Whole-body control (WBC) is a generic task-oriented control method for feedback control of loco-manipulation behaviors in humanoid robots. The combination of WBC and model-based walking controllers has been widely utilized in various humanoid robots. However, to date, the WBC method has not been employed for unsupported passive-ankle dynamic locomotion. As such, in this paper, we devise a new WBC, dubbed whole-body locomotion controller (WBLC), that can achieve experimental dynamic walking on unsupported passive-ankle biped robots. A key aspect of WBLC is the relaxation of contact constraints such that the control commands produce reduced jerk when switching foot contacts. To achieve robust dynamic locomotion, we conduct an in-depth analysis of uncertainty for our dynamic walking algorithm called time-to-velocity-reversal (TVR) planner. The uncertainty study is fundamental as it allows us to improve the control algorithms and mechanical structure of our robot to fulfill the tolerated uncertainty. In addition, we conduct extensive experimentation for: 1) unsupported dynamic balancing (i.e. in-place stepping) with a six degree-of-freedom (DoF) biped, Mercury; 2) unsupported directional walking with Mercury; 3) walking over an irregular and slippery terrain with Mercury; and 4) in-place walking with our newly designed ten-DoF viscoelastic liquid-cooled biped, DRACO. Overall, the main contributions of this work are on: a) achieving various modalities of unsupported dynamic locomotion of passive-ankle bipeds using a WBLC controller and a TVR planner, b) conducting an uncertainty analysis to improve the mechanical structure and the controllers of Mercury, and c) devising a whole-body control strategy that reduces movement jerk during walking.
Passive walking robots @cite_10 @cite_26 fall in the dynamic locomotion category too. These studies shed light on the important aspects of biped locomotion, but do not provide direct application for feedback control related to our methods. On the other hand, the progress made in actuated planar biped locomotion is impressive. @cite_21 @cite_23 show biped robots running and their capability to recover from disturbances on irregular terrains. However, there is an obvious gap between supported (or constrained) locomotion and unsupported walking. @cite_30 shows unsupported single leg hopping, which is a remarkable accomplishment. Besides the strong contribution in dynamic locomotion of that work, the study omitted several important aspects of unsupported biped locomotion such as body posture control, continuous interaction of the stance leg through the ground contact phases, and disturbances from the other limbs' motion, which are a focus of our paper.
@cite_30 @cite_26 @cite_21 @cite_23 @cite_10
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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 Poincare 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) Poincare 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. Legged locomotion on flowing ground (e.g., granular media) is unlike locomotion on hard ground because feet experience both solid- and fluid-like forces during surface penetration. Recent bioinspired legged robots display speed relative to body size on hard ground comparable with high-performing organisms like cockroaches but suffer significant performance loss on flowing materials like sand. In laboratory experiments, we study the performance (speed) of a small (2.3 kg) 6-legged robot, SandBot, as it runs on a bed of granular media (1-mm poppy seeds). For an alternating tripod gait on the granular bed, standard gait control parameters achieve speeds at best 2 orders of magnitude smaller than the 2 body lengths s (≈60 cm s) for motion on hard ground. However, empirical adjustment of these control parameters away from the hard ground settings restores good performance, yielding top speeds of 30 cm s. Robot speed depends sensitively on the packing fraction φ and the limb frequency ω, and a dramatic transition from rotary walking to slow swimming occurs when φ becomes small enough and or ω large enough. We propose a kinematic model of the rotary walking mode based on generic features of penetration and slip of a curved limb in granular media. The model captures the dependence of robot speed on limb frequency and the transition between walking and swimming modes but highlights the need for a deeper understanding of the physics of granular media. We propose a constructive control design for stabilization of non-periodic trajectories of underactuated robots. An important example of such a system is an underactuated âdynamic walkingâ biped robot traversing rough or uneven terrain. The stabilization problem is inherently challenging due to the nonlinearity, open-loop instability, hybrid (impact) dynamics, and target motions which are not known in advance. The proposed technique is to compute a transverse linearization about the desired motion: a linear impulsive system which