Simple Control Law for UAV Formation Flying

摘要

This paper presents a Lie group setting for the problem of control of formations as a natural outcome of the analysis of a planar two-vehicle formation control law. The vehicle trajectories are described using planar Frenet-Serret equations of motion, which capture the evolution of both the vehicle position and orientation for unit-speed motion subject to curvature (steering) control. The set of all possible equilibria for arbitrary G- invariant curvature controls is described (where G = SE(2) is a symmetry group for the control law). A generalization of the control law for n vehicles is presented, and the corresponding (relative) equilibria are characterized. Work is ongoing to discover stability and convergence results for the n-vehicle problem. The practical motivation for this work is the problem of formation control for meter-scale UAVs. An essential feature of the formation control problem for meter-scale UAVs is that autonomy is severely limited by cost and payload constraints. Consequently, The authors identify a few specific objectives, and attempt to formulate a control law to meet them: avoid collisions between UAVs, maintain the cohesiveness of the formation, be robust to loss of individuals, and scale favorably for large swarms. The challenge is that the physics of sensing, actuation, and communication cannot be neatly separated from the problem of coordination and control. Rather than simply extra payload, the automatic control system for formation control becomes an integral part of vehicle design. In section 2, they describe how an automatic control system for formation flying could be practically implemented. The basic idea involves providing a mechanism (based on radio-frequency pulses) by which each UAV can sense its range and relative orientation with respect to its neighbors. The hardware required for the controller on-board each UAV can, by incorporating analog VLSI circuitry, fit on a single small printed-circuit board.