Push recovery control for the underactuated lower extremity exoskeleton based on improved capture point concept

In this paper, for the first time, experimental tests of complete offline walking gaits generated by the essential model are performed. This model does not make simplifications in the dynamics of the robot, and its main advantage is the definition of desired Zero Moment Point trajectories. The designed gaits are implemented in the NAO robot, where starting and stopping stages are also included. Simulations in MATLAB and Webots, and experiments with the real robot are shown. Also, important remarks about the implementation of walking trajectories in the NAO robot are included, such as dealing with the hip joint shared by both legs. A comparison between the linear inverted pendulum (LIP) model and the essential model is also addressed in the experiments. As expected, the robot fails following the offline gait generated by the LIP model, but it does not with the essential model. Moreover, in order to push the boundaries of the essential model, a complex gait is designed with a vertical motion of the center of mass and an abrupt movement of the arms. As shown in experiments, no external balance controller is required to perform this complex gait. Thus, the efficiency of the essential model to design stable open-loop complex gaits is verified.

In order to protect sensitive residual limb soft tissues, lower limb prostheses need to control torsional loads during gait. To assist with the design of a torsional prosthesis, this paper used simple mechanical elements to model the behavior of the human ankle in the transverse plane during straight walking. Motion capture data were collected from ten able-bodied subjects walking straight ahead at self-selected walking speeds. Gait cycle data were separated into four distinct states, and passive torsional springs and dampers were chosen to model the behavior in each state. Since prosthetic design is facilitated by simplicity, it was desirable to investigate if elastic behavior could account for the physiological ankle moment and include viscous behavior only if necessary to account for the inadequacies of the spring model. In all four states, a springlike behavior was able to account for most of the physiological ankle moments, rendering the use of a damper unnecessary. In State 1, a quadratic torsional spring was chosen to model the behavior, while linear torsional springs were chosen for States 2-4. A prosthetic system that actively changes stiffness could be able to replicate the physiological behavior of the human ankle in the transverse plane. The results of this study will contribute to the mechanical design and control of a biomimetic torsional prosthesis for lower limb amputees.

A robot foot can slip when the horizontal shear force acting on the foot exceeds the frictional force between the foot and the ground. In the linear inverted-pendulum (LIP) model, the vertical height of the center of mass (COM) is kept constant, and the vertical force is always equal to the gravitational force at any walking speed. However, the horizontal force increases upon increasing the walking speed. This restriction on the vertical force in the LIP model can cause the robot foot to slip at fast walking speeds, as the horizontal force can exceed the frictional force, which is proportional to the vertical force. In this study, we present an optimization method to generate vertical COM motion to maintain the utilized coefficient of friction (uCOF) less than the available coefficient of friction between the foot and the ground, and to minimize the mechanical work of the COM. Vertical motions at various speeds are generated using the proposed optimization method. Subsequently, the generated COM motion patterns are used as reference trajectories of the COM in robot simulation. Optimization and simulation results demonstrate that the mechanical work and uCOF decrease because of the vertical motion. This study suggests a way to generate slip-safe and energy-efficient COM patterns, which, in turn, overcome the limitations of the LIP model by adding vertical COM motion.

This paper builds up on the Capture Point concept and exploits the simple form of the dynamical equations of the Linear Inverted Pendulum model when formulated in terms of the center of mass and the Capture Point. The presented methods include (i) the derivation of a Capture Point (CP) control principle based on the natural dynamics of the linear inverted pendulum (LIP), which stabilizes the walking robot and motivates (ii) the design of a CP tracking and a CP end-of-step controller. The exponential stability of the CP control law is proven. Tilting is avoided by proper projection of the commanded zero moment point. The robustness of the derived control algorithms is analyzed analytically and verified in simulation and experiments.

