Zero Moment Point Research Articles

Push Recovery of a Biped in Different Stance Scenarios

Abstract Push recovery of a biped robot is challenging because of the complexity of biped locomotion contributed by its constraints. The present work proposes a novel optimized control methodology for push recovery against external disturbances utilizing “Centroidal Momentum” and “Momentum Jacobian Matrix” (MJM). The novelty of this work lies in the optimization framework of the control problem that includes an eigenanalysis of MJM. The optimization considers various constraints associated with the biped locomotion while minimizing the necessary cost function. Successful push recoveries of a biped from different stance scenarios (single leg stance, double leg stance, double leg stance at different heights) are demonstrated using the unique methodology proposed in this work. Such a unique methodology using eigenanalysis of MJM for push recovery under diverse stance scenarios has yet to be described in the literature. The balance stability of the robot after being pushed is evaluated by its Center of Mass (CoM) motion and Zero Moment Point (ZMP) criteria. It is also demonstrated that the proposed methodology in the present work can recover a biped from a greater impulse force normalized by biped weight compared to other existing push recovery methods. A new term called “Effective Disturbance Ratio” (EDR) is introduced to perform this comparison.

Gait coordination control of bipedal modular reconfigurable robot based on adaptive neural network

This paper proposed an adaptive neural network (NN) control method to track the desired trajectory of a bipedal modular reconfigurable robot (MRR), which can solve the gait coordination problem of bipedal MRR. The leg dynamic model and the body dynamic model of bipedal MRR are established based on the Newton–Euler iterative method, and the global dynamic model is subsequently established. Aiming at the gait coordination problem between double support phase (DSP) and single support phase (SSP), the desired trajectory is generated based on the zero-moment point (ZMP) method. The adaptive NN controller is designed to track the generated desired trajectory, which also compensates interconnected dynamic coupling (IDC) effects of the bipedal MRR. The stability of bipedal MRR system is proved by Lyapunov theory. In the end, the effectiveness of the control method is verified by comparative simulation. The simulation results show that the proposed adaptive NN method reduces the position tracking error by [Formula: see text] and the control torque by [Formula: see text] compared with the existing control methods.

Control of stance-leg motion and zero-moment point for achieving perfect upright stationary state of rimless wheel type walker with parallel linkage legs

Abstract The authors have studied models and control methods for legged robots without having active ankle joints that can not only walk efficiently but also stop and developed a method for generating a gait that starts from an upright stationary state and returns to the same state in one step for a simple walker with one control input. It was clarified, however, that achieving a perfect upright stationary state including zero dynamics is impossible. Based on the observation, in this paper we propose a novel robotic walker with parallel linkage legs that can return to a perfect stationary standing posture in one step while simultaneously controlling the stance-leg motion and zero-moment point (ZMP) using two control inputs. First, we introduce a model of a planar walker that consists of two eight-legged rimless wheels, a body frame, a reaction wheel, and massless rods and describe the system dynamics. Second, we consider two target control conditions; one is control of the stance-leg motion, and the other is control of the ZMP to stabilize zero dynamics. We then determine the control input based on the two conditions with the target control period derived from the linearized model and consider adding a sinusoidal control input with an offset to correct the resultant terminal state of the reaction wheel. The validity of the proposed method is investigated through numerical simulations.

Dynamic Modeling and Control of a 4-Wheel Narrow Tilting Vehicle

The automotive industries currently face challenges such as emission limits, traffic congestion, and limited parking, which have prompted shifts in consumer preferences and modern passenger vehicle requirements towards compact vehicles. However, given the inherent limited width of compact vehicles, the potential risk of vehicle rollover is greater than that of regular vehicles. This paper addresses the safety concerns associated with vehicle rollover, focusing on narrow tilting vehicles (NTVs). Quantifying stability involves numerical indicators such as the lateral load transfer ratio (LTR). Additionally, a unique approach is taken by applying ZMP (zero moment point), commonly used in the robotics field, as an indicator of vehicle stability. Effective roll control requires a detailed analysis of the vehicle’s characteristic model and the derivation of lateral and roll dynamics. The paper presents the detailed roll dynamics of an NTV with a MacPherson strut-type suspension. A stability-enhancing method is proposed using a cascade structure based on the internal robust position controller and outer roll stability controller, addressing challenges posed by disturbances. Experimental verification using Simscape Multibody and CarSim validates the dynamic model and controller’s effectiveness, ensuring the reliability of the proposed tilting control for NTVs in practical scenarios.

