This analytic and experimental study proposes a control algorithm for coordinated position and force control for autonomous multi-limbed mobile robotic systems. The technique is called Coordinated Jacobian Transpose Control (CJTC). Such position/force control algorithms will be required if future robotic systems are to operate effectively in unstructured environments. Generalized Control Variables (GCVs), express in a consistent and coordinated manner the desired behavior of the forces exerted by the multi-limbed robot on the environment and a system's motions. The effectiveness of this algorithm is demonstrated in simulation and laboratory experiments on a climbing system.