Flying Trot Control Method for Quadruped Robot Based on Trajectory Planning

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Flying Trot Control Method for Quadruped Robot

Based on Trajectory Planning

Hongge Wanga, Hui Chai a,∗, Bin Chenb, Aizhen Xiea,b, Rui Songa, Bo Suc

aRobotics Research Center, School of Control Science and Engineering,Shandong

University, Shandong Province, China

bShandong Youbaote Intelligent Robot Co., Ltd, Jinan, Shandong Province, China

cChina North Vehicle Research Institute, Beijing, China

Abstract

An intuitive control method for the ﬂying trot, which combines oﬄine trajec-

tory planning with real-time balance control, is presented. The motion features

of running animals in the vertical direction were analysed using the spring-

load-inverted-pendulum (SLIP) model, and the foot trajectory of the robot was

planned, so the robot could run similar to an animal capable of vertical ﬂight,

according to the given height and speed of the trunk. To improve the robustness

of running, a posture control method based on a foot acceleration adjustment

is proposed. A novel kinematic based CoM observation method and CoM regu-

lation method is present to enhance the stability of locomotion. To reduce the

impact force when the robot interacts with the environment, the virtual model

control method is used in the control of the foot trajectory to achieve active

compliance. By selecting the proper parameters for the virtual model, the os-

cillation motion of the virtual model and the planning motion of the support

foot are synchronized to avoid the large disturbance caused by the oscillation

motion of the virtual model in relation to the robot motion. The simulation and

experiment using the quadruped robot Billy are reported. In the experiment,

the maximum speed of the robot could reach 4.73 times the body length per

∗Corresponding author

Email addresses: wanghg1992@outlook.com (Hongge Wang ), chaimax@sdu.edu.cn (Hui

Chai ), 15820000319@139.com (Bin Chen ), xieaizhensdu@163.com (Aizhen Xie ),

rsong@sdu.edu.cn (Rui Song ), bosu@noveri.com.cn (Bo Su )

Preprint submitted to Journal of Mechatronics October 25, 2022

arXiv:2210.13446v1 [cs.RO] 24 Oct 2022

second, which veriﬁed the feasibility of the control method.

Keywords: Quadruped Robot, Flying Trot, Trajectory Planning, Posture

Control, Kinematic Based CoM Observation, Active Compliance Control

1. Introduction

The legged robot is more adaptable to the non-structural environment than

the wheeled robot and the tracked robot. The quadruped robot has better sta-

bility than the biped robot and has a simpler structural complexity than the

hexapod robot, so the quadruped robots have attracted increasingly more at-

tention from scholars.

Improving the speed of movement is a trend in quadruped robots. The

common gaits of quadruped robots include crawl, trot, pace, bound, and gallop.

Due to the good symmetry, small posture ﬂuctuations, and the ability to balance

the movement speed and energy consumption, the trot gait is widely used in

the movement of the quadruped robot.

The ﬂying trot gait is a trot gait with ﬂying phases that can achieve higher

moving speeds. The quadruped robots that run with a ﬂying trot gait are

Quadruped, designed by the Massachusetts Institute of Technology [1, 2], Kolt

[3, 4, 5] of Stanford University and Ohio State University, HyQ [6] of the Italian

Institute of Technology, StarlETH [7, 8] of the Zurich Federal Institute of Tech-

nology, Cheetah cub [9] of Lausanne Federal Institute of Technology, Boston

Dynamics’ BigDog [10, 11], LS3 [12] and Spot [13]; in addition, Billy [14] is

the quadruped robot used in the experiments of this paper, as shown in Fig.

1a, which is cooperatively developed by Shandong University and Shandong

Youbaote Intelligent Robot Co., Ltd. The control methods of the ﬂying trot

gait that is used are summarized as follows.

The researchers of Quadruped put forward the control method, which di-

vided the control of the robot into three parts: trunk height control, posture

control and speed control, and realized a stable trot movement. Controlling the

(a) Billy quadruped robot (b) Simulation model

Figure 1: Billy, the quadruped robot used in the experiments, and its simulation model in

Webots

energy of the robot in a vertical direction realized the ﬂying of the Quadruped

robot in the trot movement [1, 15, 16]. However, because the control method

of vertical ﬂying is closely combined with the pneumatic control method of the

legs, it is not universal.

