Zero Moment Point Research Articles

Visual Lifting Approach for Bipedal Walking with Slippage

[abstFig src='/00290003/05.jpg' width='300' text='Concept of visual lifting approach' ] Biped locomotion generated by control methods based on Zero-Moment Point (ZMP) has been achieved and its efficacy for stable walking, where ZMP-based walking does not include the falling state, has been verified extensively. The walking control that does not depend on ZMP – we call it dynamical walking – can be used in walking that utilizes kicks by toes, which looks natural but is vulnerable to turnover. Therefore, keeping the walking of dynamical motion stable is indispensable to the realization of human-like natural walking – the authors perceive the human walking, which includes toe off states, as natural walking. Our research group has developed a walking model, which includes slipping, impact, surface-contacting and line-contacting of foot. This model was derived from the Newton-Euler (NE) method. The “Visual Lifting Approach” (VLA) strategy inspired from human walking motion utilizing visual perception, was used in order to enhance robust walking and prevent the robot from falling, without utilizing ZMP. The VLA consists of walking gate generation visual lifting feedback and feedforward. In this study, simulation results confirmed that bipedal walking dynamics, which include a slipping state between foot and floor, converge to a stable walking limit cycle.

Gait and trajectory rolling planning and control of hexapod robots for disaster rescue applications

Hexapod robots have stronger adaptability to dynamic unknown environments than wheeled or trucked ones due to their flexibility. In this paper, a novel control strategy based on rolling gait and trajectory planning, which enables hexapod robots to walk through dynamic environments, is proposed. The core point of this control strategy is to constantly change gait and trajectory according to different environments and tasks as well as stability state of robot. We established a gait library where different kinds of gaits are included. Zero moment point, which indicates the stability of robot, is estimated by a Kalman filter. According to this control strategy, a hierarchical control architecture consisting of a man–machine interface, a vision system, a gait and trajectory planner, a joint motion calculator, a joint servo controller, a compliance controller and a stability observer is presented. The control architecture is applied on a hexapod robot engaging in disaster rescue. Simulation and experimental results show the effectiveness of our control strategy.

Design of Optimized Multiobjective Function for Bipedal Locomotion Based on Energy and Stability

Abstract This paper presents a novel analytical method to develop the multiobjective function including energy and stability functions. The energy function has been developed by unique approach of orbital energy concept and the stability function obtained by modifying the pre-existing zero moment point (ZMP) trajectory. These functions are optimized using real coded genetic algorithm to produce an optimum set of walk parameters. The analytical results show that, when the energy function is optimized, the stability of the robot decreases. Similarly, if the stability function is optimized, the energy consumed by the robot increases. Thus, there is a clear trade-off between the stability and energy functions. Thus, we propose the multiobjective evolutionary algorithm to yield the optimum value of the walk parameters. The results are verified by Nao robot. This approach increases the energy efficiency of Nao robot by 67.05%, and stability increases by 75%. Furthermore, this method can be utilized on all ZMP classed bipeds.

Multiobjective optimized bipedal locomotion

To develop the general analytical model for the optimization of trade-off Stability and Energy functions for biped humanoid robot is very tedious work. This paper presents a novel analytical method to develop the multiobjective function includes energy and stability functions. The challenge was to develop analytical model for stability and energy for the single support phase (SSP), double support phase (DSP) and the transition to SSP-DSP and vice versa. The energy function has been developed by unique approach of orbital energy concept and the stability function obtained by modifying the pre-existing Zero Moment Point (ZMP) trajectory (the trajectories which generated by the mathematical equations of ZMP). These functions are optimized using Real Coded Genetic Algorithm to produce an optimum set of walk parameters.The analytical results show that, when the energy function is optimized, the stability of the robot decreases. Similarly, if the stability function is optimized,the energy consumed by the robot increases. Thus, there is a clear trade-off between the stability and energy functions. Thus,we propose the Multi-Objective Evolutionary Algorithm to yield the optimum value of the walk parameters. The results are verified by NaO robot.This approach increases the energy efficiency of NaO robot by 67.05% and stability increases by 75%. Furthermore, this method can be utilized on all ZMP classed bipeds(HOAP, Honda robots).

