ZMP Criterion Research Articles

Comparison of kinematic and dynamic leg trajectory optimization techniques for biped robot locomotion

The paper presents comparison analysis of two approaches in defining leg trajectories for biped locomotion. The first one operates only with kinematic limitations of leg joints and finds the maximum possible locomotion speed for given limits. The second approach defines leg trajectories from the dynamic stability point of view and utilizes ZMP criteria. We show that two methods give different trajectories and demonstrate that trajectories based on pure dynamic optimization cannot be realized due to joint limits. Kinematic optimization provides unstable solution which can be balanced by upper body movement.

Influence of Biped Robot’s Walking Parameters on its Stability

In the biped robot's walking process, walking parameters have important influence on its stability. In this arti- cle we based on the ZMP criterion, using the relationship between ZMP and the support area to judge the walking stabil- ity. Calculate the size of stability margin to analyze the influence of parameters' change on stability. By programming in MATLAB and simulating in ADAMS, get the effects of gait parameters (step length, walk cycle, etc) on stability, put forward the reasonable selecting region of parameters, using genetic algorithm to get multiple sets of comprehensive pa- rameters for analysis, the impact of each parameter on stability is identified. It may provide reference for the robot's gait planning later.

Kinematically stable bipedal locomotion using ionic polymer–metal composite actuators

Ionic conducting polymer–metal composites (abbreviated as IPMCs) are interesting actuators that can act as artificial muscles in robotic and microelectromechanical systems. Various black or gray box models have modeled the electrochemical–mechanical behavior of these materials. In this study, the governing partial differential equation of the behavior of IPMCs is solved using finite element methods to find the critical actuation parameters, such as strain distribution, maximum strain, and response time. One-dimensional results of the FEM solution are then extended to 2D to find the tip displacement of a flap actuator and experimentally verified. A model of a seven-degree-of-freedom biped robot, actuated by IPMC flaps, is then introduced. The possibility of fast and stable bipedal locomotion using IPMC artificial muscles is the main motivation of this study. Considering the actuator limits, joint path trajectories are generated to achieve a fast and smooth motion. The stability of the proposed gait is then evaluated using the ZMP criterion and motion simulation. The fabrication parameters of each actuator, such as length, platinum plating thickness and installation angle, are then determined using the generated trajectories. A discussion on future studies on force–torque generation of IPMCs for biped locomotion concludes this paper.

Online bio-inspired trajectory generation of seven-link biped robot based on T–S fuzzy system

This paper proposes a novel method for real-time trajectory generation of a seven-link planar biped robot. Individual joint trajectories are generated by specifying only two key parameters, walking speed and step length. The proposed method combines several methods and concepts including kinematics, dynamics, trajectory generation, experimental design, Takagi–Suguno fuzzy systems, central pattern generator (CPG), ZMP criterion and a dynamic balance method. A fuzzy relationship between walking and CPG parameters is learned using experimental design methodology and T–S fuzzy systems. A method based on the Fourier series is used to tune parameters of the CPG. The proposed method allows making online changes to step length and walking speed while ensuring robot's dynamic balance. A multibody simulation package is selected and the effectiveness of the method is illustrated using several examples. It is also shown that changes in joint angles, as the result of online changes to the walking parameters, occur in a smooth and continuous manner.

Optimal prediction of human postural response under anterior–posterior platform tilting

Previous studies have suggested that human beings movements can be related to the problem of cost function minimization. But at the present time it is not clear that which objective function(s) and constraints are used by central nervous system (CNS) to produce optimal reactions under perturbations. Present study has been done experimentally and by numerical simulations to explore the stability constraints which should be used in combination with energy based cost function (weighted minimum torque) to estimate the motor planning criterion is used by CNS for disturbance rejections. The influence of three stability criterions (ZMP, extrapolated center of mass and a vertical force criterion) in combination with minimum torque model on the optimal trajectory formation is investigated. First, the response of 10 male healthy persons to platform oscillation was recorded by motion analysis system and the hip, knee and ankle angular trajectories were derived from recorded data. Second, the dynamic simulation of a four-segment, three actuated degrees of freedom mechanical model of the human body was performed using predictive dynamic method which leads to an optimization problem. The simulated trajectories were then compared to the experimental data. With comparison between experimental results, the weighting coefficients of the objective function were found to achieve best estimation. It was seen that the minimum torque objective function with weighting coefficients gives trajectories that are mostly matched with experimental observation. Moreover, the results showed that between stability criterions, the ZMP predictions are near to experimental results. Although by using vertical force criterion some nearness to experimental results are lost (in comparison with ZMP criterion) but a secured flat-foot posture for the model is obtained which this posture is more applicable than others in humanoid implementations.

