In this paper we propose two open-loop control schemes for planning feasible paths for a mobile robot with trailers. Both methods use sinusoidal inputs. The first method uses sinusoids at integrally related frequencies for systems in so-called chained form This method is simple, however, it only applies to mobile robots with one trailer and it makes no provision for obstacle avoidance. The second method is very general in that it can be applied to systems which may not be convertible to chained form. An initial path through the state space is generated using well-known techniques from the literature (this path can be chosen to avoid obstacles if desired), then a feasible path is constructed which follows this nominal path arbitrarily closely. This method, however, uses inputs of arbitrarily high amplitude and high frequency. We study the connections between the two methods. We also discuss the importance of coordinates, since the first of our methods will only work on systems that can be put into "chained" coordinates, and the tracking equations are expressed. We show that our system can be converted into an approximate chained form, and that the asymptotic sinusoids method works better in these coordinates. Finally, simulation results for a mobile robot with two trailers are presented.




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