A Humanoid Robot Gait Planning and Its Stability Validation

Gait planning based on linear inverted pendulum (LIPM) on structured road surface can be quickly generated because of the simple model and definite physical meaning. However, over-simplifi- cation of the model and discontents of zero velocity and acceleration boundary conditions when robot starts and stops walking lead to obvious difference between the model and the real robot. In this paper, parameterized gait is planned and trajectories’ smoothness of each joint angle and centroid are ensured using the 3-D LIPM theory. Static walking method is used to satisfy zero velocity and acceleration boundary conditions. Besides, a multi-link model is built to validate the stability. Simulation experiments show that: despite of some deviation from the theoretical solution, the actual zero-moment point (ZMP) is still within the support polygon, and the robot walks steadily. In consequence, the rationality and validity of model simplification of LIPM is demonstrated.

Typical Gait Analysis of a Six-legged Robot in the Context of Metamorphic Mechanism Theory

The equivalent mechanism of the system is often considered as one specific mechanism in most existing studies of multi-legged robots, however the equivalent mechanism is varying while the robot moves on the ground. Four typical tripod period gaits of a radial symmetrical six-legged robot are analyzed. Similar to the metamorphic mechanism, the locomotion of multi-legged robot is considered as a series of varying hybrid serial-parallel mechanisms by assuming the constraints of the feet on the ground with hinges. One gait cycle is divided into several periods, and in different walking period there is a specific equivalent mechanism corresponding to it, and the walking process of multi-legged robot is composed by these series of equivalent mechanisms. Walking performance can be got by analyzing these series of equivalent mechanisms. Kinematics model of the equivalent mechanism is established, workspaces of equivalent mechanisms are illustrated by simulation and a concept of static stability workspace is proposed to evaluate the static stability of these four gaits. A new method to calculate the stride length of multi-legged robots is presented by analyzing the relationship between the workspace of two adjacent equivalent parallel mechanisms in one gait cycle. The stride lengths of four gaits are given by simulations. Comparison of stride length and static stability among these four typical tripod gaits are given. It has been proved that mixed gait and insect-wave gait II have better static stability than mammal kick-off gait and insect-wave gait I. Insect-wave gait II displays its advantage on stride length while the height of robot body lower than 87 mm, mammal kick-off gait has superiority on stride length while the height of robot body higher than 115 mm, and insect-wave gait I shows its shortcoming in stride length. The proposed method based on metamorphic theory and combining the footholds and body height of robot provides a new method to comprehensive analyze the performance of multi-legged robot.

Gait Analysis of Quadruped Robot Using the Equivalent Mechanism Concept Based on Metamorphosis

The previous research regarding the gait planning of quadruped robot focuses on the sequence for lifting o and placing the feet, but neglects the influence of body height. However, body height a ects gait performance significantly, such as in terms of the stride length and stability margin. We herein study the performance of a quadruped robot using the equivalent mechanism concept based on metamorphosis. Assuming the constraints between standing feet and the ground with hinges, the ground, standing legs and robot body are considered as a parallel mechanism, and each swing leg is regarded as a typical serial manipulator. The equivalent mechanism varies while the robot moves on the ground. One gait cycle is divided into several periods, including step forward stages and switching stages. There exists a specific equivalent mechanism corresponding to each gait period. The robot's locomotion can be regarded as the motion of these series of equivalent mechanisms. The kinematics model and simplified model of the equivalent mechanism is established. A new definition of the multilegged robot stability margin, based on friction coe cient, is presented to evaluate the robot stability. The stable workspaces of the equivalent mechanism in the step forward stage of trotting gait under di erent friction coe cients are analyzed. The stride length of the robots is presented by analyzing the relationship between the stable workspaces of the equivalent mechanisms of two adjacent step forward stages in one gait cycle. The simulation results show that the stride length is larger with increasing friction coe cient. We herein propose a new method based on metamorphosis, and an equivalent mechanism to analyze the stability margin and stable workspace of the multilegged robot.

