ZMP Trajectory Research Articles

A Comparison of Dynamic Gait Stability between the Young and Elderly Female Populations Using the Zero-Moment Point Method

A compromised stability in the elderly population is considered a major factor for fall risk assessment. The dynamic stability of human gait with various mathematical metrics has been extensively studied to find a prediction index and fall prevention strategies that can be embedded in a wearable monitoring sensor. In this study, the zero-moment point method (ZMP) was utilized for analyzing the gait stability of young and elderly female populations. Participants in the young and elderly female groups with no musculoskeletal disorders and fall experience were asked to walk at a habitual speed on 10 m flat ground. Dynamic instability is defined by the percentage of the ZMP values that fall outside the base of support during one gait cycle. The ZMP trajectory between the left and right leg swing was not symmetrical considering flat-ground walking. Also, there was no statistical difference in the dynamic stability in the anterior–posterior direction (71.3 ± 7.9% for the young group and 73.6 ± 7.6% for the elderly group), but walking in the medial–lateral direction was more stable in the elderly group (53.9 ± 8.6%) than in the young group (44.1 ± 11.2%) because the habitual walking speed decreased in the elderly group.

Advanced biped gait generator using NARX-MLP neural model optimized by enhanced evolutionary algorithm

A novel biped walking pattern combining robust zero-moment-point ZMP technique and pre-determined foot-lifting value is proposed in this paper. The implementation of suggested approach contains following stages. Initially, a one-step ZMP curve for a small-sized humanoid is created using the 3rd-order interpolating equation, with pre-determined velocity responding the ZMP concept. The next step, biped gait planning is modeled as a non-linear MIMO plant including ten degree-of-freedom DOF. Then, the installation of a biped walking pattern generator (WPG) based on the new hybrid Neural-NARX model is completed. Eventually, the novel Enhanced Differential Evolution (EDE) technique is applied to optimally identify the weights of the hybrid Neural-NARX structure, for ensuring robust robot walking in terms of desired ZMP trajectories and pre-determined foot-lifting value. All case studies confirm that it is surely provide a biped WPG satisfying both of the effectiveness and high robustness. The verification of the newly proposed WPG is adequately tested via both simulation and experiment results.

Human Motion Capture System Based 3D Reconstruction on Rehabilitation Assistance Stability of Lower Limb Exoskeleton Robot Climbing Upstairs Posture

Stair-climbing posture is a common motion posture of lower extremity exoskeleton robots. In the process of climbing stairs, with the change of the gravity center of system, it has a direct impact on the dynamic stability characteristics of human-machine system. Based on this, a complete diagram of the stair-climbing posture can be set up, which can be divided into the starting stage, the intermediate stage and the ending stage. The foot trajectory, COG trajectory and ZMP trajectory of human-machine system in the intermediate stage of stair-climbing posture can be analyzed by drawing stair-climbing motion diagram of six-step. Based on the inverted pendulum theory, a virtual inverted pendulum model with variable height (VCHIPM) is proposed to analyze the influence of the change of the gravity center on the dynamic stability of the human-machine system in the upstairs posture. The test results show us that COG position can be changed by adjusting the value of a, so as to adjust the position of ZMP, reduce the error of ZMP and ensure the stability of human-machine system.

Control Method Based on Sensor Data for Stable Walking of a Biped Robot under Port Environment

Jing, C.L., You, X.F., and Xia, T., 2020. Control method based on sensor data for stable walking of a biped robot under port environment. In: Guido Aldana, P.A. and Kantamaneni, K. (eds.), Advances in Water Resources, Coastal Management, and Marine Science Technology. Journal of Coastal Research, Special Issue No. 104, pp. 271–275. Coconut Creek (Florida), ISSN 0749-0208.In spite of great improvement of walking ability after the merging of various walking techniques, there still exists a large gap between a biped robot and a person. In particular, under some complex environments such as port, the development and perfection of the control theory based on the detected sensor data are of great significance to achieving ideal walking ability for the robot. In this study, the detected sensor data are merged into the established dynamic model, and then, both the force and the moment of the connecting rod are accurately calculated for programming actual ZMP trajectory. Further, the data are sent to the slave computer for robot control, thereby enhancing the walking stability. The present simulation results prove that the biped robot can successfully realize stable walking.