locally represents âtransversalâ dynamics about a target trajectory. This system is then exponentially stabilized using a modified receding-horizon control design, providing exponential orbital stability of the target trajectory of the original nonlinear system. The proposed method is experimentally verified using a compass-gait walker: a two-degree-of-freedom biped with hip actuation but pointed stilt-like feet. The technique is, however, very general and can be applied to a wide variety of hybrid nonlinear systems. While legged animals are adept at traversing rough landscapes, it remains a very challenging task for a legged robot to negotiate unknown terrain. Control systems for legged robots are plagued by dynamic constraints from underactuation, actuator power limits, and frictional ground contact; rather than relying purely on disturbance rejection, considerable advantage can be obtained by planning nominal trajectories which are more easily stabilized. In this paper, we present an approach for designing nominal periodic trajectories for legged robots that maximize a measure of robustness against uncertainty in the geometry of the terrain. We propose a direct collocation method which solves simultaneously for a nominal periodic control input, for many possible one-step solution trajectories (using ground profiles drawn from a distribution over terrain), and for the periodic solution to a jump Riccati equation which provides an expected infinite-horizon cost-to-go for each of these samples. We demonstrate that this trajectory optimization scheme can recover the known deadbeat open-loop control solution for the Spring Loaded Inverted Pendulum (SLIP) on unknown terrain. Moreover, we demonstrate that it generalizes to other models like the bipedal compass gait walker, resulting in a dramatic increase in the number of steps taken over moderate terrain when compared against a limit cycle optimized for efficiency only. Passive dynamic walking refers to a class of bipedal machines that are able to walk down a gentle slope with no external control or energy input. The legs swing naturally as pendula, and conservation of angular momentum governs the contact of the swing foot with the ground. Previous machines have been limited to planar motions. We extend the planar motions to allow for tilting side to side (roll motion). Passive walking cycles exist, but the roll motion is unstable, resembling that of an inverted pendulum. The instability is due to mismatching of roll velocity with the ground contact conditions. Several strategies are presented for stabilizing this motion, of which the quasi-static control of step width is determined to be both simple and efficient. The authors have developed five kinds of biped locomotive robots so far. They are named BIPER-1, 2, 3, 4, and 5. All of them are statically unstable but can perform a dynamically stable walk with suitable control. BIPER-1 and BIPER-2 walk only sideways. BIPER-3 is a stilt-type robot whose foot contacts occur at a point and who can walk sideways, back ward, and forward. BIPER-4's legs have the same degrees of freedom as human legs. BIPER-5 is similar to BIPER-3, but in the case of BIPER-5 all apparatus, such as the computer, are mounted on it.This paper deals with the control theory used for BIPER-3 and BIPER-4. In both cases, basically the same control method is applied. The most important point is that the mo tion of either robot during the single-leg support phase can be approximated by the motion of an inverted pendulum. Ac cordingly, in this paper, dynamic walk is considered to be a series of inverted-pendulum motions with appropriate condi tions of connection. 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. Achieving effective locomotion on diverse terrestrial substrates can require subtle changes of limb kinematics. Biologically inspired legged robots (physical models of organisms) have shown impressive mobility on hard ground but suffer performance loss on unconsolidated granular materials like sand. Because comprehensive limb–ground interaction models are lacking, optimal gaits on complex yielding terrain have been determined empirically. To develop predictive models for legged devices and to provide hypotheses for biological locomotors, we systematically study the performance of SandBot, a small legged robot, on granular media as a function of gait parameters. High performance occurs only in a small region of parameter space. A previously introduced kinematic model of the robot combined with a new anisotropic granular penetration force law predicts the speed. Performance on granular media is maximized when gait parameters utilize solidification features of the granular medium and minimize limb interference. Whole-body control (WBC) is a generic task-oriented control method for feedback control of loco-manipulation behaviors in humanoid robots. The combination of WBC and model-based walking controllers has been widely utilized in various humanoid