Simulating Adaptive Human Bipedal Locomotion Based on Phase Resetting Using Foot-Contact Information

Humans generate bipedal walking by cooperatively manipulating their complicated and redundant musculoskeletal systems to produce adaptive behaviors in diverse environments. To elucidate the mechanisms that generate adaptive human bipedal locomotion, we conduct numerical simulations based on a musculoskeletal model and a locomotor controller constructed from anatomical and physiological findings. In particular, we focus on the adaptive mechanism using phase resetting based on the foot-contact information that modulates the walking behavior. For that purpose, we first reconstruct walking behavior from the measured kinematic data. Next, we examine the roles of phase resetting on the generation of stable locomotion by disturbing the walking model. Our results indicate that phase resetting increases the robustness of the walking behavior against perturbations, suggesting that this mechanism contributes to the generation of adaptive human bipedal locomotion.     

动态双足机器人的控制与优化研究进展

对动态双足机器人的可控周期步态的稳定性、鲁棒性和优化控制策略的国内外研究现状与发展趋势进行了探讨.首先,介绍动态双足机器人的动力学数学模型,进一步,提出动态双足机器人运动步态和控制系统原理;其次,讨论动态双足机器人可控周期步态稳定性现有的研究方法,分析这些方法中存在的缺点与不足;再次,研究动态双足机器人的可控周期步态优化控制策略,阐明各种策略的优缺点;最后,给出动态双足机器人研究领域的难点问题和未来工作,展望动态双足机器人可控周期步态与鲁棒稳定性及其应用的研究思路.     

Minimalistic control of biped walking in rough terrain

Toward our comprehensive understanding of legged locomotion in animals and machines, the compass gait model has been intensively studied for a systematic investigation of complex biped locomotion dynamics. While most of the previous studies focused only on the locomotion on flat surfaces, in this article, we tackle with the problem of bipedal locomotion in rough terrains by using a minimalistic control architecture for the compass gait walking model. This controller utilizes an open-loop sinusoidal oscillation of hip motor, which induces basic walking stability without sensory feedback. A set of simulation analyses show that the underlying mechanism lies in the “phase locking” mechanism that compensates phase delays between mechanical dynamics and the open-loop motor oscillation resulting in a relatively large basin of attraction in dynamic bipedal walking. By exploiting this mechanism, we also explain how the basin of attraction can be controlled by manipulating the parameters of oscillator not only on a flat terrain but also in various inclined slopes. Based on the simulation analysis, the proposed controller is implemented in a real-world robotic platform to confirm the plausibility of the approach. In addition, by using these basic principles of self-stability and gait variability, we demonstrate how the proposed controller can be extended with a simple sensory feedback such that the robot is able to control gait patterns autonomously for traversing a rough terrain.     

Development of minimalist bipedal walking robot with flexible ankle and split-mass balancing systems

This paper presents a novel design of minimalist bipedal walking robot with flexible ankle and split-mass balancing systems.The proposed approach implements a novel strategy to achieve stable bipedal walk by decoupling the walking motion control from the sideway balancing control.This strategy allows the walking controller to execute the walking task independently while the sideway balancing controller continuously maintains the balance of the robot.The hip-mass carry approach and selected stages of walk implemented in the control strategy can minimize the efect of major hip mass of the robot on the stability of its walk.In addition,the developed smooth joint trajectory planning eliminates the impacts of feet during the landing.In this paper,the new design of mechanism for locomotion systems and balancing systems are introduced.An additional degree of freedom introduced at the ankle joint increases the sensitivity of the system and response time to the sideway disturbances.The efectiveness of the proposed strategy is experimentally tested on a bipedal robot prototype.The experimental results provide evidence that the proposed strategy is feasible and advantageous.     

An adaptive fuzzy sliding-mode controller design for walking control with functional electrical stimulation: A computer simulation study