MPC for Humanoid Gait Generation: Stability and Feasibility

We present IS-MPC, an intrinsically stable MPC framework for humanoid gait generation which incorporates an explicit stability constraint in the formulation. The proposed method uses as prediction model a dynamically extended LIP where ZMP velocities are the control inputs, producing in real time a gait (including footsteps with the associated timing) that realizes omnidirectional motion commands coming from an external source. The stability constraint links the future ZMP velocities to the current system state so as to guarantee the essential requirement that the generated CoM trajectory is bounded with respect to the ZMP trajectory. Since the control horizon of the MPC algorithm is finite, only part of the future ZMP velocities are decision variables of the QP problem; the remaining part, called tail, must be either conjectured or anticipated using preview information on the reference motion. Several possible options for the tail are discussed, and each of them is shown to correspond to a specific terminal constraint. A theoretical analysis of the feasibility of the generic MPC iteration is developed and used to obtain sufficient conditions for recursive feasibility. Finally, it is proved that IS-MPC guarantees stability of the CoM/ZMP dynamics if it is recursively feasible. Simulation and experimental results on the NAO and the HRP-4 humanoids are presented to illustrate the performance of the proposed method.

A new virtual-real gravity compensated inverted pendulum model and ADAMS simulation for biped robot with heterogeneous legs

Our research team combined humanoid robots with intelligent lower limb prostheses to study the dynamic characteristics of intelligent lower extremity prostheses for disabled people in the walking process, and proposed a biped robot with heterogeneous legs (BRHL). This paper proposes a new virtual-real inverted pendulum system model to unify the models for both single support phase and double support phase in walking process and builds a special simulation platform which can acquire the real-time center of mass (COM) trajectory. Initially, a gravity-compensated inverted pendulum model was built and improved the stability of gait, a natural ZMP trajectory improved the anthropomorphism of the gait. Furthermore, in double support phase, a virtual inverted pendulum model was established and a virtual-real inverted pendulum model was proposed and used to plan the gait of both single support phase and double support phase in the walking process. Additionally, the joint angles were obtained by inverse kinematics; the stability of the system was analyzed to be feasible and effective by phase trajectories. A special ADAMS simulation platform was built to simulate the walking process and acquire real-time COM trajectory. The feasibility of the gait planning was also verified. Finally, the trajectory of COM was optimized based on the minimum energy criterion according to the geodesic equation.

On-Site Locomotion Planning for a Humanoid Robot with Stable Whole-Body Collision Avoidance Motion Guided by Footsteps and Centroidal Trajectory

In this paper, we propose a locomotion planning framework for a humanoid robot with stable whole-body collision avoidance motion, which enables the robot to traverse an unknown narrow space on the spot based on environmental measurements. The key idea of the proposed method is to reduce a large computational cost for the whole-body locomotion planning by utilizing global footstep planning results and its centroidal trajectory as a guide. In the global footstep planning phase, we modify the bounding box of the robot approximating the centroidal sway amplitude of the candidate footsteps. This enables the planner to obtain appropriate footsteps and transition time for next whole-body motion planning. Then, we execute sequential whole-body motion planning by prioritized inverse kinematics considering collision avoidance and maintaining its ZMP trajectory, which enables the robot to plan stable motion for each step in 223[Formula: see text]ms at worst. We evaluated the proposed framework by a humanoid robot HRP-5P in the dynamic simulation and the real world. The major contribution of our paper is solving the problem of increasing computational cost for whole-body motion planning and enabling a humanoid robot to execute adaptive on-site locomotion planning in an unknown narrow space.

