Passivity-Based Pose Synchronization in Three Dimensions

• Published in: IEEE transactions on automatic control Vol. 57; no. 2; pp. 360 - 375
• Main Authors: Hatanaka, T., Igarashi, Y., Fujita, M., Spong, M. W.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.02.2012; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Adaptative systems; Applied sciences; Computer science; control theory; systems; Control theory. Systems; Convergence; Cooperative control; Delay; Exact sciences and technology; Fundamental areas of phenomenology (including applications); Interconnection; Kinematics; Law; passivity-based control; Physics; Robotics; Solid dynamics (ballistics, collision, multibody system, stabilization...); Solid mechanics; Switches; Symmetric matrices; Synchronism; Synchronization; Three dimensional; Topology; Euclidean geometry; Computer simulation; Cooperative control; Solid dynamic; Passive system; Topology; Synchronization; Adaptive control; Passivity; Transmission time; Hamiltonian graph; Symmetry group; Multiagent system; Graph connectivity; Cooperation; passivity-based control; Distributed control; Convergence rate; Numerical simulation; Motion control; Collision avoidance; Formation; Numerical convergence
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2011.2166668

This paper addresses passivity-based pose synchronization in the Special Euclidean group SE (3) . We first develop a passivity-based distributed velocity input law to achieve pose synchronization. We next show that the pose synchronizes exponentially fast under an assumption on the initial states of the bodies, with an exponential convergence rate given by algebraic connectivity of interconnection graphs. We also prove pose synchronization in the presence of communication delays and topology switches. We moreover give further extensions of the present law, where desirable velocities and collision avoidance are taken into account. Finally, the effectiveness of the present inputs is demonstrated through numerical simulations and experiments on a planar (2D) test bed.