A major challenge to developing neuroprostheses for walking and to widespread acceptance of these walking systems is the design of a robust control strategy that provides satisfactory tracking performance, to be robust against time-varying properties of neuromusculoskeletal dynamics, day-today variations, muscle fatigue, and external disturbances, and to be easy to apply without requiring offline identification during different experiment sessions. The lower extremities of human walking are a highly nonlinear, highly time-varying, multi-actuator, multi-segment with highly inter-segment coupling, and inherently unstable system. Moreover, there always exist severe structured and unstructured uncertainties such as spasticity, muscle fatigue, external disturbances, and unmodeled dynamics. Robust control design for such nonlinear uncertain multi-input multi-output system still remains as an open problem. In this paper we present a novel robust control strategy that is based on combination of adaptive fuzzy control with a new well-defined sliding-mode control (SMC) with strong reachability for control of walking in paraplegic subjects. Based on the universal approximation theorem, fuzzy logic systems are employed to approximate the neuromusculoskeletal dynamics and an adaptive fuzzy controller is designed by using Lyapunov stability theory to compensate for approximation errors. The proposed control strategy has been evaluated on a planar model of bipedal locomotion as a virtual patient. The results indicate that the proposed strategy provides accurate tracking control with fast convergence during different conditions of operation, and could generate control signals to compensate the effects of muscle fatigue, system parameter variations, and external disturbances. Interesting observation is that the controller generates muscle excitation that mimic those observed during normal walking.     

Generation of bipedal walking through interactions among the robot dynamics,the oscillator dynamics,and the environment: Stability characteristics of a five-link planar biped robot

We previously developed a locomotion control system for a biped robot using nonlinear oscillators and verified the performance of this system in order to establish adaptive walking through the interactions among the robot dynamics, the oscillator dynamics, and the environment. In order to clarify these mechanisms, we investigate the stability characteristics of walking using a five-link planar biped robot with a torso and knee joints that has an internal oscillator with a stable limit cycle to generate the joint motions. Herein we conduct numerical simulations and a stability analysis, where we analytically obtain approximate periodic solutions and examine local stability using a Poincaré map. These analyses reveal (1) stability characteristics due to locomotion speed, torso, and knee motion, (2) stability improvement due to the modulation of oscillator states based on phase resetting using foot-contact information, and (3) the optimal parameter in the oscillator dynamics for adequately exploiting the interactions among the robot dynamics, the oscillator dynamics, and the environment in order to increase walking stability. The results of the present study demonstrate the advantage and usefulness of locomotion control using oscillators through mutual interactions.     

Physics-Based Person Tracking Using the Anthropomorphic Walker

We introduce a physics-based model for 3D person tracking. Based on a biomechanical characterization of lower-body dynamics, the model captures important physical properties of bipedal locomotion such as balance and ground contact. The model generalizes naturally to variations in style due to changes in speed, step-length, and mass, and avoids common problems (such as footskate) that arise with existing trackers. The dynamics comprise a two degree-of-freedom representation of human locomotion with inelastic ground contact. A stochastic controller generates impulsive forces during the toe-off stage of walking, and spring-like forces between the legs. A higher-dimensional kinematic body model is conditioned on the underlying dynamics. The combined model is used to track walking people in video, including examples with turning, occlusion, and varying gait. We also report quantitative monocular and binocular tracking results with the HumanEva dataset.     

A Novel Method of Gait Synthesis for Bipedal Fast Locomotion

Common methods of gait generation of bipedal locomotion based on experimental results, can successfully synthesize biped joints’ profiles for a simple walking. However, most of these methods lack sufficient physical backgrounds which can cause major problems for bipeds when performing fast locomotion such as running and jumping. In order to develop a more accurate gait generation method, a thorough study of human running and jumping seems to be necessary. Most biomechanics researchers observed that human dynamics, during fast locomotion, can be modeled by a simple spring loaded inverted pendulum system. Considering this observation, a simple approach for bipedal gait generation in fast locomotion is introduced in this paper. This approach applies a nonlinear control method to synchronize the biped link-segmental dynamics with the spring-mass dynamics. This is done such that while the biped center of mass follows the trajectory of the mass-spring model, the whole biped performs the desired running/jumping process. A computer simulation is done on a three-link under-actuated biped model in order to obtain the robot joints’ profiles which ensure repeatable hopping. The initial results are found to be satisfactory, and improvements are currently underway to explore and enhance the capabilities of the proposed method.     

