Stability Control for Dynamic Walking of Bipedal Robot with Real-time Capture Point Trajectory Optimization

Human biped locomotion is an ultimate style of biological movement that is a highly evolved function. Biped locomotion by robots is a dream to be attained by the most highly evolved or integrated technology, and research on this has a history of over 30 years. Many methods of generating gaits have been proposed. There has been a tendency to reduce the complicated dynamics of a walking robot to a simple inverted pendulum (Hemami et al., 1973), and to control its motion according to pre-designed time-dependent trajectories while guaranteeing zero moment point (ZMP) conditions (Vukobratovi & Stepanenko, 1972). Although such approaches have successfully been applied to practical applications and nowadays successful biped-himanoids are developed by them, problems on gait performances still remain. Several advanced approaches on the other hand have taken the robot's dynamics into account for generating gaits based on natural dynamics. Miura and Shimoyama studied dynamic bipedal walking without ankle-joint actuation (Miura & Shimoyama, 1984) and they developed robots on stilts whose foot contact occurred at a point. Sano and Furusho accomplished natural dynamic biped walking based on angular momentum using ankle-joint actuation (Sano & Furusho, 1990). Kajita proposed a method of control based on a linear inverted pendulum model with a potential-energy-conserving orbit (Kajita et al., 1992). These approaches utilized the robot’s own dynamics effectively but did not investigate the energy-efficiency by introducing performance indices. It was unclear whether or not efficient gaits were generated. McGeer's passive dynamic walking (PDW) (McGeer, 1990) has provided clues to solve these problems. Passive-dynamic walkers can walk without any actuation on a gentle slope, and they provide an optimal solution to the problem of generating a natural and energy-efficient gait. The objective most expected to be met by PDW is to attain natural, high-speed energyefficient dynamic bipedal walking on level ground like humans do. However, we need to supply power-input to the robot by driving its joint-actuators to continue stable walking on level ground, and certain methods of supplying power must be introduced. Ankle-joint torque is mathematically very important for effectively propelling the robot's center of mass (CoM) in the walking direction, and it is thus required relatively more often than other joint torques. However, to exert ankle-joint torque on a passive-dynamic walker, we need to add feet and this creates the ZMP constraint problem. We clarified that there is a trade-off between optimal gait and ZMP conditions through parametric studies, and O pe n A cc es s D at ab as e w w w .ite ch on lin e. co m

The biped walking robot has almost the same mechanisms as a human and is suitable for moving in an environment which contains stairs, obstacles, etc. However, the complex dynamics involved make the biped robot control a challenging task. For the stability of the biped walking robot, the zero moment point (ZMP) trajectory in the robot foot support area is a significant criterion. If the ZMP during walking can be measured, it is possible to realize stable walking and to stably control the biped robot by the use of the measured ZMP. In this paper, actual ZMP data are measured in real time situations from practical biped walking robot and the obtained ZMP data are modeled by TS-type fuzzy system. By the simulation results, the TS-type fuzzy system can be effectively used to model practical biped walking robot.KeywordsMean Square ErrorFuzzy SystemFuzzy ModelingBiped RobotStep MotionThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Generating nonlinear trajectories of walking patterns is one of the most important problems in stability a humanoid robot when it walks on different ground conditions. In order to solve this problem, a desired Zero Moment Point (ZMP) trajectory is firstly designed and then a Center of Mass (CoM) trajectory will be created based on this ZMP. Hence, the preview control formulation which follows the planned ZMP patterns while reducing the jerk (acceleration derivation) is considered to implement this trajectory. In this study, the walking pattern for bipedal robot is generated by using a cart-table model. The procedure of apply a preview controller to the cart-table model will be presented in this investigation. After that, the position of each leg joint of bipedal robot is also calculated by using the proposed CoM Jacobian. Finally, computer simulations are performed by utilizing RecurDyn and MATLAB softwares to validate the proposed preview control formulation for the nonlinear walking patterns generation of a Bioloid humanoid robot.

