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Register a new userDynamics and Control of Humanoid Robots: A Geometrical Approach
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his paper reviews modern geometrical dynamics and control of humanoid robots. This general Lagrangian and Hamiltonian formalism starts with a proper definition of humanoids configuration manifold, which is a set of all robots active joint angles. Based on the `covariant force law, the general humanoids dynamics and control are developed. Autonomous Lagrangian dynamics is formulated on the associated `humanoid velocity phase space, while autonomous Hamiltonian dynamics is formulated on the associated `humanoid momentum phase space. Neural-like hierarchical humanoid control naturally follows this geometrical prescription. This purely rotational and autonomous dynamics and control is then generalized into the framework of modern non-autonomous biomechanics, defining the Hamiltonian fitness function. The paper concludes with several simulation examples. Keywords: Humanoid robots, Lagrangian and Hamiltonian formalisms, neural-like humanoid control, time-dependent biodynamics
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Humanoid robots could be versatile and intuitive human avatars that operate remotely in inaccessible places: the robot could reproduce in the remote location the movements of an operator equipped with a wearable motion capture device while sending visual feedback to the operator. While substantial progress has been made on transferring (retargeting) human motions to humanoid robots, a major problem preventing the deployment of such systems in real applications is the presence of communication delays between the human input and the feedback from the robot: even a few hundred milliseconds of delay can irreversibly disturb the operator, let alone a few seconds. To overcome these delays, we introduce a system in which a humanoid robot executes commands before it actually receives them, so that the visual feedback appears to be synchronized to the operator, whereas the robot executed the commands in the past. To do so, the robot continuously predicts future commands by querying a machine learning model that is trained on past trajectories and conditioned on the last received commands. In our experiments, an operator was able to successfully control a humanoid robot (32 degrees of freedom) with stochastic delays up to 2 seconds in several whole-body manipulation tasks, including reaching different targets, picking up, and placing a box at distinct locations.
In spite of the recent interest and advances in linear controllability of complex networks, controlling nonlinear network dynamics remains to be an outstanding problem. We develop an experimentally feasible control framework for nonlinear dynamical networks that exhibit multistability (multiple coexisting final states or attractors), which are representative of, e.g., gene regulatory networks (GRNs). The control objective is to apply parameter perturbation to drive the system from one attractor to another, assuming that the former is undesired and the latter is desired. To make our framework practically useful, we consider RESTRICTED parameter perturbation by imposing the following two constraints: (a) it must be experimentally realizable and (b) it is applied only temporarily. We introduce the concept of ATTRACTOR NETWORK, in which the nodes are the distinct attractors of the system, and there is a directional link from one attractor to another if the system can be driven from the former to the latter using restricted control perturbation. Introduction of the attractor network allows us to formulate a controllability framework for nonlinear dynamical networks: a network is more controllable if the underlying attractor network is more strongly connected, which can be quantified. We demonstrate our control framework using examples from various models of experimental GRNs. A finding is that, due to nonlinearity, noise can counter-intuitively facilitate control of the network dynamics.
We study the geometrical and topological properties of the bulk (environment space) when we modify the geometry or topology of a brane-world. Through the characterization of a spherically symmetric space-time as a local brane-world immersed into six dimensional pseudo-Euclidean spaces, with different signatures of the bulk, we investigate the existence of a topological difference in the immersed brane-world. In particular the Schwarzschilds brane-world and its Kruskal (or Fronsdal) brane-world extension are examined from point of view of the immersion formalism. We prove that there is a change of signature of the bulk when we consider a local isometric immersion and different topologies of a brane-world in that bulk.
Stable bipedal walking is a key prerequisite for humanoid robots to reach their potential of being versatile helpers in our everyday environments. Bipedal walking is, however, a complex motion that requires the coordination of many degrees of freedom while it is also inherently unstable and sensitive to disturbances. The balance of a walking biped has to be constantly maintained. The most effective way of controlling balance are well timed and placed recovery steps -- capture steps -- that absorb the expense momentum gained from a push or a stumble. We present a bipedal gait generation framework that utilizes step timing and foot placement techniques in order to recover the balance of a biped even after strong disturbances. Our framework modifies the next footstep location instantly when responding to a disturbance and generates controllable omnidirectional walking using only very little sensing and computational power. We exploit the open-loop stability of a central pattern generated gait to fit a linear inverted pendulum model to the observed center of mass trajectory. Then, we use the fitted model to predict suitable footstep locations and timings in order to maintain balance while following a target walking velocity. Our experiments show qualitative and statistical evidence of one of the strongest push-recovery capabilities among humanoid robots to date.
Issues relevant to the flow chirality and structure are focused, while the new theoretical results, including even a distinctive theory, are introduced. However, it is hope that the presentation, with a low starting point but a steep rise, is appropriate for a broader spectrum of audiences ranging from students to researchers, thus illustrations of differential forms and relevant basic topological concepts are also offered, followed by the demonstration with formulation of differential forms of the classical Navier-Stokes flow theory and the discussions of recent studies in fundamental fluid mechanics and turbulence.
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