Efficient formulation of the force distribution equations for general tree-structured robotic mechanisms with a mobile base

In this paper, an efficient and systematic formulation of the force distribution equations for general tree-structured robotic mechanisms is presented. The applicable platforms include not only systems with star topologies, such as walking machines that have multiple legs with a single body but also general tree-structured mechanisms, such as variably configured wheeled vehicles having multiple modules. The force balance equations that govern the relationship between the contact forces and the resultant inertial forces/moments of the vehicle will be derived through a recursive and computationally efficient algorithm. Also, the joint torque constraints that specify the joint actuator limits, and contact friction constraints that may be used to avoid slippage and maintain contact, are efficiently incorporated in the formulation. Based on this formulation, several standard optimization techniques, such as linear programming or quadratic programming, can be applied to obtain the solution. An algorithm summarizing the results developed, and suitable for computer implementation, is included. The algorithm has been applied to an n-module actively articulated wheeled vehicle, and the computational cost evaluated. The efficiency of the algorithm is demonstrated with results showing real-time execution on a Pentium PC.