Implicit Trajectory Planning for Feedback Linearizable Systems: A Time-varying Optimization Approach

TL;DR

This paper introduces a real-time trajectory planning and control framework for feedback-linearizable systems using a time-varying optimization approach, ensuring feasible trajectories that converge to optimal targets.

Contribution

It presents a novel optimization-based control law that transforms nonlinear systems into high-order optimization algorithms with proven exponential convergence.

Findings

Effective multi-agent tracking demonstrated

Feasible trajectories converge to optimal solutions

Global exponential convergence proved

Abstract

We develop an optimization-based framework for joint real-time trajectory planning and feedback control of feedback-linearizable systems. To achieve this goal, we define a target trajectory as the optimal solution of a time-varying optimization problem. In general, however, such trajectory may not be feasible due to , e.g., nonholonomic constraints. To solve this problem, we design a control law that generates feasible trajectories that asymptotically converge to the target trajectory. More precisely, for systems that are (dynamic) full-state linearizable, the proposed control law implicitly transforms the nonlinear system into an optimization algorithm of sufficiently high order. We prove global exponential convergence to the target trajectory for both the optimization algorithm and the original system. We illustrate the effectiveness of our proposed method on multi-target or multi-agent tracking problems with constraints.