In this work, we present an observer and continuous controller for a multiple degree of freedom robotic plant without velocity measurement. For this considered plant, we propose and present an observer/controller that estimates or observes the velocity and drives the position tracking error to zero. We prove that the combined tracking error and observer error converges to zero globally exponentially and that all closed loop signals remain bounded. A contribution of the present paper, as compared to previous work for this same plant, can be deemed to be the globally-exponential convergence of the present paper versus the semi-globally exponential and globally asymptotic results of previous papers. To the best of our knowledge, the present paper is the first proven globally-exponential result for this plant and also the first global result for which the size of the control torque does not increase exponentially with respect to the size of the tracking error. The control torque is continuous; however, the time derivative of the velocity estimate is discontinuous but only at isolated time instants. No sliding modes are used.

This work considers the problem of maximum utilization of a set of mobile robots with limited sensor-range capabilities and limited travel distances. The robots are initially in random positions. A set of robots properly guards or covers a region if every point within the region is within the effective sensor range of at least one vehicle. We wish to move the vehicles into surveillance positions so as to guard or cover a region, while minimizing the maximum distance traveled by any vehicle. This problem can be formulated as an assignment problem, in which we must optimally decide which robot to assign to which slot of a desired matrix of grid points. The cost function is the maximum distance traveled by any robot. Assignment problems can be solved very efficiently. Solution times for one hundred robots took only seconds on a Silicon Graphics Crimson workstation. The initial positions of all the robots can be sampled by a central base station and their newly assigned positions communicated back to the robots. Alternatively, the robots can establish their own coordinate system with the origin fixed at one of the robots and orientation determined by the compass bearing of another robot relative to this robot. This paper presents example solutions to the multiple-target-multiple-agent scenario using a matching algorithm. Two separate cases with one hundred agents in each were analyzed using this method. We have found these mobile robot problems to be a very interesting application of network optimization methods, and we expect this to be a fiuitful area for future research.

SUMMARYThis work presents a method of "nding near global optima to minimum-time trajectory generation problems for systems that would be linear if it were not for the presence of Coulomb friction. The required "nal state of the system is assumed to be maintainable by the system, and the input bounds are assumed to be large enough so that the role of maintaining zero acceleration during "nite time intervals of zero velocity (the role of static friction) can always be assumed by the input. Other than the previous work for generating minimum-time trajectories for robotic manipulators for which the path in joint space is already speci"ed, this work represents, to the best of our knowledge, the "rst approach for generating near global optima for minimum-time problems involving a non-linear class of dynamic systems. The reason the optima generated are near global optima instead of exactly global optima is due to a discrete-time approximation of the system (which is usually used anyway to simulate such a system numerically). The method closely resembles previous methods for generating minimum-time trajectories for linear systems, where the core operation is the solution of a Phase I linear programming problem. For the non-linear systems considered herein, the core operation is instead the solution of a mixed integer linear programming problem.

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We present a simple modification of the iterative learning control algorithm of Arimoto et al. (1984) for the case where the inputs are bounded and time-rate-limited. The Jacobian error condition for monotonicity of input-error, rather than output-error, norms, is specified, the latter being insufficient to assure convergence, as proved herein. To the best of our knowledge, these facts have not been previously pointed out in the iterative learning control literature. We present a new proof that the modified controller produces monotonically decreasing input error norms, with a norm that covers the entire time interval of a learning trial.