robots. However, to date, the WBC method has not been employed for unsupported passive-ankle dynamic locomotion. As such, in this paper, we devise a new WBC, dubbed whole-body locomotion controller (WBLC), that can achieve experimental dynamic walking on unsupported passive-ankle biped robots. A key aspect of WBLC is the relaxation of contact constraints such that the control commands produce reduced jerk when switching foot contacts. To achieve robust dynamic locomotion, we conduct an in-depth analysis of uncertainty for our dynamic walking algorithm called time-to-velocity-reversal (TVR) planner. The uncertainty study is fundamental as it allows us to improve the control algorithms and mechanical structure of our robot to fulfill the tolerated uncertainty. In addition, we conduct extensive experimentation for: 1) unsupported dynamic balancing (i.e. in-place stepping) with a six degree-of-freedom (DoF) biped, Mercury; 2) unsupported directional walking with Mercury; 3) walking over an irregular and slippery terrain with Mercury; and 4) in-place walking with our newly designed ten-DoF viscoelastic liquid-cooled biped, DRACO. Overall, the main contributions of this work are on: a) achieving various modalities of unsupported dynamic locomotion of passive-ankle bipeds using a WBLC controller and a TVR planner, b) conducting an uncertainty analysis to improve the mechanical structure and the controllers of Mercury, and c) devising a whole-body control strategy that reduces movement jerk during walking. This paper briefly presents the process of formally achieving bipedal robotic walking through controller synthesis inspired by human locomotion. Motivated by the hierarchical control present in humans, we begin by viewing the human as a "black box" and describe outputs, or virtual constraints, that appear to characterize human walking. By considering the equivalent outputs for the bipedal robot, a nonlinear controller can be constructed that drives the outputs of the robot to the outputs of the human; moreover, the parameters of this controller can be optimized so that stable robotic walking is provably achieved while simultaneously producing outputs of the robot that are as close as possible to those of a human. Finally, considering a control Lyapunov function based representation of these outputs allows for the class of controllers that provably achieve stable robotic walking can be greatly enlarged. The end result is the generation of bipedal robotic walking that is remarkably human-like and is experimentally realizable, as evidenced by the implementation of the resulting controllers on multiple robotic platforms. Physics-based simulation and control of biped locomotion is difficult because bipeds are unstable, underactuated, high-dimensional dynamical systems. We develop a simple control strategy that can be used to generate a large variety of gaits and styles in real-time, including walking in all directions (forwards, backwards, sideways, turning), running, skipping, and hopping. Controllers can be authored using a small number of parameters, or their construction can be informed by motion capture data. The controllers are applied to 2D and 3D physically-simulated character models. Their robustness is demonstrated with respect to pushes in all directions, unexpected steps and slopes, and unexpected variations in kinematic and dynamic parameters. Direct transitions between controllers are demonstrated as well as parameterized control of changes in direction and speed. Feedback-error learning is applied to learn predictive torque models, which allows for the low-gain control that typifies many natural motions as well as producing smoother simulated motion. This paper proposes a new control scheme of decentralized multi-legged robot based on Follow-the-Contact-Point (FCP) gait control. In this control scheme, the first legs contact the points allocated on the terrain and the following legs touch the foot on the point which the fore leg is contacting. By creating adequate contacting points on the environment, the robot can be navigated successfully. Since the position information of the contacting points is relayed based on physical information of the legs, each leg does not need the global position of the contacting point. As a result, the proposed control scheme realizes decentralized architecture. This paper introduces the control law for the robot walking on even terrain. Finally, the result of physical simulation of 20-legged robot shows the availability of the proposed method. The purpose of this paper is to apply methods from geometric mechanics to the analysis and control of bipedal robotic walkers. We begin by introducing a generalization of Routhian reduction, functional Routhian Reduction, which allows for the conserved quantities to be functions of the cyclic variables rather than constants. Since bipedal robotic walkers are naturally modeled as hybrid systems, which are inherently nonsmooth, in order to apply this framework