This paper proposes an analysis of the effect of vertical motion of the center of mass (COM) during humanoid walking. The linear inverted pendulum (LIP) model is classically used to deal with humanoid balance during walking. The effects on energy consumption of the COM height remaining constant for humanoid robots, or varying like human beings are studied here. Two approaches are introduced for the comparison: the LIP which offers the great advantage of analytical solving (i.e., fast and easy calculations), and a numerical solving of the IP dynamics, which allows varying the height of the center of mass during walking. The results are compared using a sthenic criterion in a 3D dynamics simulation of the humanoid robot Romeo (Aldebaran Robotics Company) and show a consequent reduction of the robot torque solicitation when the COM oscillates vertically.

In order to deal with the problem of imbalance of the elderly in the process of walking on level ground, this paper proposes a hip exoskeleton with series elastic actuator (SEA) to assist the wearer to adjust the step width, step length and step frequency in real time during walking to maintain balance walking. Through the built multi-sensor fusion gait perturbation and perception integrated platform, the experimenter’s autonomous recovery of balance experiment and exoskeleton-assisted human body's recovery of balance experiment under external wrench state were carried out respectively. The perturbations were applied in four directions to the experimenter while walking, which verified the validity of the balance evaluation model and the assisting effect of the exoskeleton in restoring the balance of human walking. Firstly, according to the established kinematics model, the displacement and velocity of the experimenter's center of mass during walking are calculated, and the system is simplified to a linear inverted pendulum model (LIPM) to evaluate the motion state. Secondly, a balance state evaluation model is established based on the instantaneous capture point (ICP) theory, and the balance state evaluation of the human body is realized by judging the positional relationship between the instantaneous capture point and the support range of the feet. Finally, according to the step strategy in the human body balance strategy, the magnitude of the auxiliary torque when the experimenter is out of balance is calculated through the relative position of the center of mass and the instantaneous capture point. Therefore, it can be shown that the balance evaluation model and exoskeleton control strategy we established can provide the balance restoring torque for the experimenter to swing the leg when the system is about to become unbalanced, which can effectively slow down the unbalanced trend.KeywordsHip exoskeletonPerturbation platformSeries elastic actuatorBalance recovery

This paper proposes an online uniform foot location planning method (UPMPC) based on model predictive control (MPC) for solving the problem of large posture changes during gait transitioning. This method converts the foot location planning into a discrete-time MPC problem. The core part of the method is to complete the planning of the foot location based on the linear inverted pendulum (LIP) model and the simplified robot dynamics model. By unifying the input foot location at each time step, the solution time is shortened. The final simulation experiment compares the results of using the UPMPC and foot location planning method with heuristic function (HF) for gait transitioning, respectively. This result demonstrates that the UPMPC can complete the gait transitioning task and adapt to large changes in posture during gait transitioning. In addition, the results also show the good performance of UPMPC in fixed gait.

The hardware compatibility of legged locomotion is often illustrated by Zero Moment Point (ZMP) that has been extensively studied for decades. One of the most popular models for computing the ZMP is the linear inverted pendulum (LIP) model that expresses ZMP as a linear function of the center of mass(COM) and its acceleration. In the real world, however, it may not accurately predict the true ZMP of hardware due to various reasons such as unmodeled dynamics and differences between simulation model and hardware. In this paper, we aim to improve the theoretical ZMP model by learning the real hardware dynamics from experimental data. We first optimize the motion plan using the theoretical ZMP model and collect COP data by executing the motion on a force plate. We then train a new ZMP model that maps the motion plan variable to the actual ZMP and use the learned model for finding a new hardware-compatible motion plan. Through various locomotion tasks of a quadruped, we demonstrate that motions planned for the learned ZMP model are compatible on hardware when those for the theoretical ZMP model are not. Furthermore, experiments using ZMP models with different complexities reveal that overly complex models may suffer from over-fitting even though they can potentially represent more complex, unmodeled dynamics.