Energy Efficiency Analysis of Quadruped Robot with Trot Gait and Combined Cycloid Foot Trajectory

Quadruped robots consume a lot of energy, which is one of the factors restricting their application. Energy efficiency is one of the key evaluating indicators for walking robots. The relationship between energy and elastic elements of walking robots have been studied, but different walking gait patterns and contact status have important influences on locomotion energy efficiency, and the energy efficiency considering the foot-end trajectory has not been reported. Therefore, the energy consumption and energy efficiency of quadruped robot with trot gait and combined cycloid foot trajectory are studied. The forward and inverse kinematics of quadruped robot is derived. The combined cycloid function is proposed to generate horizontal and vertical foot trajectory respectively, which can ensure the acceleration curve of the foot-end smoother and more successive, and reduce the contact force between feet and environment. Because of the variable topology mechanism characteristic of quadruped robot, the leg state is divided into three different phases which are swing phase, transition phase and stance phase during one trot gait cycle. The non-continuous variable constraint between feet and environment of quadruped robot is studied. The dynamic model of quadruped robot is derived considering the variable topology mechanism characteristic, the periodic contact and elastic elements of the robot. The total energy consumption of walking robot during one gait cycle is analyzed based on the dynamic model. The specific resistance is used to evaluate energy efficiency of quadruped robot. The calculation results show the relationships between specific resistance and gait parameters, which can be used to determine the reasonable gait parameters.

Gait Planning for a Quadruped Robot with One Faulty Actuator

Fault tolerance is essential for quadruped robots when they work in remote areas or hazardous environments. Many fault-tolerant gaits planning method proposed in the past decade constrained more degrees of freedom（DOFs） of a robot than necessary. Thus a novel method to realize the fault-tolerant walking is proposed. The mobility of the robot is analyzed first by using the screw theory. The result shows that the translation of the center of body（CoB） can be kept with one faulty actuator if the rotations of the body are controlled. Thus the DOFs of the robot body are divided into two parts： the translation of the CoB and the rotation of the body. The kinematic model of the whole robot is built, the algorithm is developed to actively control the body orientations at the velocity level so that the planned CoB trajectory can be realized in spite of the constraint of the faulty actuator. This gait has a similar generation sequence with the normal gait and can be applied to the robot at any position. Simulations and experiments of the fault-tolerant gait with one faulty actuator are carried out. The CoB errors and the body rotation angles are measured. Comparing to the traditional fault-tolerant gait they can be reduced by at least 50%. A fault-tolerant gait planning algorithm is presented, which not only realizes the walking of a quadruped robot with a faulty actuator, but also efficiently improves the walking performances by taking full advantage of the remaining operational actuators according to the results of the simulations and experiments.

Research on Biologically Inspired Hexapod Robot's Gait and Path Planning

Realistically there are many robot joints in the biologically inspired hexapod robot, so they will generate many complexities in the calculations of the gait and the path planning and the control variables. The software Solidworks and MSC. ADAMS are adopted to simulate and analyze the prototype model of the robot. By the simulations used in our design, the applicability of the tripod gait is validated, and the scheme which uses cubic spline curve as the endpoint of foot＇s path is feasible. The principles, methods, and processes of the simulation of hexapod robot are illustrated. A methodology is proposed to get the robot inverse solution in ADAMS, and to simplify the theoretical calculation, and further more to improve the efficiency of the design.

Coordinated control strategy for robotic-assisted gait training with partial body weight support

Walking is the most basic and essential part of the activities of daily living. To enable the elderly and non-ambulatory gait-impaired patients, the repetitive practice of this task, a novel gait training robot(GTR) was designed followed the end-effector principle, and an active partial body weight support(PBWS) system was introduced to facilitate successful gait training. For successful establishment of a walking gait on the GTR with PBWS, the motion laws of the GTR were planned to enable the phase distribution relationships of the cycle step, and the center of gravity(COG) trajectory of the human body during gait training on the GTR was measured. A coordinated control strategy was proposed based on the impedance control principle. A robotic prototype was developed as a platform for evaluating the design concepts and control strategies. Preliminary gait training with a healthy subject was implemented by the robotic-assisted gait training system and the experimental results are encouraging.