Підхід до створення системи моделювання гнучкого виробництва

This paper dealing with the problem of generation motion of biped robot, to solve this problem, was introduces a new method of implementation a biped robot walking pattern generation byusing a Model Predictive control (MPC) First, the basic of biped robots’ motion was reviewed and was discussed the elements of motion controller. The dynamics of a biped robot is modeled as a runningcart on a table which gives a convenient representation for generation ZMP trajectory. After reviewing approach of 3D Linear Inverted Pendulum Model, a pattern generator was designed, lastly in MATLAB/Simulink and using Model Predictive Control Toolbox (MPCT) which provides functions, an app, and Simulink blocks was used for designing and simulating a motion generator based on model predictive controllers (MPC).The results of simulation are shown that we can realize such controller for generating trajectory of Center of Mass and Zero Moment point by using the MPC. The smooth trajectory of CoM is generated and the resulted ZMP follows the reference with good accuracy.Ref. 13, pic. 6

Trajectory optimization for mobile robots using model predictive control

The goal of this article is trajectory generation for biped robots based on Model Predictive Control (MPC) and the receding-horizon principle. Specifically, we want to minimize the error between the desired CoM and ZMP trajectory and the actual one and the cancellation of the shock gradient of the CoM and ZMP movements. Model predictive control (MPC) consist in a finite horizon optimal control scheme which uses a prediction model to predict vehicle response and future states, thus minimizing the current error and optimizing the future trajectory within the prediction horizon. The proposed algorithm will provide a trajectory of control inputs which will optimize the system states utilizing a quadratic form cost function similar to standard linear quadratic tracking. Specific to finite horizon control, the cost is summed over the finite prediction horizon of time length, rather than over an infinite time horizon. Many techniques have been proposed, developed, and applied to solve this constrained optimization problem for the mobile robots. With our aproach we try to investigate how is the MPC framework is applicable to trajectory generation for point-to-point problems with a fixed final time and to find a set of assumptions and methods that allow for real-time solutions.

Method of Finding of Android Program Motion for the ZMP Trajectory of a Certain Type

Method of Finding of Android Program Motion for the ZMP Trajectory of a Certain Type

A novel approach for the generation of complex humanoid walking sequences based on a combination of optimal control and learning of movement primitives

We combine optimal control and movement primitive learning in a novel way for the fast generation of humanoid walking movements and demonstrate our approach at the example of the humanoid robot HRP-2 with 36 degrees of freedom. The present framework allows for an efficient computation of long walking sequences consisting of feasible steps of different kind: starting steps from a static posture, cyclic steps or steps with varying step lengths, and stopping motions back to a static posture. Together with appropriate sensors and high level decision strategies this approach provides an excellent basis for an adaptive walking generation on challenging terrain. Our framework comprises a movement primitive model learned from a small number of example steps that are dynamically feasible and minimize an integral mean of squared torques. These training steps are computed by solving three different kinds of optimal control problems that are restricted by the whole-body dynamics of the robot and the gait cycle. The movement primitive model decomposes the joint angles, pelvis orientation and ZMP trajectories in the example data into a small number of primitives, which effectively deals with the redundancy inherent in highly articulated motion. New steps can be composed by weighted combinations of these primitives. The mappings from step parameters to weights are learned with a Gaussian process approach, the contiguity of subsequent steps is promoted by conditioning the beginning of a new step on the end of the current one. Each step can be generated in less than a second, because the expensive optimal control computations, which take several hours per step, are shifted to the precomputational off-line phase. We validate our approach in the virtual robot simulation environment OpenHRP and study the effects of different kernels and different numbers of primitives. We show that the robot can execute long walking sequences with varying step lengths without falling, and hence that feasibility is transferred from optimized to generated motions. Furthermore, we demonstrate that the generated motions are close to torque optimality on the interior parts of the steps but have higher torques than their optimized counterparts on the steps boundaries. Having passed the validation in the robot simulator, we plan to tackle the transfer of this approach to the real platform HRP-2 as a next step.