The modifiable walking pattern generation (MWPG) algorithm can handle dynamic walking commands by changing the walking period, step length, and direction independently. When an infeasible command is given, the algorithm changes the command to a feasible one. After the feasibility of the navigational command is checked, it is translated into the desired center of mass (CM) state. To achieve the desired CM state, a reference CM trajectory is generated using predefined zero moment point (ZMP) functions. Based on the proposed algorithm, various complex walking patterns were generated, including backward and sideways walking. The effectiveness of the patterns was verified in dynamic simulations using the Webots simulator.

Purpose Research on tele-operated excavators that protect the operator from the risk of tip-over excavators in hazardous working areas has increased in popularity. The tele-operated excavator is able to protect workers from risks in hazardous working areas, but the operator cannot directly access the tip-over information from the tele-operated excavator. We propose the static compensation ZMP (Zero Moment Point) algorithm for preventing excavator tip-overs. Method Firstly, kinematic and kinetic analysis of the excavator was performed. Secondly, static compensation ZMP algorithm, which uses ZMP algorithm to determine gait stability of a biped walking robot, was developed to prevent tips-over of teleoperation excavator. Static compensation ZMP algorithm minimizes ZMP-error due to rapidly changing excavator acceleration using the center of gravity through a static compensation algorithm. Finally, the result of the proposed algorithm is simulated by RecurDyn model with Matlab Simulink co-simulation method. Results & Discussion In the simulation result ZMP has been compared to static compensation ZMP-algorithm using an excavator dynamic model. From these results we see that the ZMP value is bigger than the static compensation ZMP. This means that the general ZMP is disturbed due to rapidly changing excavator acceleration. This problem is minimized by the static compensation ZMPalgorithm.

In this paper, an walking pattern tuning system based on ZMP(Zero Moment Point) for a humanoid robot is proposed. Commonly, it is inevitable to handle the stage with proficient programming skill for realization of humanoid walking. The proposed walking pattern tuning system is a program tool to finely tune the walking pattern based on ZMP by adjusting intuitive parameters that ordinary user can understand easily. The walking pattern tuning system was applied to the humanoid robot of 110cm tall and the humanoid robot with the tuned walking pattern was tested.

The paper considers methods and approaches for semi-automatic motion control of bipedal walking robots in virtual environment systems. The proposed solutions include generating a walking pattern, calculating inverse kinematics, and synthesis of PD-controllers with feedback based on the angle sensor readings. To ensure the static and dynamic stability of the walking robot, generating its movement trajectories is implemented using the criterion of zero mo-ment point (ZMP) and the inverse pendulum model with virtual height. In this case, the walking pattern is generated by solving the problem of inverse kinematics using the Leven-berg-Marquardt method to calculate the rotation angles in the robot joints. To implement semi-automatic motion control of a walking robot in a virtual environment, an approach based on the technology of functional diagrams and virtual control panels is used. Testing the proposed methods and approaches is carried out in the VirSim virtual environment software package and shows their adequacy and efficiency for modelling a walking robot movement while maintaining its balance.

An inferential investigation into how stride length influences temporal parameters within the baseball pitching delivery

Repeatability and variability of baropodometric and spatio-temporal gait parameters – Results in healthy subjects and in stroke patients

To improve the stability of bipedal walking of humanoid robots, we developed a method of setting trajectory parameters using reinforcement learning on a treadmill like testbed in a real-world environment. A deep deterministic policy gradient (DDPG) was used as the reinforcement learning algorithm. By improving the reward using a zero moment point (ZMP), the optimum value of walking stability and walking speed was determined. The robot was designed to measure the ZMP and mount weights on the upper body. In addition, a treadmill was manufactured to operate at the same speed as the walking speed of the robot. Reinforcement learning was divided into unweighted cases and cases with a weight of 1kg. At approximately 100 min, 300 episodes were performed, and reward improvements of 16.71% and 26.25% reward improvements were made. The ZMP measurements indicated that bipedal walking was performed in a safe area. Therefore, we demonstrated that the biped walking performance of a humanoid robot can be improved by the reinforcement learning of walking speed and ZMP similarity.

