Zero Moment Point Research Articles

Gait modification for improving walking stability of exoskeleton assisted paraplegic patient

The currently available exoskeleton for assisting the paraplegic patient in walking usually adapts a pre-programmed gait that involves the patient following an exoskeleton lead. The system allows the patient to hold a pair of canes in order to keep balance, and does not contribute to keeping balance without the patient’s action. This paper proposes an algorithm based on the zero moment point (ZMP) to modify the gait generated through human walking synergy for paraplegic patients who make use of the exoskeleton system and hold their canes. The proposed ZMP will enable the paraplegic patient to keep balance during walking and also reduce the burden in maintaining balance. First, a pair of cane is used as an interface to control the user’s walking and then, the synergy between legs and canes is used to synchronize the user’s walking intention during the exoskeleton movement. The walking synergy is extracted from the able-bodied subject walking with a pair of canes and analyzed using principal component analysis (PCA). In order to improve the walking stability, the hip joint angle on stance leg during walking was modified based on ZMP. Furthermore, a nonlinear inverted pendulum (NIP) model was utilized in order to generate a gait with a fully stretched knee joint angle that is similar to human gait. The proposed method was verified via the Gazebo simulation using a walking robot to simulate a patient wearing an exoskeleton. The experiment results show that the walking stability was highly improved after gait modification.

Development of a Humanoid Robot for the 2018 Ski Robot Challenge

We describe in this paper, the development of a humanoid robot for the 2018 Ski Robot Challenge, which was held in Korea. The goal of this competition was to develop a humanoid robot that could autonomously perform in a ski giant slalom game. To participate in this competition, we developed the humanoid robot RoK-2 which is designed to ski on a slope. The lower body joints of the robot were developed to have high torque because it needed to perform ski motions in a situation where shock and vibration would occur. The upper body of the robot was designed to be shielded from factors that could damage electronic components such as snow. The ski robot required a ski turning mechanism so that it could make its way between the ski flags on the slope. To perform the turns accurately, a ski plate for the desired radius was selected and the robot performed a proper, humanlike motion using the extension–flexion a motion of carved turn. To verify the stability of the motion, we confirmed that the zero-moment point (ZMP) of the robot was within a support polygon of the robot. The environment of a ski slope is not good for image processing because of the changing light and weather. To overcome this problem, a deep learning based ski flag recognition algorithm was developed so that the robot could recognize ski flags correctly. Finally, RoK-2 was verified in the 2018 Ski Robot Challenge.

LQR-Assisted Whole-Body Control of a Wheeled Bipedal Robot With Kinematic Loops

We present a hierarchical whole-body controller leveraging the full rigid body dynamics of the wheeled bipedal robot Ascento. We derive closed-form expressions for the dynamics of its kinematic loops in a way that readily generalizes to more complex systems. The rolling constraint is incorporated using a compact analytic solution based on rotation matrices. The non-minimum phase balancing dynamics are accounted for by including a linear-quadratic regulator as a motion task. Robustness when driving curves is increased by regulating the lean angle as a function of the zero-moment point. The proposed controller is computationally lightweight and significantly extends the rough-terrain capabilities and robustness of the system, as we demonstrate in several experiments.

A Theoretical Framework for Stability Regions for Standing Balance of Humanoids Based on Their LIPM Treatment

The aim of this paper is to construct a theoretical framework for stability analysis relevant to standing balance of humanoids on top of the linear inverted pendulum model, in which their dynamics between the center of mass (CoM) and the zero moment point (ZMP) is dealt with. Based on the well-known sufficient condition that the contact between the ground and the support leg is stable if the corresponding ZMP is always inside the supporting region, this paper aims at characterizing three types of the associated stability regions. More precisely, assuming no external force disturbances affecting the motion of the humanoids, the stability region of the initial CoM position and velocity values can be explicitly computed by solving a finite number of linear inequalities. The stability regions of time-invariant force disturbances such as impulsive force and constant force disturbances are also dealt with in this paper, where the former is exactly obtained through a finite number of linear inequalities while the latter is approximately derived by using an idea of truncation. Furthermore, time-varying force disturbances of finite energy and finite amplitude are concerned with, and their maximum admissible ${l} _{2}$ and ${l} _{\infty }$ norms are computed in this paper, where the former can be exactly obtained by solving the discrete-time Lyapunov equation while the latter is approximately derived through an idea of truncation. It is further shown for both the truncation ideas that the approximately obtained stability regions converge to the exact stability regions with an exponential order of ${N}$ , where ${N}$ is the truncation parameter. Finally, the effectiveness of the computation methods proposed in this paper is demonstrated through some simulation results.

