  The optimal traverse of irregular terrains made by ground mobile robots
heavily depends on the adequacy of the cost models used to plan the path they
follow. The criteria to define optimality may be based on minimizing energy
consumption and/or preserving the robot stability. This entails the proper
assessment of anisotropy to account for the robot driving on top of slopes with
different directions. To fulfill this demand, this paper presents the
Continuous Anisotropic Model for Inclined Surfaces, a cost model compatible
with anisotropic path planners like the bi-directional Ordered Upwind Method.
This model acknowledges how the orientation of the robot with respect to any
slope determines its energetic cost, considering the action of gravity and
terramechanic effects such as the slippage. Moreover, the proposed model can be
tuned to define a trade-off between energy minimization and Roll angle
reduction. The results from two simulation tests demonstrate how, to find the
optimal path in scenarios containing slopes, in certain situations the use of
this model can be more advantageous than relying on isotropic cost functions.
Finally, the outcome of a field experiment involving a skid-steering robot that
drives on top of a real slope is also discussed.
