OPTIMAL LEADER-FOLLOWER FORMATION CONTROL USING DYNAMIC GAMES

Formation control is one of the salient features of multi-agent robotics. The main goal of this field is to develop distributed control methods for interconnected multi-robot systems so that robots will move with respect to each other in order to keep a formation throughout their joint mission. Numerous advantages and vast engineering applications have drawn a great deal of attention to the research in this field. Dynamic game theory is a powerful method to study dynamic interactions among intelligent, rational, and self-interested agents. Differential game is among the most important sub-classes of dynamic games, because many important problems in engineering can be modeled as differential games. The underlying goal of this research is to develop a reliable formation control algorithm for multi-robot systems based on differential games. The main idea is to benefit from powerful machinery provided by dynamic games, and design an improved formation control scheme with careful attention to practical control design requirements, namely state feedback, and computation costs associated to implementation. In this work, results from algebraic graph theory is used to develop a quasi-static optimal control for heterogeneous leader{follower formation problem. The simulations are provided to study capabilities as well as limitations associated to this approach. Based on the obtained results, a finite horizon open-loop Nash differential game is developed as adaptation of differential games methodology to formation control problems in multi-robot systems. The practical control design requirements dictate state-feedback; therefore, proposed controller is complimented by adding receding horizon approach to its algorithm. It leads to a closed loop state-feedback formation control. The simulation results are presented to show the effectiveness of proposed control scheme

Optimal Control of Two-Wheeled Mobile Robots for Patrolling Operations

Optimal Control of Two-Wheeled Mobile Robots for Patrolling Operations Walaaeldin Ahmed Ghadiry, Concordia University, 2015 This work studies the use of the two-wheeled mobile robots in patrolling operations, and provides the most distance-e�cient as well as time-e�cient trajectories to patrol a given area. Novel formulations in the context of constrained optimization are introduced which can be solved using existing software. The main concept of the problem is directly related to the well-known Traveling Salesman Problem (TSP) and its variants, where a salesman starts from a base city and visits a number of other cities with minimum travel distance while satisfying the constraint that each city has to be visited only once. Finally, the salesman returns back to the starting base city after completing the mission. Two di�erent patrolling con�gurations that are related to the TSP and its variants, namely the Single Depot multiple Traveling Salesman Problem (mTSP) and the Multidepot multiple Traveling Salesman Problem (MmTSP) are investigated. Novel algorithms are introduced for the trajectory planning of multiple two-wheeled mobile robots, either with two di�erential motors (which can turn on the spot) or with Dubins-like vehicles. The output trajectories for both types of wheeled robots are investigated by using a model predictive control scheme to ensure their kinematic feasibility for the best monitoring performance. The proposed formulations and algorithms are veri�ed by a series of simulations using e�cient programming and optimization software as well as experimental tests in the lab environment