This paper proposes a stabilization method for dynamic walking of a bipedal robot with real-time optimization of capture point trajectories. We used the capture point trajectories to generate the control input, which is the desired zero moment point (ZMP) with a sliding-mode ZMP controller to follow the desired ZMP. This method enables the robot to implement various dynamic walking commands, such as forward stride, lateral stride, walking direction, single support time, and double support time. We also adopted enhanced dynamics with the three mass linear inverted pendulum model (3M-LIPM). First, the compensated ZMP is calculated by both walking commands and kinematic configuration of the robot in closed form. Then, the walking pattern is obtained by using initial and boundary conditions of the 3M-LIPM, which satisfies the walking commands. The capture point (CP) trajectory is optimized in real time to control the walking stability and a capture point tracking controller is used for tracking the optimized CP trajectory, which generates an optimal control input that is near the center of the support polygon. The performance of the proposed stabilization method was verified by a dynamics simulator, Webots, and comparison with the original capture point controller-based walking algorithm is presented.

For decades, the biomechanical description of quiet human stance has been dominated by the single inverted pendulum (SIP) paradigm. However, in the past few years, the SIP model family has been falsified as an explanatory approach. Double inverted pendulum models have recently proven to be inappropriate. Human topology with three major leg joints suggests in a natural way to examine triple inverted pendulum (TIP) models as an appropriate approach. In this study, we focused on formulating a TIP model that can synthesise stable balancing attractors based on minimalistic sensor information and actuation complexity. The simulated TIP oscillation amplitudes are realistic in vertical direction. Along with the horizontal ankle, knee and hip positions, though, all simulated joint angle amplitudes still exceed the measured ones about threefold. It is likely that they could be eventually brought down to the physiological range by using more sensor information. The TIP systems’ eigenfrequency spectra come out as another major result. The eigenfrequencies spread across about . Our main result is that joint stiffnesses can be reduced even below statically required values by using an active hip torque balancing strategy. When reducing mono- and bi-articular stiffnesses further down to levels threatening dynamic stability, the spectra indicate a change from torus-like (stable) to strange (chaotic) attractors. Spectra of measured ground reaction forces appear to be strange-attractor-like. We would conclude that TIP models are a suitable starting point to examine more deeply the dynamic character of and the essential structural properties behind quiet human stance.Abbreviations and technical termsInverted pendulum body exposed to gravity and pivoting in a joint around position of unstable equilibrium (operating point)SIP single inverted pendulum: one rigid body pivoting around fixation to the ground (external joint)DIP double inverted pendulum: two bodies; external and internal joint operate around instabilityTIP triple inverted pendulum: three bodies; external and both internal joints operate around instabilityQIP quadruple inverted pendulum: four bodies, foot replaces external joint; all three internal joints operate around instabilityEigenfrequency characteristic frequency that a physical system is oscillating at when externally excited at a limited energy levelDOF degree of freedom; in mechanics: linear displacement or angle or combination thereof Mono-articular stiffness: coefficient of proportionality between mechanical displacement of a DOF and restoring force/torque component in the respective DOFBi-articular stiffness coefficient of proportionality between mechanical displacement of a DOF and restoring force/torque component in another DOFGRF ground reaction forceHAT segment including head, arms and trunkCOM centre of massCOP centre of pressure in the plane of the force platform surface

This paper focuses on real-time walking pattern generation for humanoid robots with linear inverted pendulum model (LIPM). In general, there are many issues in generating proper walking patterns of center of mass and zero moment point (ZMP) with the LIPM since the LIPM has two drawbacks such as instability and non-minimum phase property. For resolving these difficulties, the paper proposes a new real-time approach by combining a feedback and a feedforward controller. The feedback controller employs a pole placement method which shifts the poles of the LIPM in order to improve system stability. The feedforward controller utilizes advanced pole-zero cancelation by series approximation method (APZCSA) for reducing non-minimum phase property which occurs by an unstable zero and is not able to be dealt with by the feedback controller. In addition, the APZCSA improves the tracking error induced by finite series approximation. Using the two controllers, the proposed method makes the transfer function of overall walking pattern generation system approximately unity and consequently generates a stable walking pattern which follows a desired ZMP according to walking path. The efficiency of the proposed method is verified by walking pattern planning examples and experiments with the humanoid robot MAHRU-R.

