The exact eigenfunctions for the slewing link are found, taking into account a rotating inertia at the base and a payload at the tip. These derive from two equivalent formulations (pseudoclamped and pseudopinned) of the boundary value problem relative to the flexible slewing beam. The exactness of the solution makes it possible to prove the equivalence of these two approaches, which differ in the choice of the noninertial rotating frame. The two related dynamic linear models are then found, and a change of coordinates is given. Experimental measurements validate the theoretical results

We present IS-MPC, an intrinsically stable MPC framework for humanoid gait generation which incorporates an explicit stability constraint in the formulation. The proposed method uses as prediction model a dynamically extended LIP where ZMP velocities are the control inputs, producing in real time a gait (including footsteps with the associated timing) that realizes omnidirectional motion commands coming from an external source. The stability constraint links the future ZMP velocities to the current system state so as to guarantee the essential requirement that the generated CoM trajectory is bounded with respect to the ZMP trajectory. Since the control horizon of the MPC algorithm is finite, only part of the future ZMP velocities are decision variables of the QP problem; the remaining part, called tail, must be either conjectured or anticipated using preview information on the reference motion. Several possible options for the tail are discussed, and each of them is shown to correspond to a specific terminal constraint. A theoretical analysis of the feasibility of the generic MPC iteration is developed and used to obtain sufficient conditions for recursive feasibility. Finally, it is proved that IS-MPC guarantees stability of the CoM/ZMP dynamics if it is recursively feasible. Simulation and experimental results on the NAO and the HRP-4 humanoids are presented to illustrate the performance of the proposed method.

Capturability analysis of the linear inverted pendulum (LIP) model enabled walking with constrained height based on the capture point. We generalize this analysis to the variableheight inverted pendulum (VHIP) and show how it enables 3D walking over uneven terrains based on capture inputs. Thanks to a tailored optimization scheme, we can compute these inputs fast enough for real-time model predictive control. We implement this approach as open-source software and demonstrate it in dynamic simulations.

We report results from a collaborative project that investigated the deployment of humanoid robotic solutions in aircraft manufacturing for some assembly operations where access is not possible for wheeled or rail-ported robotic platforms. Recent developments in multi-contact planning and control, bipedal walking, embedded SLAM, whole-body multi-sensory task space optimization control, and contact detection and safety, suggest that humanoids could be a plausible solution for automation given the specific requirements in such large-scale manufacturing sites. The main challenge is to integrate these scientific and technological advances into two existing humanoid platforms: the position controlled HRP-4 and the torque controlled TORO. This integration effort was demonstrated in a bracket assembly operation inside a 1:1 scale A350 mock-up of the front part of the fuselage at the Airbus Saint-Nazaire site. We present and discuss the main results that have been achieved in this project and provide recommendations for future work.

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