Reference Trajectory Control With Learned Uncertain Dynamics
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Solution Overview
Problem
Real-world systems like autonomous vehicles and robotics face challenges in maintaining stable control due to uncertainties in dynamics, such as non-stationarity and uncalibrated sensors, making it difficult to design controllers that track reference trajectories with low error.
Innovation Solution
The system separates dynamics into known and unknown parts, using a combination of feedforward, feedback, and robust controllers to track reference trajectories with decaying bounded error, while learning the unknown dynamics using probabilistic distributions updated by Gaussian processes or deep neural networks.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If reinforcement learning algorithms are used to design a controller for tracking the desired reference profile, then the controller can adapt to uncertainties in system dynamics, but the tracking error becomes unbounded and successful operation is not guaranteed
Solution Approach 1:
The controller is segmented into two distinct components: a robust controller that guarantees bounded tracking error and stability, and a learning algorithm that adapts to uncertainties. This segmentation allows each component to specialize in its strength without compromising the other.
Solution Approach 2:
A projection operator serves as an intermediary mechanism that constrains the learning algorithm's updates to maintain stability. The projection operator ensures that learned parameters remain within bounds that guarantee bounded tracking error, acting as a mediator between adaptation and reliability.
2Reliability
If robust control methods are used to achieve stable control in presence of uncertainties, then the tracking error remains bounded, but the controller becomes suboptimal due to worst-case scenario design
Solution Approach 1:
The robust controller is designed first to establish guaranteed bounded tracking error and stability. Then, the learning algorithm performs preliminary adaptation to improve performance. This sequence allows the system to first ensure reliability, then optimize productivity.
Solution Approach 2:
The learning algorithm continuously adapts the controller parameters based on tracking performance feedback, allowing the system to move from worst-case robust control to optimized performance while maintaining bounded error guarantees through the projection operator.
3Measurement precision
If the dynamics of the system are fully modeled to improve control accuracy, then the controller can achieve better tracking performance, but the complexity of the model increases and becomes difficult to update
Solution Approach 1:
Instead of fully modeling all system dynamics, the approach uses a partial model captured by the robust controller for stability, and allows the learning algorithm to adaptively learn the remaining uncertainties. This partial action reduces model complexity while maintaining control accuracy.
Solution Approach 2:
The learning algorithm performs self-service by automatically adapting to system uncertainties without requiring manual model updates. The system learns and adjusts to changes in dynamics autonomously, reducing the complexity burden on the controller design.
Data Source
AI summary
A system for performing a task according to a reference trajectory is provided. The system includes at least one actuator configured to change a state of the system according to a control input, and a memory configured to store a model of dynamics of the system including a known part of the dynamics of the system as a function of the state of the system and the control input to the system and an unknown part of the dynamics of the system as a function of the state of the system, wherein the unknown part of the dynamics of the system is represented by parameters of a probabilistic distribution including a first-order moment and a second-order moment of the probabilistic distribution. The system also includes a control system configured to recursively determine and submit the control input to the actuator to change the state of the system.