Humans use multiple muscles to generate such joint movements as an elbow motion. With multiple lightweight and compliant actuators, joint movements can also be efficiently generated. Similarly, robots can use multiple actuators to efficiently generate a one degree of freedom movement. For this movement, the desired joint torque must be properly distributed to each actuator. One approach to cope with this torque distribution problem is an optimal control method. However, solving the optimal control problem at each control time step has not been deemed a practical approach due to its large computational burden. In this paper, we propose a computationally efficient method to derive an optimal control strategy for a hybrid actuation system composed of multiple actuators, where each actuator has different dynamical properties. We investigated a singularly perturbed system of the hybrid actuator model that subdivided the original large-scale control problem into smaller subproblems so that the optimal control outputs for each actuator can be derived at each control time step and applied our proposed method to our pneumatic-electric hybrid actuator system. Our method derived a torque distribution strategy for the hybrid actuator by dealing with the difficulty of solving real-time optimal control problems.

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In this letter, we develop an optimal control framework that takes the full-body dynamics of a humanoid robot into account. Employing full-body dynamics has been explored in, especially, an online optimal control approach known as model predictive control (MPC). However, whole-body motions cannot be updated in a short period of time due to MPC's large computational burden. Thus, MPC has generally been evaluated with a physical humanoid robot in a limited range of tasks where high-speed motion executions are unnecessary. To cope with this problem, our multi-timescale control framework drives whole-body motions with a computationally efficient hierarchical MPC. Meanwhile, a biologically inspired controller maintains the robot's posture for a very short control period. We evaluated our framework in skating tasks with simulated and real lower-body humanoids that have rollers on the feet. Our simulated robot generated various agile motions such as jumping over a bump and flipping down from a cliff in real time. Our real lower-body humanoid also successfully generated a movement down a slope.

When grasping an object, friction forces are sometimes utilized. Because of this friction forces, the object is manipulable to various direction. In this paper, we discuss which direction is best when contact points, the number of which is two in the 2D-space grasping or three in the 3D one, are assigned. To evaluate the object direction, we focus on the norm of contact forces consisting of the normal forces and friction forces. We conclude that the norm of contact force become minimal when vertical line through the center of mass of the object (i.e., gravitational line) shoots out the midpoint of two contact points in 2D space, while it does the centroid of the contact-point triangles in 3D space.