3D Dynamic Biped Walker with Flat Feet and Ankle Springs: Passive Gait Analysis and Extension to Active Walking

<div class=""abs_img""> <img src=""[disp_template_path]/JRM/abst-image/00270004/14.jpg"" width=""300"" /> A ZMP pattern of passive walker RW03</div> In the last two decades, passive dynamic walking (PDW) has attracted considerable research attention. The assumption that biped walking is based on PDW is now widely accepted. PDW bipeds change their gait to adapt to changes in body configuration and environment, and their efficiency is extremely high. PDW is generally difficult to realize because it lacks robustness. This means, for one thing, that biped walkers capable of PDW must be designed carefully. Once realized, however, the PDW bipeds are expected to have a suitable configuration for biped walking. This study then aims to analyze the fundamental properties of 3D PDW with flat soles and ankle springs and to use these properties to extend it to a horizontal surface. First, we develop a stable and relatively robust 3D PDW biped that has flat soles and ankle springs. Some sensors are implemented in order to measure the posture and the ZMP trajectory. Next, we investigate the relationship between its gait and the CoM position of each leg. We then attach a ballast to the leg to change the CoM, which effectively results in walking stability. Finally, a 3D active biped, whose knees consist of telescopic joints, is developed based on the 3D PDW biped. </span>

Trajectory Planning and Walking Pattern Generation of Humanoid Robot Motion

Walking trajectory generation for a humanoid robot is a challenging control issue. In this paper, a walking cycle has been recognized considering human motion, and nine simple steps were distinguished in a full step of walking which form motion trajectory, and generates a simplified ZMP motion formulation. This system was used in humanoid robot simulation motion and is achievable easily in walking steps of robot. A minimum DOFs humanoid robot has been considered and geometrical relationships between the robot links were presented by the Denavit-Hartenberg method. The inverse kinematics equations have been solved regarding to extracted ZMP trajectory formula, and constraints in different steps. As a result; angular velocity, acceleration and power of motors were obtained using the relationships and Jacobin. At each step, extracted data were applied on simulated robot in Matlab, and Visual Nastran software. Zero moment point trajectory was evaluated in simulation environment.

3P1-G06 ヒューマノイドにおける二足歩行行動から腕接地歩行への拡張に基づく多種歩容行動の実現(ヒューマノイド(2))

In order to enable humanoids to walk steadily, it is important to use various walking forms. For examples, humanoids should walk not in biped but in quadruped when the ground is rough or they cannot believe that the space before them is and will be clear. With having choices of walking forms, they can access wider area by therselves. In this paper, we propose a way to extend a conventional biped walking pattern generator to a generalized walking pattern generator under arm/leg coordination by forcusing on gait pattern and the way to calculate target ZMP trajectory, and conduct a walking experiment over uneven ground by switching a walking form from biped to quadruped. Also we propose an attitude stabilization control system for walking over rougher ground and conduct a simple test for its validation.

State-incremental optimal control of 3D COG pattern generation for humanoid robots

Many researchers have proposed walking pattern generation methods with zero moment point – center of gravity (ZMP–COG) constraints. Some of the researchers used a neural-networks (NN), a central pattern generator (CPG), or a genetic algorithm (GA) for ZMP–COG pattern generation. However, the parameters used in those methods are too many, and the procedure to learn or to search them costs too much computation time. Other researchers designed controllers or used analytical solution method to generate COG trajectories. These methods generate the ZMP-COG pattern very quickly, but the COG height is limited to a constant to linearize the inverted pendulum model of the robot. Due to this limitation, the robots cannot walk freely on surfaces that change in height. To solve this problem, researchers start to use the original nonlinear inverted pendulum model to make the COG height changeable such as using a numerical method or a feedback controller. In this paper, an optimal control-based pattern generator that can allow COG height change is proposed. It can solve sagittal and lateral COG patterns with arbitrarily assigned COG height and ZMP trajectories in real time. Thus, dynamic walking on height-changing surfaces can be achieved.