Purpose Walking on inclined ground is an important ability for humanoid robots. In general, conventional strategies for walking on slopes lack technical analysis in, first, the waist posture with respect to actual robot and, second, the landing impact, which weakens the walking stability. The purpose of this paper is to propose a generic method for walking pattern generation considering these issues with the aim of enabling humanoid robot to walk dynamically on a slope. Design/methodology/approach First, a virtual ground method (VGM) is proposed to give a continuous and intuitive zero-moment point (ZMP) on slopes. Then, the dynamic motion equations are derived based on 2D and 3D models, respectively, by using VGM. Furthermore, the waist posture with respect to the actual robot is analyzed. Finally, a reformative linear inverted pendulum (LIP) named the asymmetric linear inverted pendulum (ALIP) is proposed to achieve stable and dynamical walking in any direction on a slope with lower landing impact. Findings Simulations and experiments are carried out using the DRC-XT humanoid robot platform with the aim of verifying the validity and feasibility of these new methods. ALIP with consideration of waist posture is practical in extending the ability of walking on slopes for humanoid robots. Originality/value A generic method called ALIP for humanoid robots walking on slopes is proposed. ALIP is based on LIP and several changes, including model analysis, motion equations and ZMP functions, are discussed.

The authors propose learning control methods for compensative trunk motion for a biped walking robot that has a trunk, based on the ZMP (zero moment point) stability criterion, for the cases of the ZMP being inside the stable region and outside the stable region, respectively. They have developed a biped walking robot with a ZMP measurement system and a support device. The results of computer simulation and learning control experiments confirm the convergence of the learning methods and the change of the convergence rate with the change of the weight coefficient. The learning control experiments for the case of the ZMP being outside the stable region show that even though the walking state of the robot itself changes, with the support of a human and by its learning with the ZMP and the support force, stable walking even without the support of a human ultimately is realized.

This paper introduced a new walking pattern generation method for biped robots without active roll joint at the ankle and described a simple walking pattern generation method for the robot without using ZMP (Zero Moment Point) information directly. Firstly, the paper introduced a hydraulic actuated biped robot with eight degrees of freedom, which had payload capacity. Secondly, the paper provided a dynamic balance control method in the lateral plane. Not as the inverted pendulum model, this control method was also available for biped robot without active roll joint at the ankle. Thirdly, in order to decrease the vibration, the paper tried to keep the robot walking with an approximate constant speed in the frontal direction. Finally, weight loading experiments in the MD.DAMS simulation environment and physical prototype empty load experiments were used to verify the effectiveness of the proposed walking pattern methods.

The authors have been using the ZMP (zero moment point) as a criterion to distinguish the stability of walking for a biped walking robot which has a trunk. The authors introduce a control method of dynamic biped walking for a biped walking robot to compensate for the three-axis (pitch, roll and yaw-axis) moment on an arbitrary planned ZMP by trunk motion. The authors developed a biped walking robot and performed a walking experiment with the robot using the control method. The result was a fast dynamic biped walking at the walking speed of 0.54 s/step with a 0.3 m step on a flat floor. This walking speed is about 50% faster than that with the robot which compensates for only the two-axis (pitch and roll-axis) moment by trunk motion.

This paper proposes new walking pattern method for the humanoid robots. The proposed method based on the inverted pendulum uses the zero moment point(ZMP) and the center of mass(CoM). And our approach consists of feedforward controller and feedback controller. As the feedforward controller, pole-zero cancellation by series approximation(PZCSA) control plays a role of reducing the inherent property of inverted pendulum model, that is, non-minimum phase property due to the unstable zero. As the feedback controller, linear quadratic regulator(LQR) is utilized for tracking effectively the desired ZMP according to footprints of the humanoid robots. The proposed method generates the walking pattern with the combination of LQR and PZCSA. The efficiency of the proposed method is verified by simulation of generating the walking pattern.