Planning trajectories on uneven terrain using optimization and non-linear time scaling techniques

In this paper we introduce a novel framework of generating trajectories which explicitly satisfies the stability constraints such as no-slip and permanent ground contact on uneven terrain. The main contributions of this paper are: (1) It derives analytical functions depicting the evolution of the vehicle on uneven terrain. These functional descriptions enable us to have a fast evaluation of possible vehicle stability along various directions on the terrain and this information is used to control the shape of the trajectory. (2) It introduces a novel paradigm wherein non-linear time scaling brought about by parametrized exponential functions are used to modify the velocity and acceleration profile of the vehicle so that these satisfy the no-slip and contact constraints. We show that nonlinear time scaling manipulates velocity and acceleration profile in a versatile manner and consequently has exceptional utility not only in uneven terrain navigation but also in general in any problem where it is required to change the velocity of the robot while keeping the path unchanged like collision avoidance.