Visualization of the Contact Force Solution Space for Multi-Limbed Robots

This paper addresses the determination, representation, and visualization of the contact force solution space of a multi-limbed mobile robotic system with three feet in contact with its environment. Since the limbs of the robot have enough joints and are actively controlled, the contact forces at the feet need to be explicitly chosen to ensure that the robot does not lose its balance and does not slip at a foot. One of the major difficulties associated with finding the force distribution solution has been the indeterminate nature of the problem. Any system with three or more contact points makes it an underspecified system involving redundancy since there are more unknowns than the number of equations. The other major difficulty associated with the problem of multi-contact force distribution has been the nonlinear nature of the three-dimensional friction cone model. Instead of finding just a single contact force solution through optimization methods as is the case for most previous work on this subject, the presented method describes all the possible solutions solution space for the contact force distribution for a statically stable body under friction constraints. The optimal contact force solution can then be chosen in this solution space which maximizes the objectives given by the chosen optimization criteria. This two-step approach allows one to have more options and freedom in choosing the final solution and to satisfy other special conditions that might be considered at that instant. This paper presents the method for finding the solution space as the first step of finding the optimal contact force distribution. The second step of choosing the optimal solution in this solution space was presented in 1‐3.