to these systems it is necessary to first extend functional Routhian reduction to a hybrid setting. We apply this extension, along with potential shaping and controlled symmetries, to derive a feedback control law that provably results in walking gaits on flat ground for a three-dimensional bipedal walker given walking gaits in two dimensions. It is known that for a large magnitude push a human or a humanoid robot must take a step to avoid a fall. Despite some scattered results, a principled approach towards "when and where to take a step" has not yet emerged. Towards this goal, we present methods for computing capture points and the capture region, the region on the ground where a humanoid must step to in order to come to a complete stop. The intersection between the capture region and the base of support determines which strategy the robot should adopt to successfully stop in a given situation. Computing the capture region for a humanoid, in general, is very difficult. However, with simple models of walking, computation of the capture region is simplified. We extend the well-known linear inverted pendulum model to include a flywheel body and show how to compute exact solutions of the capture region for this model. Adding rotational inertia enables the humanoid to control its centroidal angular momentum, much like the way human beings do, significantly enlarging the capture region. We present simulations of a simple planar biped that can recover balance after a push by stepping to the capture region and using internal angular momentum. Ongoing work involves applying the solution from the simple model as an approximate solution to more complex simulations of bipedal walking, including a 3D biped with distributed mass. Planar, underactuated, biped walkers form an important domain of applications for hybrid dynamical systems. This paper presents the design of exponentially stable walking controllers for general planar bipedal systems that have one degree-of-freedom greater than the number of available actuators. The within-step control action creates an attracting invariant set - a two-dimensional zero dynamics submanifold of the full hybrid model $whose restriction dynamics admits a scalar linear time-invariant return map. Exponentially stable periodic orbits of the zero dynamics correspond to exponentially stabilizable orbits of the full model. A convenient parameterization of the hybrid zero dynamics is imposed through the choice of a class of output functions. Parameter optimization is used to tune the hybrid zero dynamics in order to achieve closed-loop, exponentially stable walking with low energy consumption, while meeting natural kinematic and dynamic constraints. The general theory developed in the paper is illustrated on a five link walker, consisting of a torso and two legs with knees. Legged robots can potentially venture beyond the limits of wheeled vehicles. While creating controllers for such robots by hand is possible, evolutionary algorithms are an alternative that can reduce the burden of hand-crafting robotic controllers. Although major evolutionary approaches to legged locomotion can generate oscillations through popular techniques such as continuous time recurrent neural networks (CTRNNs) or sinusoidal input, they typically face a challenge in maintaining long-term stability. The aim of this paper is to address this challenge by introducing an effective alternative based on a new type of neuron called a single-unit pattern generator (SUPG). The SUPG, which is indirectly encoded by a compositional pattern producing network (CPPN) evolved by HyperNEAT, produces a flexible temporal activation pattern that can be reset and repeated at any time through an explicit trigger input, thereby allowing it to dynamically recalibrate over time to maintain stability. The SUPG approach, which is compared to CTRNNs and sinusoidal input, is shown to produce natural-looking gaits that exhibit superior stability over time, thereby providing a new alternative for evolving oscillatory locomotion. In this work, we present WALK-MAN, a humanoid platform that has been developed to operate in realistic unstructured environment, and demonstrate new skills including powerful manipulation, robust balanced locomotion, high-strength capabilities, and physical sturdiness. To enable these capabilities, WALK-MAN design and actuation are based on the most recent advancements of series elastic actuator drives with unique performance features that differentiate the robot from previous state-of-the-art compliant actuated robots. Physical interaction performance is benefited by both active and passive adaptation, thanks to WALK-MAN actuation that combines customized high-performance modules with tuned torque velocity curves and transmission elasticity for high-speed adaptation response and motion reactions to disturbances. WALK-MAN design also includes innovative design optimization features that consider the selection of kinematic structure