On Global Optimization of Walking Gaits for the Compliant Humanoid Robot, COMAN Using Reinforcement Learning

Abstract In ZMP trajectory generation using simple models, often a considerable amount of trials and errors are involved to obtain locally stable gaits by manually tuning the gait parameters. In this paper a 15 degrees of Freedom dynamic model of a compliant humanoid robot is used, combined with reinforcement learning to perform global search in the parameter space to produce stable gaits. It is shown that for a given speed, multiple sets of parameters, namely step sizes and lateral sways, are obtained by the learning algorithm which can lead to stable walking. The resulting set of gaits can be further studied in terms of parameter sensitivity and also to include additional optimization criteria to narrow down the chosen walking trajectories for the humanoid robot.

선형 역덤벨 모델을 이용한 이족 보행 로봇의 기준 ZMP 궤적 생성 및 보행 구현

This paper presents reference ZMP trajectory generation and implementation for a biped robot via linear inverted dumbbell model (LIDM), which can consider the effect of external momentum on the center of mass (COM) of robot. Based on a reference ZMP trajectory derived by using LIDM, a base trajectory is proposed not only to make the locomotion of robot similar to that of human but also to facilitate its implementation and tuning. In order to realize a dynamic walking using the proposed trajectory, compliance, impedance and ZMP tracking controllers are adopted together. Extensive experiments show that the proposed locomotion of a biped robot is stable and also, similar to that of human. Further researches on balance recovery of a biped robot will be carried out to guarantee its robust locomotion in combination with the proposed trajectory.

인체운동학에 기반한 이족로봇의 인간형 걸음새 설계

The study of bipedal robot is towards similar shape and function with human. In this paper, we propose a human-like walking pattern compatible to the flexible foot with toe and heel structure. The new walking pattern for a bipedal robot consists of ZMP, center of mass (CoM), and ankle trajectory and is drawn by considering human kinesiology. First, the ZMP trajectory moves forward without stopping at a point even in the single support phase. The corresponding CoM trajectory to the ZMP one is derived by solving differential equations. As well, a CoM trajectory for the vertical axis is added by following the idea of human motion. The ankle trajectory closely mimics the rotational motion of human ankles during taking off and landing on the ground. The advantages of the proposed walking pattern are demonstrated by showing improved stability, decreased ankle torque, and the longer step length capability. Specifically, it is interesting to know that the vertical CoM motion is able to compensate for the initial transient response.

定常歩容に漸近する２脚ロボットの自在歩容生成

In this paper, we propose a method to generate various walking gait patterns for biped robots in real-time using an approximated dynamics model with two point masses representing motion of the feet and a linear inverted pendulum representing the horizontal motion of the torso. The motion of the inverted pendulum is calculated from the trajectories of the feet and the desired ZMP. Supposing these trajectories for the current gait and the next cyclic gait are given, the initial state of the inverted pendulum of the cyclic gait is calculated, and the desired ZMP trajectory of the current gait is modified so that the current gait converges to the cyclic gait using the concept called “the divergent component of the motion” as a relaxed boundary condition. Using these techniques, real-time gait generation is achieved which requires a comparatively small amount of modification of the desired ZMP trajectory while guaranteeing the continuity of the gait generation.

DEVELOPMENT OF A HUMANOID BIPED WALKING ROBOT HUBOT-1 INITIAL DESIGN AND RESULTS ACHIEVED

This paper presents an overview of the design process of humanoid robot HUBOT-1: mechanical design, gait planning, control architecture and sensors implementation. The robot is designed with full body in style of Vietnamese body proportion. At the present state the lower limbs with 12 DOF are considered for natural walking pattern from hip and ankle trajectories. Walking pattern based on ZMP criterion. Also, the dead-beat controller of servo motor is implemented for joint control. In addition, the robot used IMU and FSR sensors which are designed and implemented for verifying the ZMP trajectory in stability area.