Real-Time Walking Pattern Generation Method for Humanoid Robots by Combining Feedback and Feedforward Controller

This paper proposes new walking pattern method for the humanoid robots. The proposed method based on the inverted pendulum uses the zero moment point(ZMP) and the center of mass(CoM). And our approach consists of feedforward controller and feedback controller. As the feedforward controller, pole-zero cancellation by series approximation(PZCSA) control plays a role of reducing the inherent property of inverted pendulum model, that is, non-minimum phase property due to the unstable zero. As the feedback controller, linear quadratic regulator(LQR) is utilized for tracking effectively the desired ZMP according to footprints of the humanoid robots. The proposed method generates the walking pattern with the combination of LQR and PZCSA. The efficiency of the proposed method is verified by simulation of generating the walking pattern.

Generating nonlinear trajectories of walking patterns is one of the most important problems in stability a humanoid robot when it walks on different ground conditions. In order to solve this problem, a desired Zero Moment Point (ZMP) trajectory is firstly designed and then a Center of Mass (CoM) trajectory will be created based on this ZMP. Hence, the preview control formulation which follows the planned ZMP patterns while reducing the jerk (acceleration derivation) is considered to implement this trajectory. In this study, the walking pattern for bipedal robot is generated by using a cart-table model. The procedure of apply a preview controller to the cart-table model will be presented in this investigation. After that, the position of each leg joint of bipedal robot is also calculated by using the proposed CoM Jacobian. Finally, computer simulations are performed by utilizing RecurDyn and MATLAB softwares to validate the proposed preview control formulation for the nonlinear walking patterns generation of a Bioloid humanoid robot.

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> The control of a biped humanoid is a challenging task due to the hard-to-stabilize dynamics. Walking reference trajectory generation is a key problem. Linear Inverted Pendulum Model (LIPM) and Zero Moment Point (ZMP) Criterion-based approaches in stable walking reference generation are reported. In these methods, generally, the ZMP reference during a stepping motion is kept fixed in the middle of the supporting foot sole. This kind of reference generation lacks naturalness, in that the ZMP in the human walk does not stay fixed, but it moves forward under the supporting foot. This paper proposes a reference generation algorithm based on the LIPM and moving support foot ZMP references. The application of Fourier series approximation simplifies the solution, and it generates a smooth ZMP reference. A simple inverse kinematics-based joint space controller is used for the tests of the developed reference trajectory through full-dynamics 3-D simulation. A 12-DOF biped robot model is used in the simulations. Simulation studies suggest that the moving ZMP references are more energy efficient than the ones with fixed ZMP under the supporting foot. The results are promising for implementations. </para>

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, 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.

Linear Inverted Pendulum model (LIPM) is a classical theory of biped robot gait planning. However, the fixed Zero Moment Point (ZMP) of each step does not conform to the laws of human motion. In this paper, we proposed a VSP-based gait planning algorithm to make the ZMP trajectory comply the law of Heel to Toe and smooth the velocity of the center of mass (CoM). We found it remarkable that combining Virtual Supporting Point (VSP) with classical LIPM increases gait stability. The simulation and hardware experimental results on THU-Walker Platform strongly verified our algorithm.

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 research presents a simple mapping methodology for gait biomechanics of a human being into joint angles of a 10 degrees of freedom (DOF) biped robot. The joint angles are mapped by considering the zero moment point (ZMP) criterion. The walking control of the robot is performed by an optimal state feedback controller. The walking trajectories are planned in the sagittal plane, and they are generated in compliance with the ZMP of the robot – keeping the robot within the support polygon – by dividing the control process in two stages: unique support and double support. A linear inverted pendulum model (LIPM) is used as an approximate single mass model of the robot during gait. Results of this research include simulation-based analysis and real-time implementation results, which show accurate robot movements with limited robustness under slippery platforms.

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

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.

We report on a novel ZMP feedback control strategy which regulates the center of mass trajectory of a robot based on the measured zero-moment point (ZMP). Based on the trajectory generated by preview control and the linear inverted pendulum model, the controller has an extra model-based control input which is driven by the center-of-mass (CoM) acceleration, which provides sensitive response to disturbance. Thus, the robot motion is balanced between the long-term nominal CoM/ZMP trajectory tracking and the short-term trajectory modification for disturbance rejection. In addition, the controller has two layers of adjustment strategy. When the disturbance is small, the robot is regulated by merely adjusting its CoM trajectory. In contrast, when the disturbance is large, the foot position of the robot is simultaneously changed to provide a more effective response with characteristics of larger intrinsic stability. The performance of the control strategy is also experimentally evaluated using a child-size biped robot.

