Adaptive Multi-Robot Control with Minimized Accumulative Estimation Errors 12 views

This research solves two major control problems in the autonomous driving area based on the least-squares algorithm: discrete-time multi-input multi-output (MIMO) adaptive state tracking control problem for the vehicle position and velocity control application and the problem of using linear approximation models to approximate nonlinear functions for vehicle path planning applications. Due to our primary focus on the location and speed of vehicles, we simplify vehicles to robots in the control problems of this study. In the above two problems, adaptive control techniques are applied to deal with inevitable system uncertainties. The least-squares algorithms based adaptive laws for all the control problems are derived to minimize an accumulative estimation error, to ensure certain optimality for parameter estimation. For the first problem, the new adaptive state tracking schemes are based on a recently-developed new discrete-time error model which has been used for gradient algorithm based state tracking control schemes and use a least-squares algorithm for parameter adaptation. The new least-squares algorithm is derived to minimize an accumulative estimation error, to ensure certain optimality for parameter estimation. Different cases of interest are considered and the corresponding system stability and output tracking properties are studied. The developed control scheme is applied to a multiple-mobile-robot system to meet an adaptive state tracking objective. In addition, a collision avoidance mechanism is proposed to prevent collisions in the tracking process. The second problem is the main part of this research. Based on an existing optimal control algorithm for simplified multiple-mobile-vehicle (multiple-mobile-robot) systems, which computes the system optimal control input by maximizing a proposed nonlinear utility function, we develop a series of approximation models to express the nonlinear utility function linearly to transform the original complex nonlinear programming computation to simple linear programming computations for reducing the optimal control input computation time. Based on the Koopman operator, while operating on a set of observation functions of the state vector of a nonlinear system, produces a set of dynamic equations which, through a dynamic transformation, form a new dynamic system, we formulate a linear Koopman approximation model for the nonlinear function. Moreover, a bilinear Koopman approximation model is developed to improve the approximation precision based on the linear Koopman approximation model and Taylor expansion. Additionally, the decentralized bilinear Koopman approximation model is also finished to avoid the state explosion problem when a system contains too many agents in further autonomous driving applications. The least-squares algorithm is applied to unknown parameter estimation of all the Koopman approximation models. According to the simulation results, both the centralized and the decentralized bilinear approximation model based control designs are fast enough to ensure that robots arrive at their targets without collisions. To perfect the solution to the multi-robot optimal control problem, we have developed a fast network-based scheme to generate optimal control signals, which can further enhance the approximation-based control scheme.

PHD (Doctor of Philosophy)

Adaptive Control ; Least-squares; Koopman Operator ; Neural Networks; Multi-robot System; Optimal Control

English

All rights reserved by the author (no additional license for public reuse)

2025-12-10