Abstract

A skid-steer rover’s power consumption is highly dependent on the turning radius of its path. For example, a point turn consumes a lot of power compared to a straight-line motion. Thus, in path planning for this kind of rover, turning radius is a factor that should be considered explicitly.
Based on the literature, there is a lack of analytical approach for finding energy-optimal paths for skid-steer rovers. This thesis addresses this problem for such rovers, specifically on obstacle-free hard ground. The equivalency theorem in this thesis indicates that, when using a popular power model for skid-steer rovers on hard ground, all minimum-energy solutions follow the same path irrespective of velocity constraints that may or may not be imposed. This non-intuitive result stems from the fact that with this model of the system the total energy is fully parametrized by the geometry of the path alone. It is shown that one can choose velocity constraints to enforce constant power consumption, thus transforming the energy-optimal problem to an equivalent time-optimal problem. Existing theory, built upon the basis of Pontryagin’s minimum principle to find the extremals for time-optimal trajectories for a rigid body, can then be used to solve the problem. Accordingly, the extremal paths are obtained for the energy-efficient path planning problem. As there is a finite number of extremals, they are enumerated to find the minimum-energy path for a particular example.
Moreover, the analysis identifies that the turns in optimal paths (aside from a small number of special cases called whirls) are to be circular arcs of a particular turning radius, R′, equal to half of a skid-steer rover’s slip track. R′ is the turning radius at which the inner wheels of a skid-steer rover are not commanded to turn, and its description and the identification of its paramount importance in energy-optimal path planning are investigated. Experiments with a Husky UGV rover validate the energy-optimality of using R′ turns.
Furthermore, a practical velocity constraint for skid-steer rovers is proposed that maintains constant forward velocity above R’ and constant angular velocity below it. Also, in separate but related work, it is shown that almost always equal “friction requirement” can be used to obtain optimal traction forces for a common and practical type of 4-wheel rover.