This paper considers the problem of stabilizing a unicycle-type mobile robot using a time-invariant, discontinuous control law. In order to simplify the control design, most previous approaches neglect second-order system dynamics (compensating for them later using techniques such as partial feedback linearization). This paper shows that an approach based on invariant manifold theory can be extended to account for these dynamics. The performance of the resulting control law is demonstrated in simulation.
This paper considers the problem of controlling a group of microrobots that can move at different speeds but that must all move in the same direction. To simplify this problem, the movement direction is made a periodic function of time. Although the resulting control policy is suboptimal for an infinite-horizon quadratic cost, a bound is provided on how suboptimal it is. This bound is extended to show that, in theory, the design compromise making all robots move in the same direction only increases the expected cost by a factor of at most √ 2. Results are shown in simulation.
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