A General Method for Motion Planning for Quasi–Static Legged Robotic Locomotion

We present a general motion planning scheme for a class of legged robots that walk in a quasi–static manner. The method does not depend upon the number of legs, nor is it based on foot placement concepts. Instead, our method is based on an extension of a nonlinear motion planning algorithm for smooth systems to the legged case, where the relevant dynamics are not smooth. The configuration space for the legged robot is comprised of different regimes, called strata, corresponding to when various combinations of feet are in contact with the ground. On each stratum, the equations of motion can be different. If vector fields satisfy a particular relationship, called strata decoupling, then it is possible to consider components of the equations of motion for the system on different strata as part of the equations of motion on one common stratum, which facilitates the application of the aformentioned nonlinear motion planning algorithm. The algorithm is illustrated with a simple example.