Tip-Over Stability Analysis of a Pelvic Support Walking Robot.

Discussed in this paper is the tip-over stability analysis of a pelvic support walking robot. To improve the activities of daily living (ADL) in hemiplegic patients, a pelvic support walking robot is proposed to help patients facilitating their rehabilitation. During the gait training with the robot, the abnormal man-machine interaction forces may lead to the tip-over of the robot, which is not beneficial to the rehabilitation process. A new method is proposed to predict the possibility of tipping over and evaluate the stability of the robot based on statics model, dynamics model, and zero-moment point (ZMP) theory. Through the interaction forces and moments analysis with static case, the safe point (ZMP) is studied, and the influence factors of force/moment are analyzed by dynamics case. An optimization algorithm based on the genetic algorithm (GA) is proposed to reduce the risk of tipping over. The simulation results show that the optimization algorithm can keep the robot from tipping over when the interaction forces exceed the safety threshold.

Multi-Axis Force-Torque Sensors for Measuring Zero-Moment Point in Humanoid Robots: A Review

Recent advances in mobility, manipulation, and intelligence of robots have promoted the usability of humanoid robots to support humans in their daily lives in the future. The multi-axis force-torque sensor is an essential sensor for the biped humanoid robot to maintain balance during walking and running since it is used to calculate the zero-moment point, the criterion of dynamic stability. Forcetorque sensors will be widely used in the future because they are essential for service robots to interact with people in unstructured environments. However, due to special design considerations and requirements, it is difficult to find a suitable commercial force-torque sensor for biped humanoid robots and the price is very expensive. This paper reviews the multi-axis force-torque sensor used in current state-of-the-art humanoid robots based on the understanding of biped walking, zero-moment point, and ground reaction force. From an in-depth analysis of relevant information, sensor requirements are discussed with the robot performance. In addition, the structural design of the sensors is classified into four types and described in detail. This comprehensive review will facilitate the development of force-torque sensors in humanoid robots and will be helpful in extending their application in the various fields of service robots.

Natural Walking Trajectory Generator for Humanoid Robot Based on Three-Mass LIPFM

In this paper, a dynamic model named Three-mass Linear Inverted Pendulum plus Flywheel Model (TLIPFM) is proposed to approximate the walking motion of the humanoid robot. The mass distribution of the robot and the angular momentum of the robot are simultaneously considered to construct the dynamic model. In the mass distribution of the robot, the overall robot is divided into three parts: 1) the whole upper body of the robot, 2) the thigh of the robot’s support leg, and 3) the calf of the robot’s support leg, and these three weights are considered to be three masses in the proposed TLIPFM. In the angular momentum of the robot, a flywheel joint is configured at the Center of Mass (CoM) of the robot to obtain the rotational torque of the robot in biped walking. In addition, a natural walking trajectory generator based on the TLIPFM and a moving Zero Moment Point (ZMP) reference is derived to generate ZMP trajectory, CoM trajectory, and foot trajectory in three-dimensional space to let the humanoid robot walk stably. In the experiment, some results are presented to illustrate that the proposed TLIPFM can effectively reduce the model error and the proposed TLIPFM-based walking trajectory generator makes the walking trajectories more natural and walking more stable. Moreover, the proposed method is implemented on a real small-sized humanoid robot to illustrate its feasibility and practicability for the real-time biped walking.