and the placement of the actuators with the body structure to maximize the robot performance. Physical robustness is ensured with the integration of elastic transmission, proprioceptive sensing, and control. The WALK-MAN hardware was designed and built in 11 months, and the prototype of the robot was ready four months before DARPA Robotics Challenge (DRC) Finals. The motion generation of WALK-MAN is based on the unified motion-generation framework of whole-body locomotion and manipulation (termed loco-manipulation). WALK-MAN is able to execute simple loco-manipulation behaviors synthesized by combining different primitives defining the behavior of the center of gravity, the motion of the hands, legs, and head, the body attitude and posture, and the constrained body parts such as joint limits and contacts. The motion-generation framework including the specific motion modules and software architecture is discussed in detail. A rich perception system allows the robot to perceive and generate 3D representations of the environment as well as detect contacts and sense physical interaction force and moments. The operator station that pilots use to control the robot provides a rich pilot interface with different control modes and a number of teleoperated or semiautonomous command features. The capability of the robot and the performance of the individual motion control and perception modules were validated during the DRC in which the robot was able to demonstrate exceptional physical resilience and execute some of the tasks during the competition. For an effective intelligent active mobility assistance robot, the walking pattern of a patient or an elderly person has to be analyzed precisely. A well-known fact is that the walking patterns are gaits, that is, cyclic patterns with several consecutive phases. These cyclic motions can be modeled using the consecutive gait phases. In this paper, we present a completely non-invasive framework for analyzing a normal human walking gait pattern. Our framework utilizes a laser range finder sensor to collect the data, a combination of filters to preprocess these data, and an appropriately synthesized Hidden Markov Model (HMM) for state estimation, and recognition of the gait data. We demonstrate the applicability of this setup using real data, collected from an ensemble of different persons. The results presented in this paper demonstrate that the proposed human data analysis scheme has the potential to provide the necessary methodological (modeling, inference, and learning) framework for a cognitive behavior-based robot control system. More specifically, the proposed framework has the potential to be used for the recognition of abnormal gait patterns and the subsequent classification of specific walking pathologies, which is needed for the development of a contextaware robot mobility assistant. Traditional motion planning approaches for multilegged locomotion divide the problem into several stages, such as contact search and trajectory generation. However, reasoning about contacts and motions simultaneously is crucial for the generation of complex whole-body behaviors. Currently, coupling theses problems has required either the assumption of a fixed gait sequence and flat terrain condition, or nonconvex optimization with intractable computation time. In this letter, we propose a mixed-integer convex formulation to plan simultaneously contact locations, gait transitions, and motion, in a computationally efficient fashion. In contrast to previous works, our approach is not limited to flat terrain nor to a prespecified gait sequence. Instead, we incorporate the friction cone stability margin, approximate the robot's torque limits, and plan the gait using mixed-integer convex constraints. We experimentally validated our approach on the HyQ robot by traversing different challenging terrains, where nonconvexity and flat terrain assumptions might lead to suboptimal or unstable plans. Our method increases the motion robustness while keeping a low computation time. In the area of biped robot research, much progress has been made in the past few years. However, some difficulties remain to be dealt with, particularly about the implementation of fast and dynamic walking gaits, in other words anthropomorphic gaits, especially on uneven terrain. In this perspective, both concepts of center of pressure (CoP) and zero moment point (ZMP) are obviously useful. In this paper, the two concepts are strictly defined, the CoP with respect to ground-feet contact forces, the ZMP with respect to gravity plus inertia forces. Then, the coincidence of CoP and ZMP is proven, and related control aspects are examined. Finally, a virtual CoP-ZMP is defined, allowing us to extend the concept when walking on uneven terrain. This paper is a theoretical study. Experimental results are presented in a companion paper, analyzing the evolution of the ground contact forces obtained from a human walker wearing robot feet as shoes.