Clock-turning gait synthesis for humanoid robots

Turning gait is a basic motion for humanoid robots. This paper presents a method for humanoid tuming, i.e. clock-turning. The objective of clock-turning is to change robot direction at a stationary spot. The clock-turning planning consists of four steps： ankle trajectory generation, hip trajectory generation, knee trajectory generation, and inverse kinematics calculation. Our proposed method is based on a typical humanoid structure with 12 DOFs （degrees of freedom）. The final output of clock-turning planning is 12 reference trajectories, which are used to control a humanoid robot with 12 DOFs. ZMP （zero moment point） is used as stability criterion for the planning. Simulation experiments are conducted to verify the effectiveness of our proposed clock-turuing method.

Dynamic Bending of Bionic Flexible Body Driven by Pneumatic Artificial Muscles(PAMs) for Spinning Gait of Quadruped Robot

The body of quadruped robot is generally developed with the rigid structure. The mobility of quadruped robot depcnds on the mechanical properties of the body mechanism, It is difficult for quadruped robot with rigid structure to achieve better mobility walking or running in the unstructured environment. A kind of bionic flexible body mechanism for quadruped robot is proposed, which is composed of one bionic spine and four pneumatic artificial muscles（PAMs）. This kind of body imitates the four-legged creatures＇ kinematical structure and physical properties, which has the characteristic of changeable stiff＇hess, lightweight, flexible and better bionics. The kinematics of body bending is derived, and the coordinated movement between the flexible body and legs is analyzed. The relationship between the body bending angle and the PAM length is obtained. The dynamics of the body bending is derived by the floating coordinate method and Lagrangian method, and the driving tbrce of PAM is determined. The experiment of body bending is conductcd, and the dynamic bending characteristic of bionic flexible body is evaluated. Experimental results show that the bending angle of the bionic flexible body can reach 18. An innovation body mechanism for quadruped robot is proposed, which has the characteristic of flexibility and achieve bending by changing gas pressure of PAMs. The coordinated movement of the body and legs can achieve spinning gait in order to improve the mobility of quadruped robot.

Application of Optimal-Jerk Trajectory Planning in Gait-balance Training Robot

To accommodate the gait and balance disorder of the elderly with age progression and the occurrence of various senile diseases,this paper proposes a novel gait balance training robot(G-Balance)based on a six degree-of-freedom parallel platform.Using the platform movement and IMU wearable sensors,two training modes,i.e.,active and passive,are developed to achieve vestibular stimulation.Virtual reality technology is applied to achieve visual stimulation.In the active training mode,the elderly actively exercises to control the posture change of the platform and the switching of the virtual scene.In the passive training mode,the platform movement is combined with the virtual scene to simulate bumpy environments,such as earthquakes,to enhance the human anti-interference ability.To achieve a smooth switching of the scene,continuous speed and acceleration of the platform motion are required in some scenarios,in which a trajectory planning algorithm is applied.This paper describes the application of the trajectory planning algorithm in the balance training mode and the optimization of jerk(differential of acceleration)based on cubic spline planning,which can reduce impact on the joint and enhance stability.

Static Force Analysis of Foot of Electrically Driven Heavy-Duty Six-Legged Robot under Tripod Gait

