Single And Multiple Robot Control: A Geometric Approach

This report presents an approach to the control of single and multiple robot systems based on basic geometry properties of Hilbert spaces. For single robots, the control problem is defined in terms of the convergence between the set of feasible velocities, defined by the robot kinematics, and the set of goal velocities, defined by the mission specification and the sensor data acquired along the mission. Basis concepts of the geometry of Hilbert spaces are used to derive conditions on the convergence between these sets. The motion behavior of robot teams is classified, according to the robot neighboring relationships, into formation and free motions. The control of a team extends the results for single robots by constraining the set of goal velocities to account for the neighboring relationships among teammates. Each robot monitors these relationships for relevant changes that are mapped into an event set. A finite state automaton is used to map the event set into a set of motion strategies. The report presents simulation results on both single and multiple robot control using 2D holonomic, cart and car robots.

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