Controlled Gait Planning of Humanoid Robot NAO Based on 3D-LIPM Model

Gait planning is essential for biped robots because the stability of the two support is very challenging task. A special attention is required to get a stabilized gait for humanoid robots. In this paper, 3D-LIPM (linear inverted pendulum model) is used to solve the gait planning problems of humanoid robots. Humanoid robot NAO is utilized as robotic platform. The structure of the robotic platform decides the period step height and step length. The gait planning consists of model of 3D-LIPM and ZMP (zero moment point). Simulation and experiments are carried out on simulated and real NAO, and showing good agreement with each other. An ideal controlled gait is obtained using the proposed technique.

Fuzzy Dynamic Gait Pattern Generation for Real-Time Push Recovery Control of a Teen-Sized Humanoid Robot

A fuzzy dynamic gait pattern generator, which allows a teen-sized humanoid robot to generate, in real-time, a suitable gait pattern when it is hit by an unexpected force, is proposed in this paper. Conventional gait pattern generators usually utilize the ideal Zero Moment Point (ZMP) to plan the trajectory of the Center of Mass (CoM), along with a cycloid to generate steps. However, pre-planned gait patterns cannot deal with unexpected situations, especially instances when the robot experiences an unknown force. Therefore, we propose a dynamic gait pattern generator that leverages the Virtual Force Linear Inverted Pendulum Model (VFLIPM) to adjust the trajectory of the CoM, and which detects balance status by estimating the trajectory of the ZMP using eight high-precision load cell pressure sensors mounted onto the robot's soles. We integrate an accelerometer and the pressure sensors through a fuzzy controller to instantly respond to external forces and generate a suitable gait pattern. When the robot is pushed suddenly, it first adopts a pre-planned gait pattern to replace the current gait. At the same time, the fuzzy controller calculates the recovery gait, with appropriate strides and lean angles to absorb the impact. The proposed method is implemented on the teen-sized humanoid robot, David Junior II, for the Push Recovery event at RoboCup. David Junior II endured a hit with potential energy during walking, which is 1.3 times more robust than when standing.

Oscillation Preventing Closed-Loop Controllers via Genetic Algorithm for Biped Walking on Flat and Inclined Surfaces

In this study, a closed-loop controller is designed to overcome the dynamical insufficiency of the 3D Linear Inverted Pendulum Model (LIPM) via the Genetic Algorithm (GA). The main idea is to still use the 3D LIPM with a closed-loop controller because of its ease at modeling. While suppressing the dynamical flaws only the legs are used, in other words a robot is used which does not have any upper body elements to have a more modular robot. For this purpose, a biped is modeled with the 3D LIPM which is one of the most famous modeling methods of humanoid robots for the ease of modeling and fast calculations during the trajectory planning. After obtaining the simple model, Model Predictive Control (MPC) is applied to the 3D LIPM to find the reference trajectories for the biped while satisfying the Zero Moment Point (ZMP) criteria. The found reference trajectories applied to the full dynamical model on Matlab Simulink and the real biped in the laboratory at Istanbul Technical University. From the simulation results on the flat and inclined surfaces and real-time experiments on a flat surface some dynamical flaws are observed due to the simple modeling. To overcome these flaws a Proportional-Integral (PI) controller is designed, and the optimal value of the controller gains are found by the GA. The results assert that the designed controller can overcome the observed flaws and makes biped move more stable, smoother, and move without steady-state error.

Posture compensation of a walking assistive device using zero-moment point to stabilize motions on stairs

Posture compensation of a walking assistive device using zero-moment point to stabilize motions on stairs

Application of Variable Zero-Moment Point in Walking Control of the Biped Robot

Using the predictive control based on zero-moment point (ZMP), the biped robot can walk comparatively stably. However, the problems such as lack of self-adaptivity are also highlighted mainly on account of modeling errors and environmental perturbations; specifically, the tracking errors of ZMP are generated, leading to a reduced walking stability. To address this problem, in the present work, the expected ZMP was decomposed into the reference ZMP which is pre-planned offline, and the variable ZMP which can be varied in real time. With the addition of the variable ZMP, the outside interferences can be eliminated. By combining the predictive control system and the inverse system of variable ZMP, the walking pattern of the robot with favorable self-adaptivity can be achieved. Finally, the simulation results indicate that the self-adaptivity of the robot can be effectively improved using the proposed control system.

