• The Journal of Korea Robotics Society
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• v.6 no.4
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• pp.301-307
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• 2011

Based on the stability criteria of ZMP (Zero Moment Point), this paper proposes an adjusting algorithm that modifies walking trajectory of a bipedal robot for stable walking by analyzing ZMP trajectory of it. In order to maintain walking balance of the bipedal robot, ZMP should be located within a supporting polygon that is determined by the foot supporting area with stability margin. Initially tilting imposed to the trajectory of the upper body is proposed to transfer ZMP of the given walking trajectory into the stable region for the minimum stability. A neural network method is also proposed for the stable walking trajectory of the biped robot. It uses backpropagation learning with angles and angular velocities of all joints with tilting to get the improved walking trajectory. By applying the optimized walking trajectory that is obtained with the neural network model, the ZMP trajectory of the bipedal robot is certainly located within a stable area of the supporting polygon. Experimental results show that the optimally learned trajectory with neural network gives more stability even though the tilting of the pelvic joint has a great role for walking stability.

• Journal of Institute of Control, Robotics and Systems
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• v.15 no.12
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• pp.1216-1222
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• 2009

This article describes a simple method for generating the walking trajectory for the biped humanoid robot. The method used a simple inverted model instead of complex multi-mass model and a reasonable explanation for the model simplification is included. The problem of gait trajectory generation is to find the solution from the desired ZMP trajectory to CoG trajectory. This article presents the analytic solution for the bipedal gait generation on the bases of ZMP trajectory. The presented ZMP trajectory has Fourier series form, which has finite or infinite summation of sine and cosine functions, and ZMP trajectory can be designed by calculating the coefficients. From the designed ZMP trajectory, this article focuses on how to find the CoG trajectory with analytical way from the simplified inverted pendulum model. Time segmentation based approach is adopted for generating the trajectories. The coefficients of the function should be designed to be continuous between the segments, and the solution is found by calculating the coefficients with this connectivity conditions. This article also has the proof and the condition of solution existence.

• Proceedings of the KIEE Conference
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• 1998.11b
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• pp.546-548
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• 1998

This paper deals with ZMP trajectory generation in multi step walking of IWR-III(Inha Walking Robot) Biped Walking Robot. Biped walking is realized by combining 6-types of pre-defined steps and the actual ZMP can be used as a stability index of a robot. For the good tracking of actual ZMP, desired ZMP trajectory is generated during the whole walking time not for each step. Trajectory generation is performed considering velocities and accelerations of given via points using 5-th order polynomial interpolation method. As a result, balancing joints have a more smooth and continuous motion and actual ZMP has a better tracking ability. Numerical simulator is done by MATLAB to guarantee the walking of a robot satisfying the ZMP stability.

• 제어로봇시스템학회:학술대회논문집
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• 2001.10a
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• pp.137.3-137
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• 2001

Many locomotion purpose robots are being built and are under research such as mobile manipulator and biped humanoid robot, etc. Dynamic posture stability of these robots is based on the ZMP point. For getting stable ZMP trajectory, some method has been developed but is too complex and time consuming which leads to inability in generating on-line ZMP trajectory. In this paper, we give a qualitative study about behavior of ZMP in biped walking robot through visualization. This result gives intuitive understanding about behavior of ZMP under various robot state.

• The Journal of Korea Robotics Society
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• v.8 no.2
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• pp.92-103
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• 2013

Humanoid robot is the most intimate robot platform suitable for human interaction and services. Biped walking is its basic locomotion method, which is performed with combination of joint actuator's rotations in the lower extremity. The present work employs humanoid robot simulator and numerical optimization method to generate optimal joint trajectories for biped walking. The simulator is developed with Matlab based on the robot structure constructed with the Denavit-Hartenberg (DH) convention. Particle swarm optimization method minimizes the cost function for biped walking associated with performance index such as altitude trajectory of clearance foot and stability index concerning zero moment point (ZMP) trajectory. In this paper, instead of checking whether ZMP's position is inside the stable region or not, reference ZMP trajectory is approximately configured with feature points by which piece-wise linear trajectory can be drawn, and difference of reference ZMP and actual one at each sampling time is added to the cost function. The optimized joint trajectories realize three phases of stable gait including initial, periodic, and final steps. For validation of the proposed approach, a small-sized humanoid robot named DARwIn-OP is commanded to walk with the optimized joint trajectories, and the walking result is successful.

