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Convexity of stiffness matrix eigenvalues for a position controlled limb of mobile climbing robots

This paper presents a simple model of the structure stiffness of a position controlled limb designed for mobile climbing robot. The stiffness matrices of the robot limb at different configurations are investigated. Experiments are conducted to demonstrate that this model is able to predict the general trend of change of stiffness matrix as a function of end effector position. Experiments also show that the maximum eigenvalue of stiffness matrix is a convex function with respect to the effector position, which matches the prediction of theory. Other testing includes measuring the effect of motor backlash on stiffness coefficients, and gauge the amount of contribution to total compliance from joint compliance and structure compliance.