Omni-Directional Walking Pattern Generator for Child-Sized Humanoid Robot, CHARLES2

In this paper, we propose an omni-directional walking pattern generator to make a child-sized humanoid robot walk in any direction. The proposed omni-directional walking pattern generator creates walking patterns for which zero moment point (ZMP) is located on the center of the supporting foot. For humanoid robots to adapt to human’s life and perform missions, it should be taller than the minimum height of a child. In this paper, we designed a humanoid robot which is similar to a child who is taller than 1[Formula: see text]m. We show the humanoid robot’s kinematics, design of a three-dimensional (3D) model, develop mechanisms and the hardware structures with servo-motors and compact-size PC. The developed humanoid robot “CHARLES2” stands for Cognitive Humanoid Autonomous Robot with Learning and Evolutionary System-Two. The inverse kinematics of its legs is described. The principle of the omni-directional walking pattern generator is discussed to create walking motions and overcome the robot’s mechanical deficiencies. We applied the proposed omni-directional walking pattern generator based on ZMP. Through experiments, we analyzed walking patterns according to the creation and changing parameter values. The results of the experiments are presented for the efficacy of our proposed walking engine.

Technical Overview of Team DRC‐Hubo@UNLV's Approach to the 2015 DARPA Robotics Challenge Finals

This paper presents a technical overview of Team DRC‐Hubo@UNLV's approach to the 2015 DARPA Robotics Challenge Finals (DRC‐Finals). The Finals required a robotic platform that was robust and reliable in both hardware and software to complete tasks in 60 min under degraded communication. With this point of view, Team DRC‐Hubo@UNLV integrated methods and algorithms previously verified, validated, and widely used in the robotics community. For the communication aspect, a common shared memory approach that the team adopted to enable efficient data communication under the DARPA controlled network is described. A new perception head design (optimized for the tasks of the Finals) and its data processing are then presented. In the motion planning and control aspect, various techniques, such as wheel‐driven navigation, zero‐moment‐point (ZMP) ‐based locomotion, and position‐based manipulation and controls, are described in this paper. By introducing strategically critical elements and key lessons learned from DRC‐Trials 2013 and the testbed of Charleston, we also illustrate how DRC‐Hubo has evolved successfully toward the DRC‐Finals.

Adaptive synthesis of dynamically feasible full-body movements for the humanoid robot HRP-2 by flexible combination of learned dynamic movement primitives

Skilled human full-body movements are often planned in a highly predictive manner. For example, during walking while reaching towards a goal object, steps and body postures are adapted to the goal position already multiple steps before the goal contact. The realization of such highly predictive behaviors for humanoid robots is a challenge because standard approaches, such as optimal control, result in computation times that are prohibitive for the predictive control of complex coordinated full-body movements over multiple steps. We devised a new architecture that combines the online-planning of complex coordinated full-body movements, based on the flexible combination of learned dynamic movement primitives, with a Walking Pattern Generator (WPG), based on Model Predictive Control (MPC), which generates dynamically feasible locomotion of the humanoid robot HRP-2. A dynamic filter corrects the Zero Moment Point (ZMP) trajectories in order to guarantee the dynamic feasibility of the executed behavior taking into account the upper-body movements, at the same time ensuring an accurate approximation of the planned motion trajectories. We demonstrate the high flexibility of the chosen movement planning approach, and the accuracy and feasibility of the generated motion. In addition, we show that a naïve approach, which generates adaptive motion by using machine learning methods by the interpolation between feasible training motion examples fails to guarantee the stability and dynamic feasibility of the generated behaviors.

Modeling of humanoid dynamics including slipping with nonlinear floor friction

Biped locomotion created by controlling methods based on zero-moment point has been realized in real world and been well verified its efficacy for stable walking. However, the walking strategies that have been proposed so far seems to avoid such considerations as slipping of foot on the floor, even though there should exist the slipping large or small in real world. In this research, a dynamical model of humanoid robot including slipping of foot is proposed, which is derived by the Newton---Euler method. To confirm the veracity of the derived dynamical model, the model has been verified from the view point that when all friction coefficients are identical to zero, the total kinetic energy should be conserved to be unchanged, and when the coefficients are not zero, the total kinetic energy should decrease monotonously.

Energy dissipation rate control and parallel equations solving method for planar spined quadruped bouncing robot

This paper continues our investigation into Energy dissipation rate control (EDRC) and Parallel equations solving method (PESM). Our previous works showed how EDRC enables us to provide stable walking or running gaits for legged robots via controlling robot’s loss of energy rate during Impact phases (IP). This is while PESM facilitates the trajectory designing process of the robot’s active joints during each Single support phase (SSP) by solving the robot’s inverse kinematic and inverse dynamic equations in parallel. Even though PESM is very powerful and suitable for both quadruped robot, and despite the under actuation problem at the ankle joint, and biped robots, despite the presence of Zero momentum point criteria (ZMP) at the ankle joint, still, this method is limited to robots just with three and five DoFs. Therefore, the main purpose hereis to show how it is possible to extend the application of PESL to a spined quadruped robot with four DoFs by employment of the Central pattern generator (CPG) controller units and finding a connection among CPG’s output, PESM and the robot’s foot placement. Besides, as EDRC is employed to realize a stable bouncing gait for the robot, a whole numerical study is performed on the robot’s impact dynamic equations to evaluate the effect of spine joint on the robot’s impact dynamics.