Reactive bipedal balance: Coordinating compliance and stepping through virtual model imitation for enhanced stability

Compliance and step location adjustments are both important for robots to maintain balance when encountering external disturbances. Compared with controlling separately, unifying compliance with step location adjustments and integrating them into real-time pattern planning gets obvious advantages. However, the controllers’ models differ significantly from each other and from the dynamics of real position-controlled robots, compromising the stabilizing performance. In this paper, we propose a Virtual Model Imitation (VMI) strategy that unifies the controllers’ models and aligns them with actual robot dynamics. Based on this, a reactive pattern planning method is proposed which simultaneously coordinates compliance and step location adjusting strategies. The approach involves emulating the passive dynamic motion of a Linear Inverted Pendulum Model (LIPM) to enable the robot to respond to external disturbances with compliant motions automatically. Additionally, Zero Moment Point Intervened (ZI) estimation is employed to precisely determine the Center of Mass (CoM) state. Real-time optimization of step location is then conducted to stabilize the estimated CoM, actively responding to external disturbances. Importantly, the decision to adjust step location is quantitatively defined. To enhance efficiency, explicit solutions for both ZI Estimation and Step Location Optimization are provided to reduce computational costs. To validate our approach, we conducted simulations and experiments using the biped robot BHR-T, subjecting it to unexpected external pushes and obstacles during walking.

Design of dynamically balanced gait for the biped robot while crossing the obstacle

The primary objective of this research work is to generate a dynamically balanced gait for the 16-DOF biped robot while crossing an obstacle using the concept of the zero moment point (ZMP). Also, the authors discussed both the theoretical justification and its practical feasibility on real biped robot. Initially, the position and orientation of the biped robot were obtained with the help of forward kinematics while crossing the obstacle. Later on, various joint angles of the biped robot were calculated using the inverse kinematics approach. Further, the Lagrange-Euler formulation approach was employed for evaluating the dynamics of the biped robot. To generate the smooth gait of the biped robot, a cubic polynomial equation has been assigned for foot and wrist trajectories in the sagittal plane and hip trajectories in the horizontal plane. This integration allows the robot to cross the obstacles while maintaining dynamic balance, marking a significant advancement while crossing the obstacle with a height and width equal to 50 mm, which is 16.10% of the length of the robot’s leg. While crossing the obstacle, the gait of the biped robot has been considered in three stages, such as landing the foot on the obstacle, landing the foot on the ground away from the obstacle by one leg and crossing over the obstacle by another leg. A simulation study has been conducted on MATLAB to verify the dynamically balanced gait while crossing the obstacle. Finally, the generated gait angles are fed into the real 16-DOF biped robot developed by the Robotics Lab at MANIT Bhopal. It has been observed that the generated gait at three stages is more dynamically balanced while crossing the obstacle.

Three-dimensional variable center of mass height biped walking using a new model and nonlinear model predictive control

This paper presents a trajectory generation algorithm for a three-dimensional (3D) biped robot that can adjust the center of mass (CoM) according to the environment. We adopt a new abstract model that supports vertical motion and rotation. Differing from traditional abstract models, the proposed full centroid dynamics inverted pendulum model fully considers the robot’s movement and rotation. Unlike the zero moment point (ZMP), which only ensures the feet do not flip over, we also propose a new additional stability criterion, named zero frictional moment point (ZFMP), guaranteeing no yaw rotation while walking. Next, a nonlinear model predictive control is designed to generate the CoM trajectory, torso rotational angle, and adaptive footholds to induce various biped gaits. A full-dynamics 3D humanoid robot is simulated to test the proposed method while steering, walking underneath a low door, and walking with disturbances.

ZMP — Where Are We After Fifty-Five Years?

