Constructive Method for Safe Multirate Controllers for Differentially-Flat Systems

核心概念

Constructive method for designing multirate controllers for safety-critical nonlinear systems leveraging differential flatness.

摘要

Introduction

Control of nonlinear systems in constrained environments is challenging.
Multirate controllers combine planning and tracking for safety.

Differential Flatness

Systems like unicycles possess differential flatness.
Differential flatness allows for constructive controller design.

Controller Construction

High-level planner uses linear MPC for reference trajectories.
Low-level tracker ensures tracking within a safe set.

Main Result

The multirate controller is recursively feasible and ensures safety.
The controller provides formal guarantees on feasibility and safety.

Experimental Results

Simulations and experiments demonstrate the effectiveness of the controller.
Real-time implementation on ground rover and quadruped robots.

Conclusion

Constructive method for designing multirate controllers for safety-critical systems.
The controller provides formal guarantees on feasibility and safety.

統計資料

The reference trajectory is recomputed every T seconds.
The low-level controllers run at 300 Hz for the rover and 20 Hz for the quadruped.

引述

"The proposed controller differs from other planner-tracker controllers since the two levels are coupled through D."
"Our method enables safe navigation despite the presence of modeling error arising due to the robots’ actuators."

從以下內容提煉的關鍵洞見

A Constructive Method for Designing Safe Multirate Controllers for Differentially-Flat Systems

by Devansh R. A... 於 arxiv.org 03-28-2024

https://arxiv.org/pdf/2403.18015.pdf

深入探究

How can the controller handle input constraints effectively

The controller can effectively handle input constraints by incorporating them into the design of the tracking controller and the high-level planner. In the tracking controller, the input constraints can be enforced by appropriately choosing the feedback law and designing the Lyapunov function to ensure stability and robustness in the presence of constraints. Additionally, in the high-level planner, the Finite Time Optimal Control Problem (FTOCP) can be formulated to account for input constraints by including them as constraints in the optimization problem. By optimizing over a sequence of flat states and control inputs subject to these constraints, the controller can ensure that the system operates within the specified limits while achieving the desired objectives.

Does the method have limitations in terms of system complexity

While the method presented in the context is powerful and provides formal guarantees on safety and feasibility for differentially-flat systems, it may have limitations in terms of system complexity. As the complexity of the system increases, the computational burden of solving the optimization problems involved in the controller design may also increase. This could potentially lead to longer computation times, making real-time implementation challenging for highly complex systems. Additionally, the method's reliance on differential flatness properties may limit its applicability to systems that do not exhibit these characteristics, requiring alternative control strategies for non-flat systems.

How can the concept of differential flatness be applied to other types of systems

The concept of differential flatness can be applied to a wide range of systems beyond the examples mentioned in the context, such as robotic manipulators, aerospace vehicles, and chemical processes. By identifying systems that possess differential flatness properties, it becomes possible to leverage these properties for trajectory planning, tracking, and control design. For instance, in robotic manipulators, differential flatness can be utilized to generate smooth and dynamically feasible trajectories for end-effector motion. In aerospace vehicles, differential flatness can aid in designing control strategies for optimal path planning and trajectory tracking. Overall, differential flatness provides a powerful framework for system analysis and control design across various domains.