Designing magnetic compensated states in tetragonal Mn3Ge-based Heusler alloys

Magnetic compensated materials attracted much interests due to the observed large exchange bias and large coercivity, and also their potential applications in the antiferromagnetic spintronics with merit of no stray field. In this work, by using ab-initio studies, we designed several Ni (Pd, Pt) doped Mn3Ge-based D022-type tetragonal Heusler alloys with fully compensated states. Theoretically, we find the total moment change is asymmetric across the compensation point (at ~x=0.3) in Mn3-xYxGe (Y=Ni, Pd, Pt). In addition, an uncommon discontinuous jump is observed across the critical zero-moment point, indicating that some non-trivial properties may emerge at this point. Further electronic analyses of these compensated alloys reveal high spin polarizations at the Fermi level, which is advantageous for spin transfer torque applications.

Design and walking pattern generation of a biped robot

This paper presents the design of a biped robot, the walking trajectory generation method, and experimental results about biped walking. Walking trajectory generation is one of the deterministic factors in walking robot applications. Different approaches for stable walking trajectory are worked on in robotic research. The linear inverted pendulum model (LIPM) is an effective method used with the zero moment point (ZMP) criteria. Biped robot trunk and feet moving patterns are generated depending on these fundamental methods. In this study, generated trajectories were tested by a 12 degree of freedom (DOF) biped robot RUBI built at Dokuz Eylül University. In the experimental work, the joint angles obtained by using inverse kinematics from the generated trajectories were implemented on the robot. The results showed that even with a simple control system implementation of generated trajectories is very promising in terms of stability and reducing complexity.

Natural Walking Reference Generation Based on Double-Link LIPM Gait Planning Algorithm

In this paper, an enhanced linear inverted pendulum model (LIPM) and a gait planning algorithm are proposed. The LIPM is a widely used concept for gait reference generation, and it provides a simplified model for planning a center of mass trajectory when given a proper zero moment point trajectory. However, one of the assumptions of LIPM is that the legs of the robot are massless, so that the mass of the supporting leg can be neglected for simplification, and it conflicts with the mass distributions of human beings and most humanoid robots. Hence, this paper proposes a double-link LIPM (DLIPM) to eliminate the conflict about mass distribution. In addition, a gait planning algorithm is proposed for natural walking reference generation. In the simulation results, the proposed method is implemented based on a model of a teen-sized humanoid robot named David Junior. The simulation results validate the feasibility and practicability of the proposed method. Moreover, comparisons between conventional LIPM and DLIPM demonstrate the performance of the proposed DLIPM method. Eventually, the proposed method is implemented on David Junior for the weight-lifting event in the 2015 FIRA RoboWorld Cup, an event which David Junior won first place.

上体を有する劣駆動リムレスホイールのステルス歩容生成

This paper proposes a method for generating a stable stealth walking gait of an underactuated rimless wheel (URW). First, we introduce an URW model and design two controllers; one is for strictly controlling the angular positions and velocities of the stance leg during the single-limb support phase, and the other is for controlling the upper body angle to the initial one during the double-limb support phase. Second, we investigate the validity of the proposed control methods and discuss the energy efficiency of the generated gait through numerical simulations. Furthermore, we discuss the changing tendency of the ground reaction force and zero-moment point to the system parameters.

Walking Engine Using ZMP Criterion and Feedback Control for Child-Sized Humanoid Robot

In this paper, a walking engine that achieves dynamic stable walking using zero moment point (ZMP) criterion and feedback control from a gyro sensor is proposed. The ZMP criterion is used for the dynamic walking, and the feedback control from a gyro sensor is adopted for stabilization. The proposed walking engine consists of ZMP controller and the gait generator. The three-dimensional linear inverted pendulum model (3D-LIPM) is adopted for a simplified model of the humanoid robot. The ZMP equations are derived based on the 3D-LIPM and are applied to the gait generator. The walking engine is tested on a child-sized, 21-degree-of-freedom (DOF) humanoid robot cognitive humanoid autonomous robot with learning and evolutionary system (CHARLES) which stands 110[Formula: see text]cm tall and weighs only 8[Formula: see text]kg. The design concept of CHARLES is low development cost, lightweight, and simple design, which all match well with the proposed walking engine. The results of the experiments present the efficacy of the proposed walking engine.