• Journal of the Korean Society for Precision Engineering
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• v.29 no.4
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• pp.417-425
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• 2012

This paper presents reference ZMP trajectory generation and implementation for a biped robot via linear inverted dumbbell model (LIDM), which can consider the effect of external momentum on the center of mass (COM) of robot. Based on a reference ZMP trajectory derived by using LIDM, a base trajectory is proposed not only to make the locomotion of robot similar to that of human but also to facilitate its implementation and tuning. In order to realize a dynamic walking using the proposed trajectory, compliance, impedance and ZMP tracking controllers are adopted together. Extensive experiments show that the proposed locomotion of a biped robot is stable and also, similar to that of human. Further researches on balance recovery of a biped robot will be carried out to guarantee its robust locomotion in combination with the proposed trajectory.

• Journal of the Korean Society for Precision Engineering
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• v.22 no.7 s.172
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• pp.112-121
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• 2005

This paper is concerned with smooth trajectory generation of biped robot which has inverted pendulum type balancing weight. Genetic algorithm is used to generate the trajectory of the leg and balancing weight. Balancing trajectory can be determined by solving the second order differential equation under the condition that the reference ZMP (Zero moment point) is settled. Reference ZMP effect on gait pattern absolutely but the problem is how to determine the reference ZMP. Genetic algorithm can find optimal solution under the high order nonlinear situation. Optimal trajectory is generated when use genetic algorithm which has some genes and a fitness function. In this paper, minimization of balancing joints motion is used for the fitness function and set the weight factor of the two balancing joints at the fitness function. Inverted pendulum type balancing weight is very similar with human and this model can be used fur humanoid robot. Simulation results show ZMP trajectory and the walking experiment made on the real biped robot IWR-IV.

• Journal of the Korean Society for Precision Engineering
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• v.21 no.7
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• pp.115-123
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• 2004

This paper deals with the gait optimization of via points on biped robot. ZMP(Zero Moment point) is the most important index in a biped robot's dynamic walking stability. To stable walking of a biped robot, leg's trajectory and a desired ZMP trajectory is required, balancing motion is solved by FDM(Finite Difference Method). In this paper, optimal index is defined to dynamically stable walking of a biped robot, and genetic algorithm is applied to optimize gait trajectory and balancing motion of a biped robot. By genetic algorithm, the index of walking parameter is efficiently optimized, and dynamic walking stability is verified by ZMP verification equation. Genetic algorithm is only applied to balancing motion, and is totally applied to whole trajectory. All of the suggested motions of biped robot are investigated by simulations and verified through the real implementation.

• Journal of the Korea Computer Graphics Society
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• v.5 no.2
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• pp.33-41
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• 1999

This paper presents a new algorithm about motion adjustment for dynamic balance. It adjusts an unbalanced motion to an balanced motion while preserving the nuance of original motion. We solve dynamic balancing problem using the zero moment point (ZMP) which is often used for controlling the balance of biped robot. Our algorithm is consists of four steps. First, it fits joint angle data to spline curves for reducing noise. Second, the algorithm analyzes the ZMP trajectory so that it can detects the dynamically-unbalanced duration. Third, the algorithm project the ZMP trajectory into the supporting area if the trajectory deviates from the area. Finally, the algorithm produces the balanced motion that satisfies the new ZMP trajectory. In this step, the constrained optimization method is used so that the new motion keeps the original motion characteristics as much as possible. We make several experiments in order to prove that our algorithm is useful to add physical realism to a kinematically edited motion.

• Journal of Institute of Control, Robotics and Systems
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• v.17 no.7
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• pp.659-667
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• 2011

The study of bipedal robot is towards similar shape and function with human. In this paper, we propose a human-like walking pattern compatible to the flexible foot with toe and heel structure. The new walking pattern for a bipedal robot consists of ZMP, center of mass (CoM), and ankle trajectory and is drawn by considering human kinesiology. First, the ZMP trajectory moves forward without stopping at a point even in the single support phase. The corresponding CoM trajectory to the ZMP one is derived by solving differential equations. As well, a CoM trajectory for the vertical axis is added by following the idea of human motion. The ankle trajectory closely mimics the rotational motion of human ankles during taking off and landing on the ground. The advantages of the proposed walking pattern are demonstrated by showing improved stability, decreased ankle torque, and the longer step length capability. Specifically, it is interesting to know that the vertical CoM motion is able to compensate for the initial transient response.