Planning non-holonomic stable trajectories on uneven terrain through non-linear time scaling

Arun Kumar Singh1    K. Madhava Krishna1    Srikanth Saripalli2   

1 IIIT Hyderabad, India    2 School of Earth and Space Exploration, Arizona State University   

In this paper, we present a framework for generating smooth and stable trajectories for wheeled mobile robots moving on uneven terrains. Instead of relying on static stability measures, the paper incorporates velocity and acceleration based constraints like no-slip and permanent wheel ground contact conditions in the planning framework. The paper solves this complicated problem in a computationally efficient manner with full 3D dynamics of the robot. The two major aspects of the proposed work are: Firstly, closed form functional relationships are derived which describes the 6 dof evolution of the robot’s state on an arbitrary 2.5D uneven terrain. This enables us to have a fast evaluation of robot’s dynamics along any candidate trajectory. Secondly, a novel concept of non-linear time scaling is introduced through which simple algebraic relations defining the bounds on velocities and accelerations are obtained. Moreover, non-linear time scaling also provides a new approach for manipulating velocities and accelerations along given geometric paths. It is thus exploited to obtain stable velocity and acceleration profiles. Extensive simulation results are presented to demonstrate the efficacy of the proposed methodology.