Dynamical Model of Walking Transition Considering Nonlinear Friction with Floor

Biped locomotion created by a controller based on Zero-Moment Point (ZMP) known as reliable control method looks different from human’s walking on the view point that ZMP-based walking does not include falling state, and it’s like monkey walking because of knee-bended walking profiles. However, the walking control that does not depend on ZMP is vulnerable to turnover. Therefore, keeping the event-driven walking of dynamical motion stable is important issue for realization of human-like natural walking. In this research, a walking model of humanoid robot including slipping, bumping, surface-contacting and line-contacting of foot is discussed, and its dynamical equation is derived by the Extended NE method. In this paper we introduce the humanoid model which including the slipping foot and verify the model.

Gait Generation for a Small Biped Robot using Approximated Optimization Method

This paper proposes a novel approach for gait pattern generation of a small biped robot to enhance its walking behavior. This is to aim to make the robot gait more natural and more stable in the walking process. In this study, we mention the approximated optimization method which applied the Differential Evolution algorithm (DE) to objective function approximated by Artificial Neural Network (ANN). In addition, we also present a new humanlike foot structure with toes for the biped robot in this paper. To evaluate this method achievement, the robot was simulated by multi-body dynamics simulation software, Adams (MSC software, USA). As a result, we confirmed that the biped robot with the proposed foot structure can walk naturally. The approximated optimization method based on DE algorithm and ANN is an effective approach to generate a gait pattern for the locomotion of the biped robot. This method is simpler than the conventional methods using Zero Moment Point (ZMP) criterion.

A Control Framework for Anthropomorphic Biped Walking Based on Stabilizing Feedforward Trajectories.

Although dynamic walking methods have had notable successes in control of bipedal robots in the recent years, still most of the humanoid robots rely on quasi-static Zero Moment Point controllers. This work is an attempt to design a highly stable controller for dynamic walking of a human-like model which can be used both for control of humanoid robots and prosthetic legs. The method is based on using time-based trajectories that can induce a highly stable limit cycle to the bipedal robot. The time-based nature of the controller motivates its use to entrain a model of an amputee walking, which can potentially lead to a better coordination of the interaction between the prosthesis and the human. The simulations demonstrate the stability of the controller and its robustness against external perturbations.

Estimation of Zero Moment Point using Centre of Gravity based Method

Estimation of Zero Moment Point using Centre of Gravity based Method

Parameterized gait pattern generator based on linear inverted pendulum model with natural ZMP references

AbstractThis paper presents a parameterized gait generator based on linear inverted pendulum model (LIPM) theory, which allows users to generate a natural gait pattern with desired step sizes. Five types of zero moment point (ZMP) components are proposed for formulating a natural ZMP reference, where ZMP moves continuously during single support phases instead of staying at a fixed point in the sagittal and lateral plane. The corresponding center of mass (CoM) trajectories for these components are derived by LIPM theory. To generate a parameterized gait pattern with user-defined parameters, a gait planning algorithm is proposed, which determines related coefficients and boundary conditions of the CoM trajectory for each step. The proposed parameterized gait generator also provides a concept for users to generate gait patterns with self-defined ZMP references by using different components. Finally, the feasibility of the proposed method is validated by the experimental results with a teen-sized humanoid robot, David, which won first place in the sprint event at the 20th Federation of International Robot-soccer Association (FIRA) RoboWorld Cup.

Discrete-Time Circular Walking Pattern for Biped Robots

When biped robots make turns fast, they may fall due to the action of centrifugal force. This is why one needs to consider the Zero Moment Point (ZMP) equations with respect to cylindrical coordinate system. Those ZMP equations are, however, so coupled and highly nonlinear even for the simple inverted pendulum model that it is hard to find a closed-form solution. Therefore, in this paper, they have been converted through temporal discretization to difference equations that admit numerical solution by most on-board computers. Thus-obtained walking patterns have been characterized and applied to several cases of different speed for comparison purposes. In so doing, the steady patterns have been blended with a type of transitional patterns to change the walking speed in the beginning and/or mid course of walking. Finally, those combined patterns have been put to test on a multi-body robot model by ADAMS®. Test results show that the robot could walk along a sample circular path as predicted at rapid speeds despite some modeling error, distributed mass and ground contact effects, validating efficacy of the suggested approach.