Twenty years ago in the first issue of IJHR, among others, there was a published paper [M. Vukobratović and B. Borovac, Zero-moment point — Thirty five years of its life, Int. J. Humanoid Robot. 1(1) (2004) 157–173], devoted to well-known zero-moment point (ZMP) concept. Its role in biped locomotion (in the preservation of dynamic balance during walking and gait synthesis) was (and still is) extremely significant. This paper is aimed to present, how far we have gone in the past 20 years in the realization of bipedal walking, what are remaining open challenges and what we can expect in the further development. At the beginning of the paper, we will briefly refer to some still existing misinterpretations of the ZMP notion, related to specific boundary cases, when the terms Center of Pressure (CoP) and ZMP are still being mixed. Then, we will point your attention to the discussion of two important issues: attempts of generalization of ZMP notion in case of motion in the presence of multiple, spatially distributed and non-planar contacts and walk realization in a non-laboratory environment (unstructured environment and on the non-flat ground surface). Of course, looking at “how humans do it” has always been an inspiration for the realization of complex tasks by humanoids. Learning to walk is a task where several successful realizations have appeared only recently, so we will look at this topic at the end of this paper.

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.

Adaptive Switching Control Based on Dynamic Zero-Moment Point for Versatile Hip Exoskeleton Under Hybrid Locomotion

Adaptive Switching Control Based on Dynamic Zero-Moment Point for Versatile Hip Exoskeleton Under Hybrid Locomotion

Torque control of a wheeled humanoid robot with dual redundant arms

Most of conventional controllers are prone to consume more computational time for controlling a wheeled humanoid robot. A nonlinear trajectory control of a wheeled humanoid robot using a model-based controller with less computational load and energy consumption is presented in this article. The upper body of the humanoid robot consists of two 6 degrees of freedom redundant arms, a three degrees of freedom torso and a two degrees of freedom neck. The nonholonomic mobile platform consists of two actuated wheels and two caster wheels. Nonlinearity of the robot dynamic model and coupling between various branches of the upper body are taken into account. The dynamic model derived using Newton–Euler approach along with decoupled Natural Orthogonal Complement matrix approach is used to derive dynamic equations of the upper body and the wheeled platform. Zero moment point based stability approach is used for verifying stable motion of the wheeled humanoid robot with minimum energy and time consumption to complete a task. The proposed computed torque controller is compared with other similar controllers developed for the same robot model to prove advantages of the proposed torque controller. Simulation results are experimentally validated with the real robot.

Parametric Design and Prototyping of a Low-Power Planar Biped Robot.

This study proposes a design approach and the development of a low-power planar biped robot named YU-Bibot. The kinematic structure of the robot consists of six independently driven axes, and it weighs approximately 20 kg. Based on biomimetics, the robot dimensions were selected as the average anthropomorphic dimensions of the human lower extremities. The optimization of the mechanical design and actuator selection of the robot was based on the results of parametric simulations. The natural human walking gait was mimicked as a walking pattern in these simulations. As a result of the optimization, a low power-to-weight ratio of 30 W/kg was obtained. The drive system of the robot joints consists of servo-controlled brushless DC motors with reduction gears and additional bevel gears at the knee and ankle joints. The robot features spring-supported knee and ankle joints that counteract the robot's weight and compensate for the backlash present in these joints. The robot is constrained to move only in the sagittal plane by using a lateral support structure. The robot's feet are equipped with low-cost, force-sensitive resistor (FSR)-type sensors for monitoring ground contact and zero-moment point (ZMP) criterion. The experimental results indicate that the proposed robot mechanism can follow the posture commands accurately and demonstrate locomotion at moderate stability. The proposed parametric natural gait simulation-based design approach and the resulting biped robot design with a low power/weight ratio are the main contributions of this study.

Design and Optimization of Multifunctional Human Motion Rehabilitation Training Robot EEGO

A multifunctional human motion rehabilitation training robot named EEGO (electric easy go) that could achieve four functions through structural transformation was designed. The four functions achieved by four working modes: the Supporting Posture Mode (SM), the Grasping Posture Mode (GM), the Riding Posture Mode (RM), and the Pet Mode (PM), which are suitable for patients in the middle and late stages of rehabilitation. The size of the equipment under different functions is determined by the height of different postures of the human. During the design process, the equipment was lightweight using size optimization methods, resulting in a 47.3% reduction in mass compared to the original design. Based on the Zero Moment Point (ZMP) stability principle, the stability mechanism of the robot was verified under the three different functions. According to the wanted function of the equipment, the control system of the equipment was designed. Finally, a prototype was prepared based on the analysis and design results for experimental verification, which can effectively assist patients in motion rehabilitation training such as gait, walking, and other movements.