Human biped locomotion is an ultimate style of biological movement that is a highly evolved function. Biped locomotion by robots is a dream to be attained by the most highly evolved or integrated technology, and research on this has a history of over 30 years. Many methods of generating gaits have been proposed. There has been a tendency to reduce the complicated dynamics of a walking robot to a simple inverted pendulum (Hemami et al., 1973), and to control its motion according to pre-designed time-dependent trajectories while guaranteeing zero moment point (ZMP) conditions (Vukobratovi & Stepanenko, 1972). Although such approaches have successfully been applied to practical applications and nowadays successful biped-himanoids are developed by them, problems on gait performances still remain. Several advanced approaches on the other hand have taken the robot's dynamics into account for generating gaits based on natural dynamics. Miura and Shimoyama studied dynamic bipedal walking without ankle-joint actuation (Miura & Shimoyama, 1984) and they developed robots on stilts whose foot contact occurred at a point. Sano and Furusho accomplished natural dynamic biped walking based on angular momentum using ankle-joint actuation (Sano & Furusho, 1990). Kajita proposed a method of control based on a linear inverted pendulum model with a potential-energy-conserving orbit (Kajita et al., 1992). These approaches utilized the robot’s own dynamics effectively but did not investigate the energy-efficiency by introducing performance indices. It was unclear whether or not efficient gaits were generated. McGeer's passive dynamic walking (PDW) (McGeer, 1990) has provided clues to solve these problems. Passive-dynamic walkers can walk without any actuation on a gentle slope, and they provide an optimal solution to the problem of generating a natural and energy-efficient gait. The objective most expected to be met by PDW is to attain natural, high-speed energyefficient dynamic bipedal walking on level ground like humans do. However, we need to supply power-input to the robot by driving its joint-actuators to continue stable walking on level ground, and certain methods of supplying power must be introduced. Ankle-joint torque is mathematically very important for effectively propelling the robot's center of mass (CoM) in the walking direction, and it is thus required relatively more often than other joint torques. However, to exert ankle-joint torque on a passive-dynamic walker, we need to add feet and this creates the ZMP constraint problem. We clarified that there is a trade-off between optimal gait and ZMP conditions through parametric studies, and O pe n A cc es s D at ab as e w w w .ite ch on lin e. co m

Configuration synthesis of variable stiffness mechanisms based on guide-bar mechanisms with length-adjustable links

To achieve bipedal walking in real human environments, a bipedal robot should be capable of modifiable walking both on uneven terrain with different heights and on flat terrain. In this paper, a novel walking pattern generator based on a 3-D linear inverted pendulum model (LIPM) is proposed to achieve this objective. By adopting a zero moment point (ZMP) variation scheme in real time, it is possible to change the center-of-mass (COM) position and the velocity of the 3-D LIPM throughout the single support phase. Consequently, the proposed method offers the ability to generate a modifiable pattern for walking on uneven terrain without the necessity for any extra footsteps to adjust the COM motion. In addition, a control strategy for bipedal walking on uneven terrain with unknown height is developed. The torques and ground reaction force are measured through force-sensing resisters (FSRs) on each foot and the foot of the robot is modeled as three virtual spring-damper models for the disturbance compensation. The methods for generating the foot and vertical COM of 3-D LIPM trajectories are proposed to achieve modifiable bipedal walking on uneven terrain without any information regarding the height of the terrain. The effectiveness of the proposed method is confirmed through dynamic simulations.

In this paper, we present a conceptional design framework for jumping robots for lunar exploration. A method is developed for spring placement and sizing that maximises the onboard elastic potential energy storage, which is essential for space missions. In the class of rhomboidal linkage robots, the analysis shows that torsion springs placed at the knee joints store more energy than the commonly used extension or linear compression springs for a given charging-actuator force; torsion springs store around 80% of the idealized maximum attainable elastic energy storage, compared to only 60% for an extension spring. A physical demonstrator is developed using torsion springs, and exhibits repeatable jumps with an average jump height of 1.1m under earth gravity, equivalent to 6.7m under lunar gravity. However, preliminary trials show the choice of substrate is shown to influence the jump height. This effect is predicted to be pronounced when jumping from lunar regolith.