Unified Feedback Linearization for Nonlinear Systems with Dexterous and Energy-Saving Modes

TL;DR

The paper tackles energy-aware control for high-input nonlinear systems, such as omnidirectional robots, by enabling two operation modes: an energy-saving mode that disables energy-intensive inputs and a dexterous mode that leverages all inputs for an auxiliary task. It introduces a unified feedback linearization controller that uses an exogenous switching signal $\sigma$ to switch modes while guaranteeing exponential stability of the main task independent of $\sigma$, and exponential stability of the auxiliary task when in dexterous mode. The key contributions are a rigorous construction of an invertible interaction matrix $\mathbf{A}_{\sigma}(\mathbf{x})$, a closed-form control law $\mathbf{u}=\mathbf{A}_{\sigma}(\mathbf{x})^{-1}[-\mathbf{b}(\mathbf{x})+\mathbf{v}_{\sigma}]$, and a design that decouples main-task dynamics from switching; these are demonstrated on a four-Mecanum-wheel robot with simulations showing efficient switching. This framework enables energy-efficient operation of high-dimensional, omnidirectional platforms with practical guidance for future robustness enhancement and experimental validation.

Abstract

Systems with a high number of inputs compared to the degrees of freedom (e.g. a mobile robot with Mecanum wheels) often have a minimal set of energy-efficient inputs needed to achieve a main task (e.g. position tracking) and a set of energy-intense inputs needed to achieve an additional auxiliary task (e.g. orientation tracking). This letter presents a unified control scheme, derived through feedback linearization, that can switch between two modes: an energy-saving mode, which tracks the main task using only the energy-efficient inputs while forcing the energy-intense inputs to zero, and a dexterous mode, which also uses the energy-intense inputs to track the auxiliary task as needed. The proposed control guarantees the exponential tracking of the main task and that the dynamics associated with the main task evolve independently of the a priori unknown switching signal. When the control is operating in dexterous mode, the exponential tracking of the auxiliary task is also guaranteed. Numerical simulations on an omnidirectional Mecanum wheel robot validate the effectiveness of the proposed approach and demonstrate the effect of the switching signal on the exponential tracking behavior of the main and auxiliary tasks.

Figures (6)

• Figure 1: A four Mecanum wheels omnidirectional vehicle. This system is capable of lateral movement (dexterous mode), but this comes at the cost of higher power consumption compared to the more efficient forward-only motion (energy-saving mode). The application of the generic nonlinear controller introduced in this work to this system ensures independent and decoupled exponential stabilization of the position output, along with either the orientation (in dexterous mode) or the lateral speed (in energy-saving mode), depending on the a priori unknown operation mode selected by an external source.
• Figure 2: The Proposed Control Architecture.
• Figure 3: Stroboscopic highlights of two simulations. In Simulation 1 (left), the robot converges to and follows a circular trajectory. In Simulation 2 (right), the robot converges to a straight-line trajectory while carrying a load (depicted in orange) and avoiding hanging obstacles (shown in red). The robot operates in dexterity mode only when necessary (as determined by the switching signal $\sigma$), prioritizing energy-saving mode when far from obstacles.
• Figure 4: Simulation 1. A circular input reference trajectory for the position of the CoM and a square form switching signal ${\sigma}$ are given to the control system. The gray areas correspond to $\sigma=0$ whereas the orange areas correspond to $\sigma=1$. The top row shows the output variables $\mathbf{y}_1,\mathbf{y}_2$, and the bottom row shows the sagittal velocity $v_1$, the third output $v_2$ and the control input $u_3$.
• Figure 5: Simulation 2. A ramp input reference trajectory with a square form switching signal $\sigma$ are given to the control system. The gray areas correspond to $\sigma=0$ whereas the orange areas correspond to $\sigma=1$. The top row shows the output variables $\mathbf{y}_1,\mathbf{y}_2$, and the bottom row shows the sagittal velocity $v_1$, the third output $v_2$ and the control input $u_3$.

Theorems & Definitions (6)

• Lemma 1
• proof
• Theorem 1
• proof
• Remark VI.1
• Remark VII.1