By controlling the touch position of the swing foot to control the robot’s

forward velocity, lateral velocity, heading angular velocity, in addition to con-

trolling the energy injected to the support leg spring to control the trunk height

and controlling the joints’ torque of the support leg to control the pitch angle

and roll angle, Kolt can move stably with a trot gait [8]. When the descent

speed of the support foot reaches a certain value, Kolt uplifts the support foot

to achieve ﬂying in the trot gait [9]. However, the researchers did not detail the

speciﬁc process of the descent control and uplift control of the support foot, nor

did they establish the speciﬁc model of the ﬂying control.

The motion control of the quadruped robot StarlETH is divided into trunk

control, swing foot control and support foot control. The swing foot control is

mainly used to select the proper touch position to control the robot speed and

make the robot recover from an external disturbance. The trunk control mainly

calculates a desired virtual six-dimensional force acting on the trunk from the

deviation between the control target and the actual situation of trunk and then

calculates a group of optimal forces acting on the support feet through an opti-

mization method. The support foot control aims to calculate the corresponding

joint torque from the desired optimal foot forces of the support legs and execute

the torque. The ﬂying phase is achieved by controlling the height of the trunk

in the trot gait [8]. However, the researchers of StarlETH did not details the

process of the height control of the trunk to achieve the ﬂying phase.

The quadruped robot Cheetah cub uses open-loop control. Its researchers

control the movement of the quadruped robot with the method of a central

pattern generator (CPG) based on the joint workspace. Then, through a large

number of experiments, the parameters of CPG are optimized to improve the

forward speed of the quadruped robot [9]. However, the optimal parameters

of diﬀerent quadruped robots are diﬀerent, and the process of parameter op-

timization is complex. Moreover, since the quadruped robot uses the CPG

method based on joint space, this method may not be applicable once the joint

conﬁguration of the robot is changed.

The ﬂying trot of the quadruped robot HyQ is based on active compliant

control. The desired trajectory of the foot is planned by the CPG method based

on the foot workspace [17], and the desired joint angle is obtained by inverse

kinematics. PD control is then used in joint space to make the actual joint angle

follow the desired joint angle and achieve active compliance. They stabilized

the ﬂying trot by choosing an appropriate step frequency and duty factor [18]

to make the motion of the quadruped robot synchronize with the oscillation

of the virtual spring-mass system in the support phase [6]. However, the HyQ

researchers did not provide the method for selecting the step frequency and duty

factor.

The ﬂying trot control methods of BigDog, LS3, and Spot have not been

publicly disclosed. The current information of a quadruped robot that can run

with a ﬂying trot gait is shown in table 1. Cheetah cub has a ratio of speed

to body length greater than Billy, but it has no the rolling rotary joint, so it

cannot move ﬂexibly in all directions, and it is lighter because its power supply

is external.

Table 1: Flying trot speed of quadruped robots

Year Robot Mass (kg) BL (m) Speed (BL/s)

1990 Quadruped 38 0.78 2.82

2004 Kolt 80 1.75 0.63

2010 HyQ 70 1.3 1.3

2013 StarlETH 23 0.5 *

2013 Cheetah cub 1.1 0.205 6.9

BigDog 109 1.1 1.82

2004-2015 LS3 * * *

Spot 72 * *

2016 Billy 1.9 0.167 4.73

This paper takes quadruped as the research object, analyses the movement

process of a quadruped in the running of the ﬂying trot gait with the SLIP

model, and puts forward the gait control method of the ﬂying trot based on

the position planning of the foot workspace, including the control of the robot’s

eject, landing buﬀer and forward speed. To increase the robustness of movement,

a new posture control method based on position was proposed, and the method

of virtual model control was used to carry out active compliance control to

reduce the impact force when the robot interacts with the environment.

The advantages of the method proposed in this paper are as follows. (1) The

implementation method of the ﬂying trot gait based on position planning was

proposed, and the touchdown time was predicted in planning to make buﬀer

actions in advance and reduce the impact of landing. (2) A novel position-

based posture control method was proposed, which can be used to enhance the

balance of the robot. (3) To further reduce the impact of landing in running,

the method of the leg virtual model was used for active compliance control, and

a reasonable selection method of kp and kd for virtual spring and damping was

proposed for the running gait.

The simulations in Webots and the experiments of Billy prove that the

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摘要：

FlyingTrotControlMethodforQuadrupedRobotBasedonTrajectoryPlanningHonggeWanga,HuiChaia,,BinChenb,AizhenXiea,b,RuiSonga,BoSucaRoboticsResearchCenter,SchoolofControlScienceandEngineering,ShandongUniversity,ShandongProvince,ChinabShandongYoubaoteIntelligentRobotCo.,Ltd,Jinan,ShandongProvince,ChinacChin...

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Flying Trot Control Method for Quadruped Robot Based on Trajectory Planning

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