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State Observer for Linear Systems with Explicit Constraints: Orthogonal Decomposition Method.

Sergei Savin¹, Oleg Balakhnov¹, Ramil Khusainov¹

¹Center for Technologies in Robotics and Mechatronics Components, Innopolis University, Innopolis 420500, Russia.

Sensors (Basel, Switzerland)

|September 28, 2021

Summary

This study introduces a novel state observer for constrained systems, improving robotic control. The method effectively handles explicit mechanical constraints in general linear systems.

Keywords:

dynamic output feedback explicit constraints state observer walking robots

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Area of Science:

Robotics
Control Theory
System Dynamics

Background:

State observers are crucial for dynamic state feedback control in robotic systems.
Existing observer designs for systems with explicit mechanical constraints are limited to special cases with restrictive assumptions.
A general framework for observer design in constrained systems is needed.

Purpose of the Study:

To propose an orthogonal decomposition-based state observer for general linear time-invariant systems with explicit constraints.
To develop a method that addresses the limitations of current observer designs for constrained mechanical systems.
To provide a unified framework for observer design applicable to a broader range of constrained systems.

Main Methods:

Utilizing orthogonal decomposition to identify lower-dimensional observable subspaces within the state space.
Formulating an observer design that leverages these subspaces for feedback and feed-forward control.
Demonstrating the recovery of minimal coordinates when sufficient for control law generation.
Retaining non-minimal coordinates when necessary for feed-forward control.

Main Results:

The proposed observer design framework is effective for general linear time-invariant systems with explicit constraints.
The method successfully balances the need for minimal and non-minimal coordinate representations based on control requirements.
The observer's performance was validated on complex robotic systems, including a flywheel inverted pendulum and a quadruped robot (Unitree A1).

Conclusions:

The developed orthogonal decomposition-based state observer provides a robust solution for systems with explicit constraints.
This framework advances the field of state estimation for constrained robotic systems, enabling more effective dynamic control.
The successful application to diverse robotic platforms highlights the generalizability and practical utility of the proposed method.