Abstract
This paper studies formation keeping along with obstacle avoidance for second-order multi-agent systems. First, the flexible virtual structure (FVS) approach, used to model the communication topology between the agents of the formation, is recalled and relationship with graph theory-based communication exchange to achieve consensus is established. Second, using the regulation function (RF) which permits to change the behaviour of the system's solution without affecting convergence, obstacle avoidance is investigated for one agent (leader/co-leader) of the formation. Particularly, RF was used to ensure obstacle avoidance for first order agents and is extended in this work for second order agents. Relationship between the dynamic agent and a sliding surface with first order kinematics is established and condition on the sliding surface parameter is developed to ensure obstacle avoidance. Also, new shapes of the obstacle are considered namely square and rhombus. Finally, in order to perform a coordinated obstacle avoidance of a multi-agent system when only a subset of agents namely co-leaders, selected from the boarder, has obstacle information, one defines control laws which permit to control motions of the remaining formation agents.