Cooperative manipulators have uncertainties in their structure; therefore, an optimal sliding mode control method is derived from a combination of the sliding mode control (SMC) and the state-dependent Riccati equation (SDRE) technique. This proposed combination is applied to a class of non-linear closed-loop systems. One of the distinguished features of this control method is its robustness toward uncertainty. Due to the lack of optimality in the SMC method, in this paper, a robust and optimal method is presented by considering the SDRE in design of the sliding surface. Due to the fact that cooperative manipulators have been used for carrying loads, the percentage of load distributions between each manipulator has been derived to increase the dynamic load carrying capacity (DLCC). The proposed control structure is implemented on a Scout robot with two manipulators in cooperative mode, theoretically and practically using LabVIEW software; and the results were compared by considering the uncertainty in its structure. In comparison with the SDRE, the proposed method increased the DLCC almost 10% in the Scout case.

This paper proposes a novel shuffle turning method for a humanoid robot that controls the load distribution of the soles of the robot's feet. Turning motions of a humanoid robot are conventionally performed through a repeated foot stepping motion. However, this motion is inefficient and time-consuming. In our method, the feet are slid along the floor without a stepping movement. In order to reduce the friction with the floor and to achieve the correct shuffle turning motion, a non-uniform load distribution of the soles is controlled. Experiments using a humanoid robot were conducted on two floors with differing friction amounts, and the validity of the proposed method was verified.

The concept of the force ellipsoid and the manipulability ellipsoid of robotic mechanism is extended to two cooperating robot arms, and the equations of the dual arm force and manipulability ellipsoids are derived. The load distribution problem for two cooperating robots is studied using the concept of the force ellipsoid. The problem is usually underspecified mathematically and a variety of optimal solutions may exist. A new solution approach utilizing the force ellipsoid is proposed in this paper. The load distribution problem is formulated as a nonlinear optimization problem with a quadratic cost function and inequality constraints. The optimality criterion is the minimum energy, and two different cases are considered depending on the presence of the constraints on joint torques.