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

Real-Time Feasible Footstep Planning for Bipedal Robots in Three-Dimensional Environments Using Particle Swarm Optimization

Footstep planning in various three-dimensional environments is formulated as an optimization problem, which is solved using a particle swarm optimi-zation. The objective function for optimization is designed to achieve real-time footstep planning considering arrival at the goal with effective not only foot placements but also walking periods, kinematic constraints: obstacle avoidance and hardware limitations, and dynamic constraints for the bipedal dynamics: stability while walking and feasibility of footsteps in a walking pattern generator. Specifically, optimization objectives are to minimize remaining distance to the goal, lateral movement, rotational movement, and walking period variation. Three penalties are also consid-ered depending on the situations. The first penalty is for obstacle collision avoidance along with prevention of unstable walking due to excessive footstep height variation. The second penalty is for walking satisfying stable zero-moment point condition along with the foot collision avoidance. The third penalty is for feasible footstep planning in a walking pattern generator. Any approxi-mation or precomputation is not required for the proposed footstep planning method. The validity of the proposed method is verified through experiments in various 3-D environments with static and dynamic obstacles.

Perfect tracking of ZMP trajectory for humanoid locomotion using repetitive control

In this paper, the tracking of the zero moment point (ZMP) trajectory for humanoid locomotion is addressed. For that, a combination of a repetitive controller (RC) and a linear quadratic regulator (LQR) is proposed. The RC controller achieves a zero steady state tracking error for any periodic desired output with a fixed period. Here, the robot model is simplified as a cart table model. In the first stage, a walking pattern with constant gait is considered to allow the use of a repetitive controller. The results are then compared to a classical PD control. In the second part, the proposed controller is applied to track a desired ZMP profile generated using a central pattern generator (CPG). Here, the speed of the oscillator is adjusted via a proper selection of the parameters of the CPG and the RC design is simultaneously updated to assure the perfect tracking of the ZMP.

CYCLOIDAL GAIT WITH DOUBLE SUPPORT PHASE FOR THE NAO HUMANOID ROBOT

The commercial Nao humanoid robot has 11 DOF in legs. Even if these legs include 12 revolute joints, only 11 actuators are employed to control the walking of the robot. Under such conditions, the mobility of the pelvis and that of the oscillating foot are mutually constrained at each step. Besides, the original gait provided by the manufacturer company of the Nao employs only single support phases during the walking. Because of both issues, the reduced mobility in legs and the use of only single support phases, the stability of the walking is affected. To contribute to improving such stability, in this paper an approach is proposed that incorporates a double support phase and a gait based on cycloidal time functions for motions of the pelvis and those of the oscillating foot. To assess the stability of the walking an index is applied, which is based on the notion of zero-moment point (ZMP) of the static foot at each step. Results of experimental tests show that the proposed gait enhances the stability of the robot during the walking.

WITHDRAWN: The optical multi-camera based motion Analysis of Walking Attitude Stability of Lower Limb Exoskeleton Robot using movement image segmentation

Abstract Aiming at the stable walking problem of lower limb exoskeleton robot, the instability mechanism of the robot during walking is analyzed based on the zero-moment point theory. It is found that the zero-moment point theory has certain limitations in a complete walking cycle. Based on this, the stability criterion of the biped projection polygon method is proposed, and the stable polygon in the walking process is established. The segmentation method is used to divide the stable polygon of each pose into several triangles, and the point Zero Moment Point (ZMP) law changes of zero-moment in a walking cycle is analyzed, qualitatively determine the dynamic stability characteristics of the human-machine system. Based on the shortest distance stability margin, the concept of instability rate is proposed. Based on several stable triangles, the dynamic stability characteristics are quantitatively calculated. The optical multi-camera motion capture system, which is a multi-media measurement technology, is used to collect the gravity center data of the human-machine system in the course of walking. The multi-media technology is used to process the data and provide the test data.The experimental results show that by calculating the stability criterion and instability rate of the biped projection polygon method are obtained, more accurate expression of the stability characteristics of the human-machine system in the walking posture motion cycle can be expressed.

