Reducing the complexity of higher order problems can enable solving them in analytical ways. In this paper, we propose an analytic whole body motion generator for humanoid robots. Our approach targets inexpensive platforms that possess position controlled joints and have limited feedback capabilities. By analysing the mass distribution in a humanoid-like body, we find relations between limb movement and their respective CoM positions. A full pose of a humanoid robot is then described with five point-masses, with one attached to the trunk and the remaining four assigned to each limb. The weighted sum of these masses in combination with a contact point form an inverted pendulum. We then generate statically stable poses by specifying a desired upright pendulum orientation, and any desired trunk orientation. Limb and trunk placement strategies are utilised to meet the reference CoM position. A set of these poses is interpolated to achieve stable whole body motions. The approach is evaluated by performing several motions with an igus Humanoid Open Platform robot. We demonstrate the extendability of the approach by applying basic feedback mechanisms for disturbance rejection and tracking error minimisation.
Reducing the complexity of a humanoid robot representation, while retaining most of the relevant information for control purposes led to the development of various models. @cite_6 introduced the 3D Linear Inverted Pendulum, which allowed for generation of a biped walk depending on desired velocity and direction. In this model, the mass stays at a constant height and a change in the robot's configuration cannot influence it by definition. The Reaction Mass Pendulum described by @cite_17 is a more comprehensive model, that uses three pairs of equal point masses at different radial distances to shape the inertia of the robot. These masses are abstract however, and do not map directly to a specific limb or body part. Describing the robot by distributed masses was also done by @cite_7 for the purpose of fast gait generation. Their simplified model allows for fast calculations, but does not consider upper body movement and kinematic constraints.
@cite_7 @cite_6 @cite_17
2126729486 2138136244 2139612757
Bipedal running can easily result in a fall due to poor availability of the ground reaction force at the boundary of the flight and support phases. We propose methods to decompose and synthesize a running gait pattern into vertical, horizontal and rotational components so that time-dependent ground friction limits are satisfied. We also extend previously proposed boundary condition, the divergent component of motion, for switching walking gait patterns into running which involves vertical acceleration of the center of gravity. Using these techniques, running at 10 km h is achieved on a real robot whose dimension are same as ASIMO. For 3D walking control of a biped robot we analyze the dynamics of a 3D inverted pendulum in which motion is constrained to move along an arbitrarily defined plane. This analysis yields a simple linear dynamics, the 3D linear inverted pendulum mode (3D-LIPM). Geometric nature of trajectories under the 3D-LIPM and a method for walking pattern generation are discussed. A simulation result of a walking control using a 12-DOF biped robot model is also shown. A number of conceptually simple but behavior-rich "inverted pendulum" humanoid models have greatly enhanced the understanding and analytical insight of humanoid dynamics. However, these models do not incorporate the robot's angular momentum properties, a critical component of its dynamics. We introduce the reaction mass pendulum (RMP) model, a 3D generalization of the better-known reaction wheel pendulum. The RMP model augments the existing models by compactly capturing the robot's centroidal momenta through its composite rigid body (CRB) inertia. This model provides additional analytical insights into legged robot dynamics, especially for motions involving dominant rotation, and leads to a simpler class of control laws. In this paper we show how a humanoid robot of general geometry and dynamics can be mapped into its equivalent RMP model. A movement is subsequently mapped to the time evolution of the RMP. We also show how an "inertia shaping" control law can be designed based on the RMP.