This paper presents a template-based control method for achieving diverse trotting motions in quadrupedal systems,with a focus on smooth transitions between walking trot,regular trot,and flying(running)trot.First,we e...This paper presents a template-based control method for achieving diverse trotting motions in quadrupedal systems,with a focus on smooth transitions between walking trot,regular trot,and flying(running)trot.First,we extend the Clock Torque Actuated Spring-Loaded Inverted Pendulum(CT-SLIP)template to three dimensions,creating a comprehensive control framework.A template-based control strategy is then developed to compute joint torques for stable locomotion,along with a detailed approach for transitioning between gaits.To enable the flight phase in the running trot,a projectile motion model is incorporated into the template.For improved turning,we implement a yaw control method that rotates the swing foot plane to enhance stability,enabling higher turning rates while maintaining steady forward motion and balance.To further enhance locomotion stability and performance,a Whole-Body Controller(WBC)is integrated.The proposed method is implemented and rigorously evaluated in the MuJoCo simulator,with experiments testing gait transitions and disturbance rejection.Additionally,comparative studies assess the impacts of both swing foot plane rotation and the WBC on overall system performance.Furthermore,the approach is validated through real hardware experiments on Unitree GO1 quadrupedal robot,successfully demonstrating smooth gait transitions,stable locomotion,and practical applicability in real-world scenarios.展开更多
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 el...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.展开更多
The dynamic stability of a quadruped robot trotting on slope was analyzed.Compared with crawl gait,trot gait can improve walking speed of quadruped robots.When a quadruped robot trots,each leg is in the alternate stat...The dynamic stability of a quadruped robot trotting on slope was analyzed.Compared with crawl gait,trot gait can improve walking speed of quadruped robots.When a quadruped robot trots,each leg is in the alternate state of swing phase or supporting phase,and two legs in the diagonal line are in the same phase.The feet in the supporting phase form a supporting region on the ground.When a quadruped robot walks on slope,the vertical distance from zero moment point(ZMP) to the supporting diagonal line is defined as ZMP offset distance.Whether this distance is less than the maximum offset distance or not,the stability of robot trotting on slope can be judged.The foot trajectory was planned with the sinusoidal function.Based on the kinematic analysis,the ZMP offset distance of quadruped robot under different slope angles,step length and step height was calculated,then the reasonable slope angle,step length and step height for quadruped robot trotting on slope to keep dynamic stability can be determined.On the other hand,the posture angle of quadruped robot should be controlled within the desired range.Computer simulations were executed to verify the theoretical analysis.The study will provide reference for determining reasonable step parameters of the quadruped robot.展开更多
A compliant landing strategy for a trotting quadruped robot on unknown rough terrains based on contact force control is presented. Firstly, in order to lower the disturbance caused by the landing impact force, a landi...A compliant landing strategy for a trotting quadruped robot on unknown rough terrains based on contact force control is presented. Firstly, in order to lower the disturbance caused by the landing impact force, a landing phase is added between the swing phase and the stance phase, where the desired contact force is set as a small positive constant. Secondly, the joint torque optimization of the stance legs is formulated as a quadratic programming(QP) problem subject to equality and inequality/bound constraints. And a primal-dual dynamical system solver based on linear variational inequalities(LVI) is applied to solve this QP problem. Furthermore, based on the optimization results, a hybrid motion/force robust controller is designed to realize the tracking of the contact force, while the constraints of the stance feet landing angles are fulfilled simultaneously. Finally, the experiments are performed to validate the proposed methods.展开更多
This work presents a controller designed for position-controlled quadrupedal dynamic locomotion,aiming at simple and robust trotting control. The controller takes the torso attitude angles and velocities into planning...This work presents a controller designed for position-controlled quadrupedal dynamic locomotion,aiming at simple and robust trotting control. The controller takes the torso attitude angles and velocities into planning foot trajectories. Firstly design of the servo motor actuated quadruped robot is introduced and the kinematic equations are deduced. Then a scheme is presented for controlling the robot torso attitude based on the virtual leg model. Furthermore,it demonstrates the design of the controller which enables the robot to have a wide range of trotting gaits and omni-directional motions. Finally,results of robust trotting in various speeds,path tracking and push recovery in simulation are reported,and results of trotting on real quadruped robots will be studied.展开更多
基金supported by The Scientific and Technological Research Council of Türkiye(TUBITAK)1515 Frontier R&D Laboratories Support Program for Turk Telekom neXt Generation Technologies Lab(XGeNTT)under Project No.5249902supported by the Scientific Research Projects Coordination Unit of Middle East Technical University(METU)under Project No.ADEP-301-2025-11613.
