Zero Moment Point Error Research Articles

A New Stability Framework for Trajectory Tracking Control of Biped Walking Robots

This article proposes a new stability criterion for biped walking systems on the linear inverted pendulum model, in which the dynamic relationship between the center of mass (CoM) and the zero moment point (ZMP) is dealt with. More precisely, based on the fact that a biped walking robot is stable if its ZMP is always located in the supporting region, we consider whether the ZMP error between its reference and real values stays inside a certain area to guarantee the stability condition. To this end, a norm-based new stability criterion is introduced, in which the temporal supremum of the ZMP error is concerned. Regarding the applicability of the stability criterion, we propose two control approaches to biped walking systems with the consideration of the norm-based stability criterion. In other words, full-state and observer-based feedback control approaches are analyzed in this article, and the initial CoM conditions with respect to the stability criterion are obtained for the two control approaches. We call the sets derived by such conditions the stability regions. Toward a more practical significance, we also deal with the effect of unknown disturbances and sensor noises on the stability of biped walking systems. More importantly, even though computing stability regions intrinsically involves an infinite number of linear inequalities, all the stability regions are shown to be explicitly obtained through only finite numbers of computations in this article. Finally, some simulation results are provided to demonstrate the validity as well as the practical applicability of the developed computation methods.

Balance recovery through model predictive control based on capture point dynamics for biped walking robot

This study proposes an online walking-pattern generation algorithm with footstep adjustment. The algorithm enables a biped walking robot to effectively recover balance following external disturbance. The external disturbance is measured as a capture-point error, and a desired zero-moment point (ZMP) is determined to compensate for the capture-point error through a capture-point control method. To follow the desired ZMP, the optimal ZMP and the position of the foot to be changed are determined through model predictive control (MPC). In the MPC, quadratic programming is implemented considering a cost function that minimizes the ZMP error, the constraints that the ZMP maintains within the support polygon, and the constraints on the varying foot positions. The proposed algorithm helps a humanoid robot (DRC-HUBO+) to regain balance following disturbance, i.e., from strong pushing or stepping on unexpected obstacles.

Learning and Generalization of Compensative Zero-Moment Point Trajectory for Biped Walking

This paper presents an online learning framework for improving the robustness of zero-moment point (ZMP)-based biped walking controllers. The key idea is to learn a feedforward compensative ZMP (CZMP) trajectory from measured ZMP errors during repetitive walking motions by applying iterative learning control theory. The learned CZMP trajectory adjusts the reference ZMP and reduces the effect of unmodeled dynamics at the pattern-generation stage. From individual learned CZMP trajectories of typical walking parameters, we can build up a CZMP database. This database can be used for generating an initial CZMP whenever a new walking pattern is executed. A prediction from the database is done by $k$ -nearest neighbor regression based on the Mahalonobis distance. Compared with state-of-the-art model-based methods, the proposed learning approach is model free and allows online adaptation to constant unknown disturbances. Enhanced walking robustness can be observed from reduced average ZMP error and more robust reaction against external disturbances on the DLR humanoid robot TORO.

Walking control of humanoid robot based on extreme learning machine

This paper investigates the dynamic balance problem of humanoid robot and presents a systematic control architecture. In order to achieve better locomotion stability and control performance, a hybrid offline and online control algorithm based on all robot joints is proposed. Considering the complicated nonlinear relationship between zero-moment-point (ZMP) and robot joints, an offline learning algorithm based on extreme learning machine (ELM) is adopted to approximate the centre of mass (CoM) correction value according to ZMP error. Then, an online control method is employed to adjust all joints trajectories according to CoM position by minimising energy consumption. Given the optimised joints motion, an adaptive control system is proposed to track the desired trajectories and the stability proof is provided. The simulation results validate the proposed method.

Tuning a PD Controller Based on an SVR for the Control of a Biped Robot Subject to External Forces and Slope Variation

Real-time balance control of an eight-link biped robot using a zero moment point (ZMP) dynamic model is difficult to achieve due to the processing time of the corresponding equations. To overcome this limitation an intelligent computing technique based on Support Vector Regression (SVR) is developed and presented in this paper. To implement a PD controller the SVR uses the ZMP error relative to a reference and its variation as inputs, and the output is the correction of the angle of the robot's torso, necessary for its sagittal balance. The SVR was trained based on simulation data generated using a PD controller. The initial values of the parameters of the PD controller were obtained by the second Ziegler-Nichols method. In order to evaluate the balance performance of the biped robot, three performance indexes are used.The ZMP is calculated by reading four force sensors placed under each of the robot's feet. The gait implemented in this biped is similar to a human gait, which is acquired and adapted to the robot's size.The main contribution of this paper is the fine-tuning of the ZMP controller based on the SVR. To implement and test this, the biped robot was subjected to external forces and slope variation. Some experiments are presented and the results show that the implemented gait combined with the correct tuning of the SVR controller is appropriate for use with this biped robot. The SVR controller runs at 0.2 ms, which is about 50 times faster than a corresponding first-order TSK neural-fuzzy network.