The electrically driven six-legged robot with high carrying capacity is an indispensable equipment for planetary exploration, but it hinders its practicability because of its low efficiency of carrying energy. Meanwhile, its load capacity also affects its application range. To reduce the power consumption, increase the load to mass ratio, and improve the stability of robot, the relationship between the walking modes and the forces of feet under the tripod gait are researched for an electrically driven heavy-duty six-legged robot. Based on the configuration characteristics of electrically driven heavy-duty six-legged, the typical walking modes of robot are analyzed. The mathematical models of the normal forces of feet are respectively established under the tripod gait of typical walking modes. According to the MATLAB software, the variable tendency charts are respectively gained for the normal forces of feet. The walking experiments under the typical tripod gaits are implemented for the prototype of electrically driven heavy-duty six-legged robot. The variable tendencies of maximum normal forces of feet are acquired. The comparison results show that the theoretical and experimental data are in the same trend. The walking modes which are most available to realize the average force of distribution of each foot are confirmed. The proposed method of analyzing the relationship between the walking modes and the forces of feet can quickly determine the optimal walking mode and gait parameters under the average distribution of foot force, which is propitious to develop the excellent heavy-duty multi-legged robots with the lower power consumption, larger load to mass ratio, and higher stability.

Immediate muscle strengthening by an end-effector type gait robot with reduced real-time use of leg muscles: A case series and review of literature

BACKGROUND De-afferentation or non-weight bearing induces rapid cortical and spinalα-motor neuron excitability.Author supposed that an end-effector type gait robot(EEGR)could provide patients with a training condition that was specific enough to activate rapid cortical/spinal neuroplasticity,leading to immediate muscle strengthening.The electromyographic and biomechanical comparisons were conducted.AIM To compare the electromyographic activities of the thigh and shank muscles and isometric peak torque(PT)before and after walking training on a floor or in the end-effector gait robot.METHODS Twelve outpatients without ambulatory dysfunction were recruited.Order of two interventions(5-min training on a floor at a comfortable pace or training in an EEGR with non-weight bearing on their feet and 100%guidance force at 2.1 km/h)were randomly chosen.Isometric PT,maximal ratio of torque development,amplitude of compound motor action potential(CMAP),and area under the curve(AUC)were evaluated before and 10 min after both interventions.RESULTS The degree of PT improvement of the dominant knee flexors was larger in the EEGR than on the floor(9.6±22.4 Nm/BW,P<0.01).The EEGR-trained patients had greater PT improvement of the dominant knee extensors than those who trained on the floor(4.5±28.1 Nm/BW,P<0.01).However,all electromyographic activities of the thigh and shank muscles(peak CMAP,mean and peak AUC)were significantly lower for the use of the EEGR than walking on the floor.CONCLUSION Immediate strengthening of the knee flexors and extensors was induced after the 5-min EEGR training,despite reduced muscular use.

Stability margin of the quadruped bionic robot with spinning gait

Spinning gait is valuable for quadruped robot,which can be used to avoid obstacles quickly for robot walking in unstructured environment. A kind of bionic flexible body is presented for quadruped robot to perform the spinning gait. The spinning gait can be achieved by coordinated movement of body laterally bending and legs swing,which can improve the mobility of robot walking in the unstructured environments. The coordinated movement relationship between the body and the leg mechanism is presented. The stability of quadruped robot with spinning gait is analyzed based on the center of gravity( COG) projection method. The effect of different body bending angle on the stability of quadruped robot with spinning gait is mainly studied. For the quadruped robot walking with spinning gait,during one spinning gait cycle,the supporting polygon and the trajectory of COG projection point under different body bending angle are calculated. Finally,the stability margin of quadruped robot with spinning gait under different body bending angle is determined,which can be used to evaluate reasonableness of spinning gait parameters.

Bionic Quadruped Robot Dynamic Gait Control Strategy Based on Twenty Degrees of Freedom

Quadruped robot dynamic gaits have much more advantages than static gaits on speed and efficiency, however high speed and efficiency calls for more complex mechanical structure and complicated control algorithm. It becomes even more challenging when the robot has more degrees of freedom.As a result, most of the present researches focused on simple robot, while the researches on dynamic gaits for complex robot with more degrees of freedom are relatively limited. The paper is focusing on the dynamic gaits control for complex robot with twenty degrees of freedom for the first time. Firstly, we build a relatively complete 3 D model for quadruped robot based on spring loaded inverted pendulum(SLIP) model, analyze the inverse kinematics of the model, plan the trajectory of the swing foot and analyze the hydraulic drive. Secondly, we promote the control algorithm of one-legged to the quadruped robot based on the virtual leg and plan the state variables of pace gait and bound gait. Lastly, we realize the above two kinds of dynamic gaits in ADAMS-MATLAB joint simulation platform which testify the validity of above method.