Liquid State Machine to Generate the Movement Profiles for the Gait Cycle of a Six Degrees-of-Freedom Bipedal Robot in a Sagittal Plane

Abstract In this paper, an approach based on a liquid state machine (LSM) to compute the movement profiles to achieve a gait pattern subject to different variations in its trajectory is presented. At the same time, the position of the zero moment point (ZMP) to determine the stability of the six degrees-of-freedom (6DOF) bipedal robot in the sagittal plane during the gait cycle is calculated. The system is constructed as a supervised machine learning model. The time series of the oscillating foot trajectory obtained by direct kinematics with a multilayer perceptron neural network (MLP), to strengthen the kinematic model, is considered as input values for training. The target movement profiles are acquired of a human gait cycle analysis in three different scenarios: normal gait, climbing stairs, and descending stairs. In training, this model also gets the trajectories of the ZMP position during the gait cycle, as target time series. The LSM formed by spiking neurons, considered as third-generation neural networks, is compared in the accuracy of prediction, by the dynamic time warping (DTW) technique and correlation analysis, against the human gait analysis database. With this neuronal system, the joint positions to generate a trajectory of the oscillating foot and the ZMP position of the bipedal in the sagittal plane in different scenarios are obtained, proving the robustness of the LSM.

Humanoid Locomotion Control and Generation Based on Contact Wrench Cones

This paper presents a general framework for locomotion control and generation of humanoid robots. Different from most of the existing work which uses the zero-moment point (2mp) to determine the feasibility of robot’s motion, we use the so-called contact wrench cone to derive motion feasibility conditions, whole-body motion controllers, and locomotion generators. The contact wrench cone consists of all feasible wrenches that can be applied to the robot through contacts, which provide allowable external forces and moments for realizing the robot’s motion. Algorithms are proposed to compute quantities defined on linear representations of a general convex cone, which can be various contact wrench cones as needed in developing motion generators and controllers. Based on the contact wrench cone for contact links and the proposed algorithms as well as a decomposition of the whole-body dynamics of a floating-base humanoid robot, we derive two motion tracking controllers. One controller contains a single quadratic program with linear inequality constraints, while the other consists of two quadratic programs which can be quickly solved by one of the proposed algorithms and in a closed form, respectively. Both controllers can be applied in real-time and achieve similar motion tracking performance in simulation. Based on contact wrench cones, furthermore, we derive two motion generation methods for humanoid robots. The first method adapts a reference motion, most often infeasible, to the robot by warping the motion’s time line so that the motion trajectory will remain the same but the velocity and acceleration profiles will be changed. The second method generates bipedal locomotion for given footsteps. All the proposed motion controllers and generators are applicable to general scenarios including uneven terrains and motions with the support of other links besides feet.

A Robust Balance-Control Framework for the Terrain-Blind Bipedal Walking of a Humanoid Robot on Unknown and Uneven Terrain.

Research on a terrain-blind walking control that can walk stably on unknown and uneven terrain is an important research field for humanoid robots to achieve human-level walking abilities, and it is still a field that needs much improvement. This paper describes the design, implementation, and experimental results of a robust balance-control framework for the stable walking of a humanoid robot on unknown and uneven terrain. For robust balance-control against disturbances caused by uneven terrain, we propose a framework that combines a capture-point controller that modifies the control reference, and a balance controller that follows its control references in a cascading structure. The capture-point controller adjusts a zero-moment point reference to stabilize the perturbed capture-point from the disturbance, and the adjusted zero-moment point reference is utilized as a control reference for the balance controller, comprised of zero-moment point, leg length, and foot orientation controllers. By adjusting the zero-moment point reference according to the disturbance, our zero-moment point controller guarantees robust zero-moment point control performance in uneven terrain, unlike previous zero-moment point controllers. In addition, for fast posture stabilization in uneven terrain, we applied a proportional-derivative admittance controller to the leg length and foot orientation controllers to rapidly adapt these parts of the robot to uneven terrain without vibration. Furthermore, to activate position or force control depending on the gait phase of a robot, we applied gain scheduling to the leg length and foot orientation controllers, which simplifies their implementation. The effectiveness of the proposed control framework was verified by stable walking performance on various uneven terrains, such as slopes, stone fields, and lawns.