Feedforward Compensation Methods for Zero Moment Point Error from Gyrating Locomotion of Wheel-Legged Mobile Robot based on Previewing Centrifugal Force

Feedforward Compensation Methods for Zero Moment Point Error from Gyrating Locomotion of Wheel-Legged Mobile Robot based on Previewing Centrifugal Force

Adaptive PD Controller Modeled via Support Vector Regression for a Biped Robot

The real-time balance control of an eight link biped robot using a zero moment point (ZMP) dynamic model is difficult due to the processing time of the corresponding equations. To overcome this limitation, an intelligent computing control technique is used. This technique is based on support vector regression (SVR). The method uses the ZMP error and its variation as inputs, and the output is the correction of the robot's torso necessary for its sagittal balance. The SVR is trained based on simulation data and their performance is verified with a real biped robot. The ZMP is calculated by reading four force sensors placed under each robot's foot. The gait implemented in this biped is similar to a human gait that is acquired and adapted to the robot's size. Some experiments are presented, and the results show that the implemented gait combined with the SVR controller can be used to control this biped robot. The SVR controller performs the control in 0.2 ms.

Walking Control for Humanoid Robot Based on ZMP Error Correction

Both undesirable walking environment and external perturbations will cause the ZMP(zero moment point) error and affect the walking stability of the humanoid robot.Since ZMP is affected by angles of all robot joints,it is difficult to achieve good walking-control performance if only correcting the ankle or hip angles of the support leg.Therefore,considering the influence of all joint angles on ZMP,the way to calculate the CoM(center of mass) position displacement of robot is studied by fuzzy controller based on ZMP error.Then angle corrections of all joints to match the CoM position displacement are computed by using quadratic programming and CoM Jacobian matrix.The simulation results show that by this method,the desired ZMP trajectory can be tracked very well,and the walking stability margin is improved,which helps the humanoid robot walk stably.

Dynamic Balance Control for Biped Robot Walking Using Sensor Fusion, Kalman Filter, and Fuzzy Logic

The walking ability is a fundamental research for biped robots, and there always needs to be a criterion used for judging the walking stability. The zero moment point (ZMP) criterion is one of the useful standards for measuring biped robot walking. Here, a new ZMP trajectory model with adjustable parameters is proposed to modulate the ZMP trajectory both in sagittal and lateral planes and make the ZMP trajectory more flexible. A dynamic balance control (DBC), which includes Kalman filter (KF) and the fuzzy motion controller (FMC), is also designed to keep the body balance and make the biped walking following the desired ZMP reference. In addition, KF is utilized to estimate the system states and reduce the effect caused by noise. Using sensor fusion technique, ZMP error and trunk inclination measured by the force sensor and accelerometer are served as the inputs for FMC, which is presented to correct each joint of the biped robot dynamically. When a biped robot walks under different ground conditions, the coordination of the designed ZMP trajectory and proposed DBC can achieve a successful biped walking. Finally, there are several experiments presented to demonstrate the feasibility and effectiveness of the proposed control scheme.

SVR CONTROLLER FOR A BIPED ROBOT IN THE SAGITTAL PLANE WITH HUMAN-BASED ZMP TRAJECTORY REFERENCE AND GAIT

This paper introduces two new important issues to be considered in the design of the zero moment point (ZMP) trajectory of a biped robot. It was verified experimentally that in the human gait the ZMP trajectory moves along the foot in a way that it is shifted forward relative to its center. To take this into account a shift parameter is then proposed. It was also verified experimentally that in the human gait the ZMP trajectory amplitude depends on the swing time, reducing to zero for a static gait. It is then proposed a parameter to take into account this variation with the swing time of the gait. Six experiments were carried out for three different X ZMP trajectory references. In order to evaluate and compare the performance of the biped robot using the three X ZMP trajectory references two performance indexes are proposed. For the real-time balance control of this 8 link biped robot it was used an intelligent computing control technique, the Support Vector Regression (SVR). The control method uses the ZMP error and its variation as inputs and the output is the correction of the robot's ankle and torso angles, necessary for the sagittal balance of the biped robot.

Enhancing Zero Moment Point-Based Control Model: System Identification Approach

The approximation of a humanoid robot by an inverted pendulum is one of the most frequently used models to generate a stable walking pattern using a planned zero moment point (ZMP) trajectory. However, on account of the difference between the multibody model of the humanoid robot and the simple inverted pendulum model, the ZMP error might be bigger than the polygon of support and the robot falls down. To overcome this limitation, we propose to improve the accuracy of the inverted pendulum model using system identification techniques. The candidate model is a quadratic in the state space representation. To identify this system, we propose an identification method that is the result of the comprehensive application of system identification to dynamic systems. Based on the quadratic system, we also propose controlling algorithms for on-line and off-line walking pattern generation for humanoid robots. The efficiency of the quadratic system and the walking pattern generation methods has been successfully shown using dynamical simulation and conducting real experiments on the cybernetic human HRP-4C.