Gait planning and intelligent control for a quadruped robot

We present a method for designing free gaits for a structurally symmetrical quadruped robot capable of performing statically stable, omnidirectional walking on irregular terrain. The robot＇s virtual model is constructed and a control algorithm is proposed by applying virtual components at some strategic locations. The deliberative-based controller can generate flexible sequences of leg transferences while maintaining walking speed, and choose optimum foothold for moving leg based on integration data of exteroceptive terrain profile. Simulation results are presented to show the gait＇s efficiency and system＇s stability in adapting to an uncertain terrain.

Optimal sagittal gait with ZMP stability during complete walking cycle for humanoid robots

A parametric method to generate low energy gait for both single and double support phases with zero moment point（ZMP） stability is presented. The ZMP stability condition is expressed as a limit to the actuating torque of the support ankle, and the inverse dynamics of both walking phases is investigated. A parametric optimization method is implemented which approximates joint trajectories by cubic spline functions connected at uniformly distributed time knots and makes optimization parameters only involve finite discrete states describing key postures. Thus, the gait optimization is transformed into an ordinary constrained nonlinear programming problem. The effectiveness of the method is verified through numerical simulations conducted on the humanoid robot THBIP-I model.

On Transit Gait Programming of Six-legged Wall-climbing Robot

Transit gait programming is a key problem for a multi-legged robot to climb automatically from the ground up the wall, as well as between wall intersections. In this paper, a new idea is put forward by which the complex transit gait is decomposed into a sequence of two relatively simpler parts - single-leg motion and body pitching motion. An algorithm based on the above concept shows its feasibility and effectiveness in the graphic kinematics simulation.

Free gait generation method for omnidirectional locomotion on abrupt terrain with multi-legged biomimetic robot

In order to achieve omnidirectional locomotion on rough terrain with multi-legged biomimetic robot,a free gait generation approach is proposed based on local rules.The phase coordinates of each operation leg was established according to the motion task and a universal depiction of leg-end locomotion was implemented;the mathematical relation of gait pattern and walking velocity of multi-legged robot was put forward;combined polynomial curve was adopted to generate the leg-end trajectory,which was capable of accomplishing walking missions and accommodating to landform conditions;a distributed network of local rules for gait control was constructed based on a set of local rules operating between adjacent legs.In the simulation experiments,adaptive regulation of inter-leg phase sequence,omnidirectional locomotion and ground accommodation were realized.Moreover,statically stable free gait was obtained simultaneously,which provided multi-legged robot with the capability of walking on irregular terrain reliably and expeditiously.

A New Method of Desired Gait Synthesis for Biped Walking Robot Based on Ground Reaction Force

A new method of desired gait synthesis for biped walking robot based on the ground reaction force was proposed. The relation between the ground reaction force and joint motion is derived using the D’Almbert principle. In view of dynamic walking with high stability, the ZMP(Zero Moment Point)stability criterion must be considered in the desired gait synthesis. After that, the joint trajectories of biped walking robot are decided by substituting the ground reaction force into the aforesaid relation based on the ZMP criterion. The trajectory of desired ZMP is determined by a fuzzy logic based upon the body posture of biped walking robot. The proposed scheme is simulated and experimented on a 10 degree of freedom biped walking robot. The results indicate that the proposed method is feasible.

Emotional Gait Generation for a Humanoid Robot

In this paper, an emotional mathematical model and affective state probability description space of a humanoid robot are set up on the basis of psycho-dynamics＇ psychological energy and affective energy conservation law. The emotional state transferring process and hidden Markov chain algorithm of stimulating transition process are then studied. The simulation results show that the mathematical model is applicable to the authentic affective state change rule of human beings. Finally, the gait generation experiment results of control signal and electric current tracking wave-form are presented to demonstrate the validity of the proposed mathematical model.