Dynamics and Control of Humanoid Robots: A Geometrical Approach

his paper reviews modern geometrical dynamics and control of humanoid robots. This general Lagrangian and Hamiltonian formalism starts with a proper definition of humanoid's configuration manifold, which is a set of all robot's active joint angles. Based on the `covariant force law', the general humanoid's 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 biodynamicsComment: 27 pages, 9 figures, Late

Jet Methods in Time-Dependent Lagrangian Biomechanics

In this paper we propose the time-dependent generalization of an `ordinary' autonomous human biomechanics, in which total mechanical + biochemical energy is not conserved. We introduce a general framework for time-dependent biomechanics in terms of jet manifolds associated to the extended musculo-skeletal configuration manifold, called the configuration bundle. We start with an ordinary configuration manifold of human body motion, given as a set of its all active degrees of freedom (DOF) for a particular movement. This is a Riemannian manifold with a material metric tensor given by the total mass-inertia matrix of the human body segments. This is the base manifold for standard autonomous biomechanics. To make its time-dependent generalization, we need to extend it with a real time axis. By this extension, using techniques from fibre bundles, we defined the biomechanical configuration bundle. On the biomechanical bundle we define vector-fields, differential forms and affine connections, as well as the associated jet manifolds. Using the formalism of jet manifolds of velocities and accelerations, we develop the time-dependent Lagrangian biomechanics. Its underlying geometric evolution is given by the Ricci flow equation. Keywords: Human time-dependent biomechanics, configuration bundle, jet spaces, Ricci flowComment: 13 pages, 3 figure

Adaptive, fast walking in a biped robot under neuronal control and learning

Human walking is a dynamic, partly self-stabilizing process relying on the interaction of the biomechanical design with its neuronal control. The coordination of this process is a very difficult problem, and it has been suggested that it involves a hierarchy of levels, where the lower ones, e.g., interactions between muscles and the spinal cord, are largely autonomous, and where higher level control (e.g., cortical) arises only pointwise, as needed. This requires an architecture of several nested, sensori–motor loops where the walking process provides feedback signals to the walker's sensory systems, which can be used to coordinate its movements. To complicate the situation, at a maximal walking speed of more than four leg-lengths per second, the cycle period available to coordinate all these loops is rather short. In this study we present a planar biped robot, which uses the design principle of nested loops to combine the self-stabilizing properties of its biomechanical design with several levels of neuronal control. Specifically, we show how to adapt control by including online learning mechanisms based on simulated synaptic plasticity. This robot can walk with a high speed (> 3.0 leg length/s), self-adapting to minor disturbances, and reacting in a robust way to abruptly induced gait changes. At the same time, it can learn walking on different terrains, requiring only few learning experiences. This study shows that the tight coupling of physical with neuronal control, guided by sensory feedback from the walking pattern itself, combined with synaptic learning may be a way forward to better understand and solve coordination problems in other complex motor tasks

Jet Spaces in Modern Hamiltonian Biomechanics

In this paper we propose the time-dependent Hamiltonian form of human biomechanics, as a sequel to our previous work in time-dependent Lagrangian biomechanics [1]. Starting with the Covariant Force Law, we first develop autonomous Hamiltonian biomechanics. Then we extend it using a powerful geometrical machinery consisting of fibre bundles and jet manifolds associated to the biomechanical configuration manifold. We derive time-dependent, dissipative, Hamiltonian equations and the fitness evolution equation for the general time-dependent human biomechanical system. Keywords: Human biomechanics, covariant force law, configuration manifold, jet manifolds, time-dependent Hamiltonian dynamicsComment: 16 pages, 3 figure

Anthropomorphic Robot Design and User Interaction Associated with Motion

Though in its original concept a robot was conceived to have some human-like shape, most robots now in use have specific industrial purposes and do not closely resemble humans. Nevertheless, robots that resemble human form in some way have continued to be introduced. They are called anthropomorphic robots. The fact that the user interface to all robots is now highly mediated means that the form of the user interface is not necessarily connected to the robots form, human or otherwise. Consequently, the unique way the design of anthropomorphic robots affects their user interaction is through their general appearance and the way they move. These robots human-like appearance acts as a kind of generalized predictor that gives its operators, and those with whom they may directly work, the expectation that they will behave to some extent like a human. This expectation is especially prominent for interactions with social robots, which are built to enhance it. Often interaction with them may be mainly cognitive because they are not necessarily kinematically intricate enough for complex physical interaction. Their body movement, for example, may be limited to simple wheeled locomotion. An anthropomorphic robot with human form, however, can be kinematically complex and designed, for example, to reproduce the details of human limb, torso, and head movement. Because of the mediated nature of robot control, there remains in general no necessary connection between the specific form of user interface and the anthropomorphic form of the robot. But their anthropomorphic kinematics and dynamics imply that the impact of their design shows up in the way the robot moves. The central finding of this report is that the control of this motion is a basic design element through which the anthropomorphic form can affect user interaction. In particular, designers of anthropomorphic robots can take advantage of the inherent human-like movement to 1) improve the users direct manual control over robot limbs and body positions, 2) improve users ability to detect anomalous robot behavior which could signal malfunction, and 3) enable users to be better able to infer the intent of robot movement. These three benefits of anthropomorphic design are inherent implications of the anthropomorphic form but they need to be recognized by designers as part of anthropomorphic design and explicitly enhanced to maximize their beneficial impact. Examples of such enhancements are provided in this report. If implemented, these benefits of anthropomorphic design can help reduce the risk of Inadequate Design of Human and Automation Robotic Integration (HARI) associated with the HARI-01 gap by providing efficient and dexterous operator control over robots and by improving operator ability to detect malfunctions and understand the intention of robot movement