Hybrid-state driven autonomous control for planar bipedal locomotion

The focus of this paper is on the development of a human inspired autonomous control scheme for a planar bipedal robot in a hybrid dynamical framework to realize human-like walking projected onto sagittal plane. In addition, a unified modelling scheme is presented for the biped dynamics incorporating the effects of various locomotion constraints due to varying feet-ground contact states, unilateral ground contact force, contact friction cone, passive dynamics associated with floating base etc. along with a practical impact velocity map on heel strike event. The autonomous control synthesis is formulated as a two-level hierarchical control algorithm with a hybrid-state based supervisory control in outer level and an integrated set of constrained motion control primitives, called task level control, in inner level. The supervisory level control is designed based on a human inspired heuristic approach whereas the task level control is formulated as a quadratic optimization problem with linear constraints. The explicit analytic solution obtained in terms of joint acceleration and ground contact force is used in turn to generate the joint torque command based on inverse dynamics model of the biped. The proposed controller framework is named as Hybrid-state Driven Autonomous Control (HyDAC). Unlike many other bipedal control schemes, HyDAC does not require a preplanned trajectory or orbit in terms of joint variables for locomotion control. Moreover, it is built upon a set of basic motion control primitives similar to those in human walk which provides a transparent and easily adaptable structure for the controller. These features make HyDAC framework suitable for bipedal walk on terrain with step and slope discontinuities without a priori gait optimization. The stability and agility of the proposed control scheme are demonstrated through dynamic model simulation of a 12-link planar biped having similar size and mass properties of an adult sized human being restricted to sagittal plane. Simulation results show that the planar biped is able to walk for a speed range of 0.1–2 m/s on level terrain and for a ground slope range of $+/-$20 deg for 1 m/s speed.     

Robot-environment dynamic interaction survey and future trends

Our aim was to consider interaction control problems from different viewpoints, primarily taking into account practical problems and needs. Basic strategies for controlling the interaction of a robot with the environment are the subject of the paper. The paper also provides a historical perspective on interaction control, summarizing the major achievements in this area for the last 25 years. After this long period of investigation we are now faced with an inevitable change of generation in this field. Many young enthusiastic researchers are focusing now on various attractive issues in human-robot-environment interaction control, especially from the viewpoint of novel disciplines such as artificial intelligence, mechatronics, augmented reality, etc. Considering more complex tasks, the application of force sensors and interaction control techniques is certainly not sufficient to provide the robot with a required degree of autonomy and intelligence. The paper attempts to provide unified theoretical force and position control paradigms considering basic control issues: stability, performance, and robustness. This framework assumes a general dynamic environment and uses an inverse dynamic control strategy to design various controllers for specific force and position stabilization tasks. Stability problems during the dynamic control tasks are also considered in the paper using different stability criteria. The established contact stability theory has been expanded to the control and synthesis. Therefore, one of the basic characteristics of regular bipedal walk of humanoid robots is the maintenance of their dynamic balance during the walk, whereby a decisive role is played by the unpowered degrees of freedom arising at the foot-ground contact. Hence, the role of Zero-Moment Point (ZMP) as an indicator of dynamic balance is indispensable. On the other hand, we are witnesses of the diverse realizations of locomotion systems, from those with human-like feet, aiming to mimic in full the human gait, passive walkers, which practically roll on specially profiled feet, to the footless locomotion systems. It is quite clear that any of these systems can realize a gait (very often such gait is not dynamically balanced), but our present study shows that the performances of such walking systems are essentially different and inapt to meet the requirements that are stated for the humanoids in a human environment. This study points out the indispensability of the regular, fully dynamically balanced gait for the simultaneous realization of locomotion-manipulation activities, as well as for the walk in an unstructured environment.     

Controlled symmetries and passive walking

In this note, we investigate the relationship between nonlinear control and passive walking in bipedal locomotion for the general case of an n degree-of-freedom biped in three dimensional space. We introduce the notion of controlled symmetry to capture the effect of the control input on the invariance of the system Lagrangian under group action. We then show the existence of a controlled symmetry for general bipeds under the action of SO(3) taking into account not only the kinetic energy but also the potential energy and impact dynamics. We use this result to show the existence of a nonlinear control law that reproduces so-called passive gaits independent of the particular ground slope. Our contribution in this note is two-fold. First, our result contains the first rigorous proof of the existence of so-called passivity mimicking control laws that explicitly accounts for the impact dynamics. Second, whereas previous papers have studied only planar bipeds with and without knees, our result is completely general. Our results can be viewed as direct extensions of several previous results, such as passivity-based control, virtual gravity, and virtual passive dynamic walking from the planar case to general n-degrees-of-freedom (DOF) robots in three-dimensional space.     