Mechanical Design of a Biped Robot FORREST and an Extended Capture-Point-Based Walking Pattern Generator

In recent years, many studies have shown that soft robots with elastic actuators enable robust interaction with the environment. Compliant joints can protect mechanical systems and provide better dynamic performance, thus offering huge potential for further developments of humanoid robots. This paper proposes a new biped robot. The new robot combines a torque sensor-based active elastic hip and a spring-based passive elastic knee/ankle. In the first part, the mechanical design is introduced, and in the second part, the kinematics and dynamics capabilities are described. Furthermore, we introduce a new extended capture-point-based walking pattern generator that calculates footstep positions, which are used as input for the controller of our new biped robot. The main contribution of this article is the novel mechanical design and an extended walking pattern generator. The new design offers a unique solution for cable-driven bipeds to achieve both balancing and walking. Meanwhile, the new walking pattern generator can generate smooth desired curves, which is an improvement over traditional generators that use a constant zero-moment-point (ZMP). A simple cartesian controller is applied to test the performance of the walking pattern generator. Although the robot has been built, all experiments regarding the pattern generator are still simulated using MATLAB/Simulink. The focus of this work is to analyze the mechanical design and show the capabilities of the robot by applying a new pattern generator.

Increasing step size of the 4-link robotic simulator in stable state

In this research, the 4-Link Robotic Simulator program in MATLAB is utilized to find the relation between the length of the links and the length of the two feet. While a few previous research focused on the zero-moment point (ZMP) of the robot geometry, this neglects the change of the position of ZMP in the processes of locomotion. The simulation model is introduced to present an integrated locomotion process of the robot. The testing method was developed based on the comparison between the simulation results from MATLAB. Three different scenarios are analyzed and compared to the original outcome. The main finding of this research is concluded as the length of L5 and L6 should not be smaller than the length of L2 and L3. The critical length of the L5 and L6 was determined as 3.0065.

Center of Pressure Control for Balancing Humanoid Dance Robot Using Load Cell Sensor, Kalman Filter and PID Controller

Balance control on the Lanage Jagad humanoid dance robot is one of the means to create flexible dance movements in the robot movement system to make it more stable and can reduce the frequency of the robot falling or being unable to maintain balance when performing the dance. For the position of the robot, it can use a weight sensor or load cell sensor, the sensor measures the resistance value that can control the weight of 4 weight points on each robot leg which will later be converted into a pressure value at each point, in the study. This test was carried out with the same control behavior using an inertial sensor MPU6050. The balance on the robot uses a balance based on a load cell, which is a situation where the position of the robot in coordinates approaches the center of balance or CoP (Center of Pressure) at coordinates (0,0) or if using MPU6050 it is in a far error value condition so that it can balance the conditions so as not to falls close to the value of the robot state based on ZMP (Zero Moment Point) and CoG (Central of Gravity) as the MPU6050 sensor placement. In this study, for the balance control system using the Arduino MEGA 2560 PRO Board as a complement to the OpenCM 9.04 microcontroller, using 8 load cell sensors to determine the balance point which has been made predictions of pressure from the load cell using a kalman filter also PID control to handle the servo motor. The results from the center point of the robot's pressure have succeeded in determining the center of balance or CoP based on the X coordinates of 0 and the Y coordinates of 0 and the quadrant direction based on the center of gravity, so that the results of the balance system in standing and dancing conditions are based on the center of balance using a load cell, the success rate when standing by 87.5% and balance when dancing by 89%.

