Xu Chu Ding

Multi-UAV Convoy Protection: An Optimal Approach to Path Planning and Coordination

In this paper, we study the problem of controlling a group of unmanned aerial vehicles (UAVs) to provide convoy protection to a group of ground vehicles. The UAVs are modeled as Dubins vehicles flying at a constant altitude with bounded turning radius. We first present time-optimal paths to provide convoy protection to stationary ground vehicles. Then, we propose a control strategy to provide convoy protection to ground vehicles moving in straight lines. The minimum number of UAVs required to provide perpetual convoy protection, in both cases, are derived.

On-Line Optimization of Switched-Mode Dynamical Systems

This paper considers an optimization problem in the setting of switched-mode hybrid dynamical systems, where the control variable (independent variable) consists of the mode-switching times, and the performance criterion is a cost functional defined on the systems state trajectory. The system is deterministic, nonlinear, and autonomous, and its state variable cannot be measured and hence it has to be estimated. We propose an on-line, Newton-like optimization algorithm that recomputes the control variable by attempting to optimize the cost-to-go at equally-spaced epochs. The main result concerns the algorithms convergence rate, which can vary from sublinear to quadratic depending on its computing rate and the state estimation error.

Executive decision support

One challenge facing coordination and deployment of unmanned aerial vehicles (UAVs) today is the amount of human involvement needed to carry out a successful mission. Currently, control and coordination of UAVs typically involves multiple operators to control a single agent. The aim of this article is to invert this relationship, enabling a single pilot to control and coordinate a group of UAVs. Furthermore, decision support is provided to the pilot to facilitate effective control of the UAV team. In the scenario envisioned in this article, the human operator (the pilot) is operating along-side a team of UAVs. The pilot communicates with the UAV team remotely and controls the UAV team to execute a surveillance mission.

Optimization of switched-mode systems with switching costs

This paper concerns the problem of optimizing switched-mode hybrid dynamical systems, where it is required to balance the tracking of a reference signal with an attempt to reduce a state-dependent cost-penalty associated with the switchings among the modes. We propose an algorithmic approach to the problem and we illustrate it on a specific example. The investigation has been motivated by design issues in power electronics, where it is desirable to regulate the load current in a switching circuit by controlling the state of a switch. On one hand tighter regulation requires switching at a higher frequency, and on the other hand each switching requires a certain amount of energy. Our algorithmic approach brings together various techniques that we recently have developed for optimizing hybrid systems, and its demonstrated application on a specific example suggests its potential viability in a broader array of problems in power electronics.

Design of optimal switching surfaces for switched autonomous systems

This paper presents a novel, computationally feasible procedure for computing optimal switching surfaces, i.e. optimal feedback controllers for switched autonomous nonlinear systems. Such systems are regulated by appropriately scheduling their operation modes over time. Given a finite mode sequence, the control task is to determine switching surfaces, which implicitly encode locally optimal switching times for a family of trajectories emerging from a pre-specified initial state set. Optimality of the switching times is assessed according to a nonlinear performance criterion.

Optimal multi-UAV convoy protection

In this paper, we study time-optimal trajectories for unmanned aerial vehicles (UAVs) to provide convoy protection to a group of stationary ground vehicles. The UAVs are modelled as Dubins vehicles flying at a constant altitude. Due to kinematic constraints of the UAVs, it is not possible for a single UAV to provide convoy protection indefinitely. In this paper, we derive time-optimal paths for a single UAV to provide continuous ground convoy protection for the longest possible time. Furthermore, this paper provides optimal trajectories for multiple UAVs to achieve uninterrupted convoy protection. The minimum number of UAVs required to achieve this task is determined.

On-line optimization of switched-mode systems: Algorithms and convergence properties

This paper concerns the problem of on-line (realtime) computation of solutions to the optimal switching time problem in hybrid systems. The systems under consideration are autonomous, and the performance measure to be optimized has the form of a cost functional defined on the state trajectory. The state variable cannot, however, be measured directly and it has to be estimated by a suitable observer. In this paper, we propose an on-line optimization algorithm based on the state observer, and derive bounds on its convergence rate.

Real-time optimal feedback control of switched autonomous systems

Abstract This paper presents a novel optimal adaptive feedback control concept for nonlinear switched autonomous systems. Our proposed controller implements a closed-loop switching law, which is represented by a parametrized switching plane in the state space. During the plant operation, the plane parameters are incrementally adapted to state measurements in real time by iteratively solving an associated nonlinear optimization problem over a finite time horizon. The combination of this control approach with ideas from model predictive control yields the so-called crawling window optimal control scheme that achieves the optimal stabilization of periodically operated switched systems.

An optimal timing approach to controlling multiple UAVs

In this paper we address the problem of having a single operator control a team of unmanned aerial vehicles (UAVs). This is achieved by having the team execute a leader-follower coordinated behavior, where the leader is responsible for the execution of the high-level mission. The operator interacts with the system by selecting a leader and a decision support mechanism is provided whereby the system computes the best choice of leader in the current situation. This feedback is obtained through a novel, receding horizon optimal timing control that computes an on-line estimate as to the relative merits of selecting different vehicles as leaders. The method is implemented in a dynamic, 3D simulation environment, illustrating the soundness of the proposed approach.

On-line adaptive optimal timing control of switched systems

In this paper we consider the problem of optimizing over the switching times for a multi-modal dynamic system when the complete cost-to-go is not available. The instantaneous cost is assumed to be unavailable before run-time, but can be measured in real time. Since the cost-to-go for optimization is time-varying, this problem falls under the category of on-line optimization of switched systems. The goal of the paper is to present an iterative process to update the switching times for the system in such a way that they remain optimal with respect to the changing cost-to-go function. It is shown that the information required to update the switching times is the ‘rate of change’ of the instantaneous cost, which is in the form of the partial derivative of the instantaneous cost function.