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The inverse kinematics problem is formulated as a parameterized autonomous dynamical system problem, and respective analysis is carried out. It is shown that a singular point of work space can be mapped either as a critical or a noncritical point of the autonomous system, depending on the direction of approach to the singular point. Making use of the noncritical mapping, a closed-loop kinematic controller with asymptotic stability and velocity limits along degenerate singular or near-singular paths is designed. The authors introduce a specific type of motion along the reference path, the so-called natural motion. This type of motion is obtained in a straightforward manner from the autonomous dynamical system and always satisfies the motion constraint at a singular point. In the vicinity of the singular point, natural motion slows down the end-effector speed and keeps the joint velocity bounded. Thus, no special trajectory replannin

Upper-Body Kinesthetic Teaching of a Free-Standing Humanoid Robot

Abstract — We present an integrated approach allowing a free-standing humanoid robot to acquire new motor skills by kinesthetic teaching. The proposed method controls simultaneously the upper and lower body of the robot with different control strategies. Imitation learning is used for training the upper body of the humanoid robot via kinesthetic teaching, while at the same time Reaction Null Space method is used for keeping the balance of the robot. During demonstration, a force/torque sensor is used to record the exerted forces, and during reproduction, we use a hybrid position/force controller to apply the learned trajectories in terms of positions and forces to the end effector. The proposed method is tested on a 25-DOF Fujitsu HOAP-2 humanoid robot with a surface cleaning task. I

The DCM generalized inverse: efficient body-wrench distribution in multi-contact balance control

<p>A computationally efficient solution of the body- wrench distribution  problem for bipeds and multi-legged robots is introduced. The method is based on a weighted generalized inverse, the weights being determined from relationships pertinent to the divergent component of motion (DCM), base-of-support (BoS) geometry, friction constraints and center of pressure allocation. The user (or the robot) specifies appropriate weights only indirectly, by setting the desired contact transition boundaries within the net BoS. It is shown that the proposed weighted generalized inverse  ensures body- wrench distribution  in a way consistent with both the static and dynamic states. The dependency on the DCM yields an important advantage when the method is applied to reactive balance control in response to unknown disturbances. An admittance-type stabilizer is obtained by setting the reference DCM at the current center of mass position. This stabilizer does not require reference values for the centers of pressures and the contact wrenches. The method is implemented with a whole-body, torque-based balance controller. Its performance is examined through simulations with planar and non-coplanar contacts, during proactive and reactive tasks.</p