Optimal force distribution for the legs of a walking machine with friction cone constraints

The authors examine different methods of solving the force distribution problem for the limbs of a legged vehicle with friction cone constraints. A key concept in the proposed formulations is the use of pseudoinverses to provide a decomposition of the original problem in a form that is more amenable to optimization. The new formulations can be described as being either interior- or exterior-based methods. Geometrically, interior methods start a search in force space with a force that is inside the friction cone constraints but does not necessarily meet the required body forces and torques. Exterior methods start with forces that meet the required body forces and torques but may be outside the friction cone constraints. It is shown that exterior methods have the potential for providing better force command continuity when the solution from the previous control cycle is considered or, alternatively, these methods can be used to minimize the maximum friction cone angle over all the legs