In this paper, an walking pattern tuning system based on ZMP(Zero Moment Point) for a humanoid robot is proposed. Commonly, it is inevitable to handle the stage with proficient programming skill for realization of humanoid walking. The proposed walking pattern tuning system is a program tool to finely tune the walking pattern based on ZMP by adjusting intuitive parameters that ordinary user can understand easily. The walking pattern tuning system was applied to the humanoid robot of 110cm tall and the humanoid robot with the tuned walking pattern was tested.

Previous research related to walking on an inclined plane for humanoid robots, including the 3-D linear inverted pendulum model (3D-LIPM) approach, were unable to modify walking period, step length, and walking direction independently without any additional step for adjusting the center of mass (CoM) motion. Moreover, the inclination along the pitch direction was only considered for walking. To solve these problems, a novel command state (CS)-based modifiable walking pattern generator for humanoid robots is proposed for modifiable walking on an inclined plane in both pitch and roll directions. The dynamic equation of the 3D-LIPM on the inclined plane in both pitch and roll directions is derived to obtain the CoM motion. Using the CoM motion, a method for modifiable walking pattern generation on the inclined plane is developed to follow a given CS composed of walking periods, step lengths, and walking directions for both legs. The effectiveness of the proposed walking pattern generator is demonstrated through both simulation and experiment for the small-sized humanoid robot, HanSaRam-IX (HSR-IX).

The cerebellum has been hypothesized to form a crucial part of the speech motor control network. Evidence for this comes from patients with cerebellar damage, who exhibit a variety of speech deficits, as well as imaging studies showing cerebellar activation during speech production in healthy individuals. To date, the precise role of the cerebellum in speech motor control remains unclear, as it has been implicated in both anticipatory (feedforward) and reactive (feedback) control. Here, we assess both anticipatory and reactive aspects of speech motor control, comparing the performance of patients with cerebellar degeneration and matched controls. Experiment 1 tested feedforward control by examining speech adaptation across trials in response to a consistent perturbation of auditory feedback. Experiment 2 tested feedback control, examining online corrections in response to inconsistent perturbations of auditory feedback. Both male and female patients and controls were tested. The patients were impaired in adapting their feedforward control system relative to controls, exhibiting an attenuated anticipatory response to the perturbation. In contrast, the patients produced even larger compensatory responses than controls, suggesting an increased reliance on sensory feedback to guide speech articulation in this population. Together, these results suggest that the cerebellum is crucial for maintaining accurate feedforward control of speech, but relatively uninvolved in feedback control.SIGNIFICANCE STATEMENT Speech motor control is a complex activity that is thought to rely on both predictive, feedforward control as well as reactive, feedback control. While the cerebellum has been shown to be part of the speech motor control network, its functional contribution to feedback and feedforward control remains controversial. Here, we use real-time auditory perturbations of speech to show that patients with cerebellar degeneration are impaired in adapting feedforward control of speech but retain the ability to make online feedback corrections; indeed, the patients show an increased sensitivity to feedback. These results indicate that the cerebellum forms a crucial part of the feedforward control system for speech but is not essential for online, feedback control.

Walking motion planning based on Divergent Component of Motion (DCM) and Linear Inverted Pendulum Model (LIPM) is one of the alternatives that could be implemented to generate online humanoid robot gait trajectories. This algorithm requires different parameters to be adjusted. Herein, we developed a framework to attain optimal parameters to achieve a stable and energy-efficient trajectory for real robot’s gait. To find the optimal trajectory, four cost functions representing energy consumption, the sum of joints velocity and applied torque at each lower limb joint of the robot, and a cost function based on the Zero Moment Point (ZMP) stability criterion were considered. Genetic algorithm was employed in the framework to optimize each of these cost functions. Although the trajectory planning was done with the help of the simplified model, the values of each cost function were obtained by considering the full dynamics model and foot-ground contact model in Bullet physics engine simulator. The results of this optimization yield that walking with the most stability and walking in the most efficient way are in contrast with each other. Therefore, in another attempt, multi-objective optimization for ZMP and energy cost functions at three different speeds was performed. Finally, we compared the designed trajectory, which was generated using optimal parameters, with the simulation results in Choreonoid simulator.