Online Trajectory Optimization Using Inexact Gradient Feedback for Time-Varying Environments

TL;DR

This paper introduces a novel online gradient ascent algorithm for trajectory optimization in time-varying environments with noisy feedback, providing theoretical regret bounds and demonstrating effectiveness in communication and maritime applications.

Contribution

It presents a new algorithm for online trajectory optimization under noisy gradient feedback with theoretical regret analysis and practical validation in communication and maritime scenarios.

Findings

Achieves sublinear regret relative to path variations and gradient errors.

Establishes a lower bound on offline dynamic regret.

Demonstrates effectiveness through simulations on real and synthetic data.

Abstract

This paper considers the problem of online trajectory design under time-varying environments. We formulate the general trajectory optimization problem within the framework of time-varying constrained convex optimization and proposed a novel version of the online gradient ascent algorithm for such problems. Moreover, the gradient feedback is noisy and allows us to use the proposed algorithm for a range of practical applications where it is difficult to acquire the true gradient. In contrast to the most available literature, we present the offline sublinear regret of the proposed algorithm up to the path length variations of the optimal offline solution, the cumulative gradient, and the error in the gradient variations. Furthermore, we establish a lower bound on the offline dynamic regret, which defines the optimality of any trajectory. To show the efficacy of the proposed algorithm, we consider two practical problems of interest. First, we consider a device to device (D2D) communications setting, and the goal is to design a user trajectory while maximizing its connectivity to the internet. The second problem is associated with the online planning of energy-efficient trajectories for unmanned surface vehicles (USV) under strong disturbances in ocean environments with both static and dynamic goal locations. The detailed simulation results demonstrate the significance of the proposed algorithm on synthetic and real data sets. Video on the real-world datasets can be found at {https://www.youtube.com/watch?v=FcRqqWtpf\_0}