Optimization-based multibody dynamics modeling method for team lifting simulation

A novel optimization-based multibody dynamics modeling method is proposed for two-dimensional (2D) team lifting prediction. The box itself is modeled as a floating-base rigid body in Denavit-Hartenberg representation. The interactions between humans and box are modeled as a set of grasping forces which are treated as unknowns (design variables) in the optimization formulation. An inverse dynamics optimization is used to simulate the team lifting motion where the dynamic effort of two humans is minimized subjected to physical and task-based constraints. The design variables are control points of cubic B-splines of joint angle profiles of two humans and the box, and the grasping forces between humans and the box. Analytical sensitivities are derived for all constraints and objective functions, including the varying unknown grasping forces. Two numerical examples are successfully simulated: one is to lift a 10 Kg box with the center of mass (COM) in the middle, and the other is the same weight box with the COM off the center. The humans' joint angle, torque, ground reaction force, and grasping force profiles are reported. The optimal solution is obtained in 151.99 seconds. The simulated motions are validated against the experimental joint angle profiles. Reasonable team lifting motion, kinematics, and kinetics are predicted using the proposed novel multibody dynamic modeling approach and optimization formulation

Adaptive, fast walking in a biped robot under neuronal control and learning

Human walking is a dynamic, partly self-stabilizing process relying on the interaction of the biomechanical design with its neuronal control. The coordination of this process is a very difficult problem, and it has been suggested that it involves a hierarchy of levels, where the lower ones, e.g., interactions between muscles and the spinal cord, are largely autonomous, and where higher level control (e.g., cortical) arises only pointwise, as needed. This requires an architecture of several nested, sensori–motor loops where the walking process provides feedback signals to the walker's sensory systems, which can be used to coordinate its movements. To complicate the situation, at a maximal walking speed of more than four leg-lengths per second, the cycle period available to coordinate all these loops is rather short. In this study we present a planar biped robot, which uses the design principle of nested loops to combine the self-stabilizing properties of its biomechanical design with several levels of neuronal control. Specifically, we show how to adapt control by including online learning mechanisms based on simulated synaptic plasticity. This robot can walk with a high speed (>3.0 leg length/s), self-adapting to minor disturbances, and reacting in a robust way to abruptly induced gait changes. At the same time, it can learn walking on different terrains, requiring only few learning experiences. This study shows that the tight coupling of physical with neuronal control, guided by sensory feedback from the walking pattern itself, combined with synaptic learning may be a way forward to better understand and solve coordination problems in other complex motor tasks

Bio­-inspired approaches to the control and modelling of an anthropomimetic robot

Introducing robots into human environments requires them to handle settings designed specifically for human size and morphology, however, large, conventional humanoid robots with stiff, high powered joint actuators pose a significant danger to humans. By contrast, “anthropomimetic” robots mimic both human morphology and internal structure; skeleton, muscles, compliance and high redundancy. Although far safer, their resultant compliant structure presents a formidable challenge to conventional control. Here we review, and seek to address, characteristic control issues of this class of robot, whilst exploiting their biomimetic nature by drawing upon biological motor control research. We derive a novel learning controller for discovering effective reaching actions created through sustained activation of one or more muscle synergies, an approach which draws upon strong, recent evidence from animal and humans studies, but is almost unexplored to date in musculoskeletal robot literature. Since the best synergies for a given robot will be unknown, we derive a deliberately simple reinforcement learning approach intended to allow their emergence, in particular those patterns which aid linearization of control. We also draw upon optimal control theories to encourage the emergence of smoother movement by incorporating signal dependent noise and trial repetition. In addition, we argue the utility of developing a detailed dynamic model of a complete robot and present a stable, physics-­‐‑based model, of the anthropomimetic ECCERobot, running in real time with 55 muscles and 88 degrees of freedom. Using the model, we find that effective reaching actions can be learned which employ only two sequential motor co-­‐‑activation patterns, each controlled by just a single common driving signal. Factor analysis shows the emergent muscle co-­‐‑activations can be reconstructed to significant accuracy using weighted combinations of only 13 common fragments, labelled “candidate synergies”. Using these synergies as drivable units the same controller learns the same task both faster and better, however, other reaching tasks perform less well, proportional to dissimilarity; we therefore propose that modifications enabling emergence of a more generic set of synergies are required. Finally, we propose a continuous controller for the robot, based on model predictive control, incorporating our model as a predictive component for state estimation, delay-­‐‑ compensation and planning, including merging of the robot and sensed environment into a single model. We test the delay compensation mechanism by controlling a second copy of the model acting as a proxy for the real robot, finding that performance is significantly improved if a precise degree of compensation is applied and show how rapidly an un-­‐‑compensated controller fails as the model accuracy degrades