Motion Analysis of the Torso and the Elbow During Picking and Placing Heavy Object on Shelf

In recent years, labor shortages and workforce aging have become problematic. One solution to this problem is introducing humanoid robots to perform human tasks. This research is aimed at analyzing the posture and preparation posture of the torso and elbow in human motions for improving the motion planning of humanoid robots utilizing the redundant part. We analyze the frontal tilt angle of the torso, time of backward bending the torso, and lateral tilt angle of the elbow when humans apply force. In the experiments, we focused on picking and placing heavy objects on the shelf, which requires maintaining balance and exerting force, and confirmed the differences in movements by changing the weight of the objects. An optical motion capture system and a six-axis load cell were used for measuring the motion. The subjects were asked to approach the shelf from a distance of 1 m and move a heavy object from the upper to the middle height of the shelf. As a result, the heavier the object, the earlier the preparation posture of a backward bending of the torso before grasping. The heavier the object, the larger the tilt angle of the torso forward. Significant differences were observed between the time of backward bending and picking the object, distances from the shoulder to wrist joint, and tilt angle of the torso. We identified the posture and time required to bend the torso for holding a heavier object in front of the shelf, considering the dynamic stability of the Zero-Moment Point.

Online Running-Gait Generation for Bipedal Robots with Smooth State Switching and Accurate Speed Tracking.

Smooth state switching and accurate speed tracking are important for the stability and reactivity of bipedal robots when running. However, previous studies have rarely been able to synthesize these two capabilities online. In this paper, we present an online running-gait generator for bipedal robots that allows for smooth state switching and accurate speed tracking. Considering a fluctuating height nature and computational expediency, the robot is represented by a simplified variable-height inverted-pendulum (VHIP) model. In order to achieve smooth state switching at the beginning and end of running, a segmented zero moment point (ZMP) trajectory optimization is proposed to automatically provide a feasible and smooth center-of-mass (CoM) trajectory that enables the robot to stably start or stop running at the given speed. To accurately track online the desired speed during running, we propose an iterative algorithm to compute target footholds, which allows for the robot to follow the interactive desired speed after the next two steps. Lastly, a numerical experiment and the simulation of online variable speed running were performed with position-controlled bipedal robot BHR7P, and the results verified the effectiveness of the proposed methods.

Robust inverse dynamics by evaluating Newton–Euler equations with respect to a moving reference and measuring angular acceleration

Maintaining stability while walking on arbitrary surfaces or dealing with external perturbations is of great interest in humanoid robotics research. Increasing the system’s autonomous robustness to a variety of postural threats during locomotion is the key despite the need to evaluate noisy sensor signals. The equations of motion are the foundation of all published approaches. In contrast, we propose a more adequate evaluation of the equations of motion with respect to an arbitrary moving reference point in a non-inertial reference frame. Conceptual advantages are, e.g., getting independent of global position and velocity vectors estimated by sensor fusions or calculating the imaginary zero-moment point walking on different inclined ground surfaces. Further, we improve the calculation results by reducing noise-amplifying methods in our algorithm and using specific characteristics of physical robots. We use simulation results to compare our algorithm with established approaches and test it with experimental robot data.

A Novel Low-Cost ZMP Estimation Method for Humanoid Gait using Inertial Measurement Devices: Concept and Experiments

Estimation and control of zero-moment point (ZMP) is a widely used concept for planning the locomotion of bipedal robots and is commonly measured using integrated joint angle encoders and foot force sensors. Contemporary methods for ZMP measurement involve built-in contact sensors such as joint encoders or instrumented foot force sensors. This paper presents a novel approach for computing ZMP for a humanoid robot using inertial sensor-based wireless foot sensor modules (WFSMs). The developed WFSMs, strapped at different limb segments of a bipedal robot, measure lower limb joint angles in real time. The joint angle trajectories, further transformed into Cartesian position coordinates, are used for estimating the ZMP positions of humanoid robots using the planar biped model. The whole framework is presented through experimental studies for different real-life walking scenarios. Since the modules work based on the limb motion and inclination, any ground unevenness would be automatically reflected in the module output. Hence, this measurement process can be a convenient method for applications requiring humanoid control on uneven surfaces/outdoor terrains. To compare the performance of the proposed model, ZMP is simultaneously measured from inbuilt foot force sensors and joint encoders of the robot. Statistical tests exhibit a high linear correlation between the proposed method with integrated encoders and foot force sensors (Pearson’s coefficient, [Formula: see text]). Results indicate that ZMP estimated by WFSM is a viable method to monitor the dynamic gait balance of a humanoid robot and has potential application in outdoor and uneven terrains.