文摘This paper presents a template-based control method for achieving diverse trotting motions in quadrupedal systems,with a focus on smooth transitions between walking trot,regular trot,and flying(running)trot.First,we extend the Clock Torque Actuated Spring-Loaded Inverted Pendulum(CT-SLIP)template to three dimensions,creating a comprehensive control framework.A template-based control strategy is then developed to compute joint torques for stable locomotion,along with a detailed approach for transitioning between gaits.To enable the flight phase in the running trot,a projectile motion model is incorporated into the template.For improved turning,we implement a yaw control method that rotates the swing foot plane to enhance stability,enabling higher turning rates while maintaining steady forward motion and balance.To further enhance locomotion stability and performance,a Whole-Body Controller(WBC)is integrated.The proposed method is implemented and rigorously evaluated in the MuJoCo simulator,with experiments testing gait transitions and disturbance rejection.Additionally,comparative studies assess the impacts of both swing foot plane rotation and the WBC on overall system performance.Furthermore,the approach is validated through real hardware experiments on Unitree GO1 quadrupedal robot,successfully demonstrating smooth gait transitions,stable locomotion,and practical applicability in real-world scenarios.
基金supported by National Natural Science Foundation of China(Grant No.51375289)Shanghai Municipal National Natural Science Foundation of China(Grant No.13ZR1415500)Innovation Fund of Shanghai Education Commission of China(Grant No.13YZ020)
文摘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.
基金Supported by the National Natural Science Foundation of China(No.51375289)Shanghai Municipal National Natural Science Foundation of China(No.13ZR1415500)Innovation Fund of Shanghai Education Commission(No.13YZ020)
文摘The dynamic stability of a quadruped robot trotting on slope was analyzed.Compared with crawl gait,trot gait can improve walking speed of quadruped robots.When a quadruped robot trots,each leg is in the alternate state of swing phase or supporting phase,and two legs in the diagonal line are in the same phase.The feet in the supporting phase form a supporting region on the ground.When a quadruped robot walks on slope,the vertical distance from zero moment point(ZMP) to the supporting diagonal line is defined as ZMP offset distance.Whether this distance is less than the maximum offset distance or not,the stability of robot trotting on slope can be judged.The foot trajectory was planned with the sinusoidal function.Based on the kinematic analysis,the ZMP offset distance of quadruped robot under different slope angles,step length and step height was calculated,then the reasonable slope angle,step length and step height for quadruped robot trotting on slope to keep dynamic stability can be determined.On the other hand,the posture angle of quadruped robot should be controlled within the desired range.Computer simulations were executed to verify the theoretical analysis.The study will provide reference for determining reasonable step parameters of the quadruped robot.
基金Project(61473304)supported by the National Natural Science Foundation of ChinaProject(2015AA042202)supported by Hi-tech Research and Development Program of China
文摘A compliant landing strategy for a trotting quadruped robot on unknown rough terrains based on contact force control is presented. Firstly, in order to lower the disturbance caused by the landing impact force, a landing phase is added between the swing phase and the stance phase, where the desired contact force is set as a small positive constant. Secondly, the joint torque optimization of the stance legs is formulated as a quadratic programming(QP) problem subject to equality and inequality/bound constraints. And a primal-dual dynamical system solver based on linear variational inequalities(LVI) is applied to solve this QP problem. Furthermore, based on the optimization results, a hybrid motion/force robust controller is designed to realize the tracking of the contact force, while the constraints of the stance feet landing angles are fulfilled simultaneously. Finally, the experiments are performed to validate the proposed methods.
基金Supported by the National Natural Science Foundation of China(No.61233014,61305130)China Postdoctoral Science Foundation(No.2013M541912)the Shandong Provincial Natural Science Foundation(No.ZR2013FQ003,ZR2013EEM027)
文摘This work presents a controller designed for position-controlled quadrupedal dynamic locomotion,aiming at simple and robust trotting control. The controller takes the torso attitude angles and velocities into planning foot trajectories. Firstly design of the servo motor actuated quadruped robot is introduced and the kinematic equations are deduced. Then a scheme is presented for controlling the robot torso attitude based on the virtual leg model. Furthermore,it demonstrates the design of the controller which enables the robot to have a wide range of trotting gaits and omni-directional motions. Finally,results of robust trotting in various speeds,path tracking and push recovery in simulation are reported,and results of trotting on real quadruped robots will be studied.
