account for potential deviations from the Gaussian assumption, thereby maintaining control accuracy without sacrificing computational ease.
Solution Approach 2:
The patent prepares for potential model inaccuracies by incorporating risk-sensitivity parameters beforehand in the bilevel framework. This allows the system to cushion against the effects of Gaussian assumption limitations by adjusting the control policy in advance based on the KL divergence bound, ensuring robust performance even when the simplified model does not perfectly match reality.
3Measurement precision
If computationally intensive sampling methods are used, then measurement precision is improved, but productivity deteriorates
Solution Approach 1:
The patent changes the approach from direct sampling to parameter optimization. Instead of using computationally intensive sampling to characterize distributions, it formulates the problem as a bilevel optimization where the inner level uses efficient Gaussian-based methods and the outer level optimizes risk-sensitivity parameters. This parameter-based approach achieves accurate distributional robustness without the computational burden of sampling.
Solution Approach 2:
The patent replaces the mechanical sampling process with an optimization-based approach. Rather than physically or computationally generating samples to characterize distributions, it substitutes this with a mathematical optimization framework that directly computes robust control policies by adjusting risk-sensitivity parameters, dramatically reducing computational requirements for real-time control.
4Device complexity
If limited knowledge of the system is used, then device complexity is reduced, but reliability deteriorates
Solution Approach 1:
The patent compensates for limited system knowledge by introducing risk-sensitivity parameters that adjust the control policy based on the KL divergence bound between the modeled and actual distributions. This parameter adjustment mechanism allows the simple Gaussian model to produce reliable control by accounting for uncertainty in the underlying system characteristics.
Solution Approach 2:
The patent prepares for potential model inaccuracies due to limited system knowledge by incorporating robustness considerations beforehand through the bilevel optimization framework. The risk-sensitivity parameters are designed to cushion against the effects of model mismatch, ensuring reliable control performance even when the simple Gaussian model does not perfectly capture the true system behavior.
Data Source
AI summary
Systems and methods described herein relate to controlling a robot. One embodiment receives an initial state of the robot, an initial nominal control trajectory of the robot, and a Kullback-Leibler (KL) divergence bound between a modeled probability distribution for a stochastic disturbance and an unknown actual probability distribution for the stochastic disturbance; solves a bilevel optimization problem subject to the modeled probability distribution and the KL divergence bound using an iterative Linear-Exponential-Quadratic-Gaussian (iLEQG) algorithm and a cross-entropy process, the iLEQG algorithm outputting an updated nominal control trajectory, the cross-entropy process outputting a risk-sensitivity parameter; and controls operation of the robot based, at least in part, on the updated nominal control trajectory and the risk-sensitivity parameter.