When an external force is applied to a legged robot that has manipulation capabilities, it may cause the robot to slip, lose contact between a foot and the environment, or to fail to track the desired path. In each of these cases, the robot motion fails because the external force causes a violation of the so-called motion constraints.

To avoid such situations, it is essential to robustly optimize dynamic trajectories allowing the system to deal with disturbance forces and uncertain payloads. The problem can be modeled using advanced mathematical programs involving many nonlinearities

Thanks to its efficient interior-point method, Artelys Knitro allows researchers to determine highly robust dynamic trajectories. The benefits of robust optimization have been demonstrated using a quadruped robot equipped with a manipulator able to execute a pick-and-place of a bottle on a table, even on a skateboard.