Force Maximization of Biarticularly Actuated Manipulators Using Infinity Norm

There is a rising interest in biologically inspired manipulators equipped with biarticular actuators-actuators that span two joints-for solving the known limitations of conventional systems. In contrast with kinematic redundancy, actuator redundancy resulting from the presence of biarticular actuators has the added advantages of bringing more stability, reducing the inertia of the robot links, and decreasing the nonlinearity of the end effector force as a function of force direction. In this paper, the advantage of the infinity norm optimization criteria on a robot designed under the actuator redundancy paradigm is investigated. A closed form solution based on the infinity norm for a manipulator with mono- and biarticular actuators is derived. The proposed infinity norm-based approach is compared with the conventional method based on pseudoinverse matrix by both calculation and experiment. Under the same actuator limitations, the maximum end effector force produced with the proposed method is significantly greater than the one produced by the conventional method. The proposed closed form solution is suitable for redundant systems with three inputs and two outputs, bringing the advantage of an higher maximum output without the need for iterative algorithms.