A Gait Planning Method for Biped Heel-and-toe Robot

The paper taking the 6-DOF biped heel-and-toe robot as the research object, according to the expected walking pose and gravity center of the robot, using the Denavit-Hartenberg formula to establish the kinematics model and kinematics equation of the biped heel-and-toe robot. Under the ZMP criterion conditions, the kinematics equations in each discrete point are solved out via the walking pose, and constituted the motion joints curves. The simulation results of motion joints curves from the Matlab proved that the method of gait planning can achieve the aim of biped heel-and-toe robot's stable dynamic walking.

Design, Modeling, and Prototyping of a Simple Semi-Modular Biped Actuated by Shape Memory Alloys

In this article, a prototype of a biped robot actuated by SMA springs with minimum degrees of freedom is presented. SMA springs are a class of smart materials that are known for their high energy to weight ratios. It is shown that utilizing spring type SMAs has many advantages as large deformation, smooth and silent motion compared to ordinary type of actuators. A modular concept is applied for the development of the proposed biped robot where the SMA springs are utilized as actuators. A module with proper DOF is developed, that is its position and stiffness is controllable and makes the biped stable with five DOFs. Walking trajectory is generated validating the ZMP criteria and it is shown that this criterion can be simplified to the COG criteria due to slow response nature of the SMAs. To verify the design, a complete model of the biped actuated with SMA is developed through simulation with the help of MATLAB and Visual.Nastaran software. Finally to validate the results, a prototype is manufactured and tested. Experimental results show reasonable agreement with simulation results which resulted in stable walking of the proposed biped.

Application and Research of Humanoid Robot Based on Second-Order Cone Programming

It is an extremely complex process of controlling walking motion for humanoid robot, and its dynamics model has many rich features. The article puts forward a kind of optimization design method on any time humanoid robot walking movement. Firstly, this article makes a stability analysis of walking humanoid robot based on the ZMP criterion, at the same time with the design of using a humanoid robot walking movement by the criterion of the error between the expectations and kinetic energy of the weighted kinetic minimum norm make the problem into a second-order cone programming (SOCP) optimization problem, then use the interior point method to solve the kinetic energy of optimization coefficient of the humanoid robot walking movement, and by compares with the LMS design method and genetic algorithms, finally the algorithm is validated in the simulation and experiment, the numerical results are present for illustration.

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.

Biological inspiration used for robots motion synthesis

This work presents a biologically inspired method of gait generation. Bipedal gait pattern (for hip and knee joints) was taken into account giving the reference trajectories in a learning task. The four coupled oscillators were taught to generate the outputs similar to those in a human gait. After applying the correction functions the obtained generation method was validated using ZMP criterion. The formula suitable for real-time motion generation taking into account the positioning errors was also formulated. The small real robot prototype was tested to be able walk successfully following the elaborated motion pattern.

A consideration on biped lateral motion planning with robot experiment of adaptive frontal-plane stepping

In this paper, an method for biped lateral motion control is discussed, taking into consideration that the main purpose of frontal-plane is the stabilization of the inverted pendulum. Usually, the ZMP criterion is adopted to the biped control. However, the joint or the CoG reference trajectories generated based on the ZMP criterion sometimes have to be modified in relation to environmental changes. From this point of view, a control method without their reference trajectories is proposed for the biped frontal-plane motion. This control method using ground reaction force information is equivalent to the ZMP feedback control. The experiments of a biped robot whose degrees of freedom of motion is limited in the frontal plane demonstrate the effectiveness of this control method.

