Event-Triggered Polynomial Control for Trajectory Tracking by Unicycle Robots

TL;DR

This work addresses resource-constrained trajectory tracking for unicycle robots by introducing Event-Triggered Polynomial Control (ETPC), where each control input between communication events is a degree-$p$ polynomial updated at event times. A finite-horizon, strictly convex optimization computes the polynomial coefficients to best approximate the continuous-time control signal, while a Lyapunov-based event rule ensures uniform ultimate boundedness of the tracking error and non-Zeno inter-event times. Theoretical guarantees accompany practical validation through simulations and real experiments, demonstrating substantially fewer events than time-triggered or ZOH-based ETC without sacrificing tracking accuracy. The approach enables time-varying actuator inputs with limited communication bandwidth, offering a scalable solution for resource-limited robotic networks and multi-robot coordination scenarios.

Abstract

This paper proposes an event-triggered polynomial control method for trajectory tracking by unicycle robots. In this method, each control input between two consecutive events is a polynomial and its coefficients are chosen to minimize the error in approximating a continuous-time control signal. We design an event-triggering rule that guarantees uniform ultimate boundedness of the tracking error and non-Zeno behavior of inter-event times. We illustrate our results through a suite of numerical simulations and experiments, which indicate that the number of events generated by the proposed controller is significantly less compared to that by a time-triggered controller or a event-triggered controller based on zero-order hold while guaranteeing similar tracking performance.

Figures (8)

• Figure 1: Event-triggered polynomial control configuration
• Figure 2: Reference trajectories under consideration a) Path $1$ , b) Path $2$, c) Path $3$, d) Path $4$
• Figure 3: Comparison of number of events for simulated paths for algorithms under consideration.
• Figure 4: UU bound for all simulated paths.
• Figure 5: Results of a simulation of robot tracking the reference trajectory that generates Path 3.

Theorems & Definitions (10)

• Remark 1
• Proposition 2
• proof
• Lemma 3
• proof
• Remark 4
• Lemma 5
• proof
• Theorem 6
• proof