The Reaction Mass Biped: Geometric Mechanics and Control

Inverted Pendulum based reduced order models offer many valuable insights into the much harder problem of bipedal locomotion. While they help in understanding leg behavior during walking, they fail to capture the natural balancing ability of humans that stems from the variable rotational inertia on the torso. In an attempt to overcome this limitation, the proposed work introduces a Reaction Mass Biped (RMB). It is a generalization of the previously introduced Reaction Mass Pendulum (RMP), which is a multi-body inverted pendulum model with an extensible leg and a variable rotational inertia torso. The dynamical model for the RMB is hybrid in nature, with the roles of stance leg and swing leg switching after each cycle. It is derived using a variational mechanics approach, and is therefore coordinate-free. The RMB model has thirteen degrees of freedom, all of which are considered to be actuated. A set of desired state trajectories that can enable bipedal walking in straight and curved paths are generated. A control scheme is then designed for asymptotically tracking this set of trajectories with an almost global domain-of-attraction. Numerical simulation results confirm the stability of this tracking control scheme for different walking paths of the RMB. Additionally, a discrete dynamical model is also provided along-with an appropriate Geometric Variational Integrator (GVI). In contrast to non-variational integrators, GVIs can better preserve energy terms for conservative mechanical systems and stability properties (achieved through energy-like lyapunov functions) for actuated systems.     

Evolution of central pattern generators for bipedal walking in areal-time physics environment

We describe an evolutionary approach to the control problem of bipedal walking. Using a full rigid-body simulation of a biped, it was possible to evolve recurrent neural networks that controlled stable straight-line walking on a planar surface. No proprioceptive information was necessary in order to achieve this task. Furthermore, simple sensory input to locate a sound source was integrated to achieve directional walking. To our knowledge, this is the first work that demonstrates the application of evolutionary optimization to 3D physically simulated biped locomotion     

Optimization-based locomotion planning,estimation, and control design for the atlas humanoid robot

This paper describes a collection of optimization algorithms for achieving dynamic planning, control, and state estimation for a bipedal robot designed to operate reliably in complex environments. To make challenging locomotion tasks tractable, we describe several novel applications of convex, mixed-integer, and sparse nonlinear optimization to problems ranging from footstep placement to whole-body planning and control. We also present a state estimator formulation that, when combined with our walking controller, permits highly precise execution of extended walking plans over non-flat terrain. We describe our complete system integration and experiments carried out on Atlas, a full-size hydraulic humanoid robot built by Boston Dynamics, Inc.     

Sensory regulation of stance-to-swing transition in generation of adaptive human walking: A simulation study

In this paper, we investigated sensory mechanisms to regulate the transition from the stance to swing phases in the generation of adaptive human bipedal walking based on a neuromusculoskeletal model. We examined the contributions of the sensory information from the force-sensitive afferents in the ankle extensor muscle and from the position-sensitive afferents from the hip, inspired by a neuro-mechanical simulation for the stepping of the hind legs of cats. Our simulation results showed that the sensory signals related to the force in the ankle extensor muscle make a larger contribution than sensory signals related to the joint angle at the hip to produce robust walking against disturbances, as observed in the simulation results of cat locomotion. This suggests that such a sensorimotor mechanism is a general property and is also embedded in the neuro-control system of human bipedal walking.     

Toward a human-like biped robot with compliant legs

Conventional models of bipedal walking generally assume rigid body structures, while elastic material properties seem to play an essential role in nature. On the basis of a novel theoretical model of bipedal walking, this paper investigates a model of biped robot which makes use of minimum control and elastic passive joints inspired from the structures of biological systems. The model is evaluated in simulation and a physical robotic platform by analyzing the kinematics and ground reaction force. The experimental results show that, with a proper leg design of passive dynamics and elasticity, an attractor state of human-like walking gait patterns can be achieved through extremely simple control without sensory feedback. The detailed analysis also explains how the dynamic human-like gait can contribute to adaptive biped walking.     

Pseudo-passive dynamic walkers designed by coupled evolution of the controller and morphology

In this paper we investigated the morphology and controller of biped robots. We viewed them as design components that together can induce dynamically stable bipedal locomotion. We conducted coupled evolution of the morphology and controller of a biped robot, consisting of nine links and eight joints, actuated by oscillators without sensor feedback in three-dimensional simulation. As a result, both pseudo-passive dynamic walkers and active-control walkers emerged, but the pseudo-passive dynamic walkers showed more dynamic stability than the active-control walkers. This is because compliant components in morphology function as noise filters and passive oscillators. Analysis on this latter class of walkers revealed that this was achieved by two novel functions: self-stabilization and self-regulation. Because these functions were handled by the passive dynamics induced in the robot morphology, due to its compliance, we concluded that a computational trade-off between the controller and morphology occurs in these devices. Finally, we have concluded that appropriate compliance is a key to achieving dynamical stability during locomotion.     

