A Framework for Optimized Topology Design and Leader Selection in Affine Formation Control

Abstract

This paper studies the problem of topology design and leader selection to activate affine formation control schemes. The <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">affine formation control</i> enjoys a distinguishing feature from other control methods in that the whole formation can be dynamically maneuvered by controlling a small number of agents called leaders. This relies on the stress matrix which defines the inter-agent communication/sensing topology determining the dynamic performance for an autonomous system. In the first step, a topology design algorithm based on <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">mixed integer semi-definite programming</i> (MISDP) is proposed to obtain the stress matrix with low communication cost, fast convergence speed and high tolerance to time-delay. Secondly, the proposed leader selection algorithm focuses on two objectives of practical significance: convergence speed and control energy, which are tailored to two optimization problems based on MISDP. At last, the collective agents are driven to the target formation via their local interactions and leaders’ external control inputs. The effectiveness of the overall framework is validated by both simulations and physical experiments.