Sagittal stability PD controllers for a biped robot using a neurofuzzy network and an SVR

SUMMARYThe real-time balance PD control of an eight-link biped robot using a zero-moment point (ZMP) dynamic model is implemented using two alternative intelligent computing control techniques that were compared: one based on support vector regression (SVR) and another based on a first order Takagi–Sugeno–Kang (TSK) -type neural-fuzzy (NF). Both methods use the ZMP error, and its variation as inputs and the output is the correction of the robot's torso necessary for its sagittal balance. The SVR and the NF were trained based on simulation data, and their performance was verified with a real biped robot. Two performance indexes are proposed to evaluate and compare the online performance of the two control methods.The ZMP is calculated by reading four force sensors placed under each robot's foot. The gait implemented in this biped is based on ankle and hip human trajectories that were acquired and adapted to the robot's size. Some experiments are presented and the results show that the implemented gait combined either with the SVR controller or with the TSK NF network controller can be used to control this biped robot. The SVR and the NF controllers exhibit similar stability, but the SVR controller runs at 0.2 ms, about 50 times faster than the NF controller and much faster than a controller based on full ZMP dynamic model equations.

SVR Versus Neural-Fuzzy Network Controllers for the Sagittal Balance of a Biped Robot

The real-time balance control of an eight-link biped robot using a zero moment point (ZMP) dynamic model is difficult due to the processing time of the corresponding equations. To overcome this limitation, two alternative intelligent computing control techniques were compared: one based on support vector regression (SVR) and another based on a first-order Takagi-Sugeno-Kang (TSK)-type neural-fuzzy (NF) network. Both methods use the ZMP error and its variation as inputs and the output is the correction of the robot's torso necessary for its sagittal balance. The SVR and the NF were trained based on simulation data and their performance was verified with a real biped robot. Two performance indexes are proposed to evaluate and compare the online performance of the two control methods. The ZMP is calculated by reading four force sensors placed under each robot's foot. The gait implemented in this biped is similar to a human gait that was acquired and adapted to the robot's size. Some experiments are presented and the results show that the implemented gait combined either with the SVR controller or with the TSK NF network controller can be used to control this biped robot. The SVR and the NF controllers exhibit similar stability, but the SVR controller runs about 50 times faster.

Policy Gradient Fuzzy Reinforcement Learning Control of Humanoid Walking

This paper presents a novel dynamic control approach to acquire biped walking of humanoid robots focussed on policy gradient reinforcement learning with fuzzy evaluative feedback. The proposed structure of controller involves two feedback loops: conventional computed torque controller including impact-force controller and reinforcement learning computed torque controller. Reinforcement learning part includes fuzzy information about Zero-Moment Point errors. To demonstrate the effectiveness of our method, we apply it in simulation to the learning of a biped walking.

Dynamic Control Algorithm for Biped Walking Based on Policy Gradient Fuzzy Reinforcement Learning

This paper presents a novel dynamic control approach to acquire biped walking of humanoid robots focussed on policy gradient reinforcement learning with fuzzy evaluative feedback. The proposed structure of controller involves two feedback loops: conventional computed torque controller including impact-force controller and reinforcement learning computed torque controller. Reinforcement learning part includes fuzzy information about Zero-Moment Point errors. To demonstrate the effectiveness of our method, we apply it in simulation to the learning of a biped walking.

An effective trajectory generation method for bipedal walking

This paper presents the virtual height inverted pendulum mode (VHIPM), which is a simple and effective trajectory generation method for the stable walking of biped robots. VHIPM, which is based on the inverted pendulum mode (IPM), can significantly reduce the zero moment point (ZMP) error by adjusting the height in the inverted pendulum. We show the relationship between VHIPM and other popular trajectory generation methods, and compare the ZMP errors in walking when trajectories are generated by various methods including VHIPM. We also investigate the sensitivity of the ZMP error in VHIPM to the step length, walking period and mass distribution of a robot. The simulation results show that VHIPM significantly reduces the ZMP errors compared to other methods under various circumstances.

BALANCE CONTROL OF HUMANOID ROBOT FOR HUROSOT

This paper presents balance control of humanoid robot for HuroSot using its upper body motion and swinging two arms. The upper body is modeled as an inverted pendulum for an on-line compensation. By using the upper body motion it compensates ZMP (Zero Moment Point) error, obtained by FSR (Force Sensitive Resistor) sensors attached on the sole of the foot. Also by swinging the arms it can cancel the yawing moment such that it can walk properly by keeping its overall balance. Experimental results of balance control of HSR-V, a small sized humanoid robot for HuroSot designed and developed in the RIT laboratory at KAIST, are described to demonstrate the effectiveness and applicability of the proposed method.