Control of many robots moving in the same direction with different speeds: A decoupling approach

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 radic2. Results are shown in simulation.