Asymptotically Stable Walking of a Five-Link Underactuated 3-D Bipedal Robot

This paper presents three feedback controllers that achieve an asymptotically stable, periodic, and fast walking gait for a 3-D bipedal robot consisting of a torso, revolute knees, and passive (unactuated) point feet. The walking surface is assumed to be rigid and flat; the contact between the robot and the walking surface is assumed to inhibit yaw rotation. The studied robot has 8 DOF in the single support phase and six actuators. In addition to the reduced number of actuators, the interest of studying robots with point feet is that the feedback control solution must explicitly account for the robot's natural dynamics in order to achieve balance while walking. We use an extension of the method of virtual constraints and hybrid zero dynamics (HZD), a very successful method for planar bipeds, in order to simultaneously compute a periodic orbit and an autonomous feedback controller that realizes the orbit, for a 3-D (spatial) bipedal walking robot. This method allows the computations for the controller design and the periodic orbit to be carried out on a 2-DOF subsystem of the 8-DOF robot model. The stability of the walking gait under closed-loop control is evaluated with the linearization of the restricted PoincarÉ map of the HZD. Most periodic walking gaits for this robot are unstable when the controlled outputs are selected to be the actuated coordinates. Three strategies are explored to produce stable walking. The first strategy consists of imposing a stability condition during the search of a periodic gait by optimization. The second strategy uses an event-based controller to modify the eigenvalues of the (linearized) PoincarÉ map. In the third approach, the effect of output selection on the zero dynamics is discussed and a pertinent choice of outputs is proposed, leading to stabilization without the use of a supplemental event-based controller.      

Towards goal-directed biped locomotion: Combining CPGs and motion primitives

In this paper it is presented a CPG approach based on phase oscillators to bipedal locomotion where the designer with little a priori knowledge is able to incrementally add basic motion primitives, reaching bipedal walking and other locomotor behaviors as final result. The proposed CPG aims to be a model free solution for the generation of bipedal walking, not requiring the use of inverse kinematical models and previously defined joint trajectories.The proposed incremental construction of bipedal walking allows an easier parametrization and performance evaluation throughout the design process. Furthermore, the approach provides for a developmental mechanism, which enables progressively building a motor repertoire. It would easily benefit from evolutionary robotics and machine learning to explore this aspect.The proposed CPG system also offers a good substrate for the inclusion of feedback mechanisms for modulation and adaptation. It is explored a phase regulation mechanism using load sensory information, observable in vertebrate legged animals.Results from simulations, on HOAP and DARwIn-OP in Webots software show the adequacy of the locomotor system to generate bipedal walk on different robots. Experiments on a DARwIn-OP demonstrates how it can accomplish locomotion and how the proposed work can generalize, achieving several distinct locomotor behaviors.     

A new artificial life body: biologically inspired dynamic bipedal humanoid robots

Recently, a biologically inspired, bipedal, dynamic, humanoid robot was developed at the Artificial Life and Robotics Laboratory of Oita University. This bipedal humanoid robot is able to walk dynamically and to go up and down stairs. The central pattern generator developed produces various types of walking pattern. This robot has a pair of small CMOS color CCD cameras, a speaker, and a microphone in the head part, and will have a GPS, a portable telephone, and other sensors in the body part, so that the integration of locomotion and behavior to achieve specific demonstrations will be realized. This project develops dynamic mobility and the ability for autonomous recognition and navigation using the biological central nervous system, the brain system, and the real-time control system. Also, the design principles that demonstrate the dynamic interaction between neural and mechanical controls will be clarified. In Phase I, the platform of a small, bipedal, humanoid robot is used to develop autonomous locomotion and autonomous sensing and navigation. In Phase II of the project, an iteration on the platform design for human-size, bipedal, humanoid robots will be performed for operational testing. The development of bipedal humanoid robots that capture biological systems with unique principles and practices could dramatically increase their performance in tasks for national security needs.This work was presented in part at the 8th International Symposium on Artificial Life and Robotics, Oita, Japan, January 24–26, 2003