2A1-E07 ZMP修正指標マップを用いた連続不整地歩行

2A1-E07 ZMP修正指標マップを用いた連続不整地歩行

Cooperation of Humanoid Robots Using Teleoperation for Transferring an Object

In this paper, a method is proposed for humanoid robots performing object transfering task in a teleoperated cooperative paradigm. The cooperative task is accomplished using simple communication among two humanoid robots and then switch between modes according to the situation. In case of object passing with two humanoid robots, mutual position shifts may occur while they are moving. Therefore, it is necessary to correct the position in a real-time manner. To control the arm and hand of the robot remotely we use master arm and hand while it carries and passes the object, the dynamic stability during the execution of walking is ensured by incorporating the ZMP criterion and the desired spacing between the robots is controlled by Leader follower type control. Object passing cooperation for two humanoid robots is based on computer control, wireless LAN, vision, cooperative handling control and text commands. The method is applied as key software of the system. The effectiveness of the proposed methodology for performing cooperatively real time tasks is discussed.

2A1-D19 踵接地・爪先離地動作に着目したヒューマノイドロボットのヒト歩行模擬

A humanoid robot -WABIAN-2R- capable of human-like walks with knees stretched, heel-contact and toe-off motion is proposed in this paper. WABIAN-2R has two 1-DOF passive joint in its feet to bend toes in steady walking. Also it has two 6-DOF legs, a 2-DOF pelvis, a 2-DOF trunk, two 7-DOF arms with 3-DOF hands, and a 3-DOF neck. Furthermore a new pattern generation algorithm for walking patterns with knee stretched, heel-contact and toe-off motion based on ZMP criterion is described. In this pattern generation, some parameters of foot trajectories of a biped robot are optimized by using a Genetic Algorithm in order to generate a continuous and smooth leg motion. Software simulations and walking experiments are conducted, and the effectiveness of the pattern generation and mechanism of WABIAN-2R that have an ability to realize more human-like walking styles of a humanoid robot. is confirmed.

Yabiro, a new approach for small biped robots

In this paper, we present a new biped robot design, called YABIRO. This is a small robot that can walk autonomously. We present a low cost robot platform with a structure based on low cost materials, like servomotors, inexpensive sensors, microcontrollers, etc. The robot has a total of 14 DOF. This number of joints enables YABIRO to produce many different gait configurations. The control system has been implemented on an embedded Power PC platform that is connected through a CAN network to a ZMP sensor system and a host PC. This control system implements a control architecture based on ZMP criteria. The goal of this design is to obtain a low cost and open platform for future research on bipedal robot systems.

Trajectory Planning of Mobile Manipulator with Stability Considerations

In this paper, a problem of trajectory planning for a mobile manipulator with stability considerations is presented. We derive the dynamics of the mobile manipulator considering it as the combined system of the manipulator and the mobile platform. As a measure for the system stability, a ZMP criterion is used. The planning problem is formulated as an optimal control problem with some constraints. To solve the problem, we use a hierarchical gradient method which synthesizes the gradient function in a hierarchical manner based on the order of priority. The simulation results of the 2-link planar nonholonomic mobile manipulator are given to show the effectiveness of the proposed algorithm.

Cooperative Biped Locomotion Control Based on the Posture of Supporting Leg

Stable biped locomotion is realized under cooperation between motions on frontal plane and on sagittal plane. Therefore, regulating motion on frontal plane has much effect on stabilizing locomotion. However, few discussions about motion control on frontal plane have been taking place. We propose cooperative control that regulates motion on frontal plane so that the cooperation may be kept. In the method, motion on frontal plane is approximated with an inverted pendulum model, and interference of motion on sagittal plane with that on frontal plane is regarded as external force. Then, compliance controller on frontal plane is designed to achieve cooperative control objective that is set up based on ZMP criterion. The compliance controller and the rhythm-correction feedback control system proposed by S. Kawaji et al. [13, 14] are integrated into cooperative biped locomotion control system. The effectiveness of the system in stabilizing locomotion was verified through a locomotion simulation.