IROS2019国际学术会议论文集 0201

Abstract This paper investigates dynamic and compliant control based on joint output torque estimation for electrically actuated quadruped robots with large reduction ratio harmonic gear Compared with position control force control exhibits better performance of dynamics and compliance for the robot s interactions with complex environments However force control without direct feedbacks from torque sensors may come with poor tracking performance of joint compliance when the robot equipped with gears of high reduction To solve this problem we propose a new method to estimate joint torque from motor current and rotation velocity detected on each joint using a more precise friction model of the harmonic gear We also introduce a pre stance phase to the whole cycle of leg alternating swing stance based on hybrid force and position control to dynamically absorb feet impacts on the ground Our controller performance is validated by standing experiment and walking experiment I INTRODUCTION Compared with wheeled or tracked robot legged robots have the advantage of better adapting to complex environments 1 However while walking a legged robot gets ground reaction force GRF for horizontal mobility by alternating its feet on the ground And the swing speed of foot end before impact on the ground is quite high when the robot walks dynamically or jumps Usually the impulsive GRF might damage the structure of the robot if the robot doesn t have enough compliance Leg compliance can assist to reduce the foot impact on the ground by involving additional elastic structures and prolonging the braking time It is straightforward to use elastic material for this approach such as cushioning rubber springs 2 and many other Series Elastic Actuators SEA 3 5 StarlETH 4 6 and its successor ANYmal 5 employed an SEA arrangement of the motor gearbox and spring between the fixed link and moving link which have demonstrated dynamic and compliant performance However the dynamics of these systems with flexible structures are much more This work was supported in part by the National Natural Science Foundation of China Grant No U1613223 in part by the Shenzhen Natural Science Foundation Grant No JCYJ20180508163015880 and in part by funding from Shenzhen Institute of Artificial Intelligence and Robotics for Society All authors are with Institute of Robotics and Intelligent Manufacturing IRIM the Chinese University of Hong Kong CUHK Shenzhen China also with Shenzhen Institute of Artificial Intelligence and Robotics for Society AIRS Shenzhen China also with Robotics Research Center Peng Cheng Laboratory Shenzhen China Corresponding author Dr Caiming SUN cmsun Fig 1 The Pegasus quadruped robot a machine can actively control hip abduction adduction HAA hip flexion extension HFE and knee flexion extension KFE complex than those of a stiff robot The elastic material provides passive elasticity which can reduce impact But the elasticity with fixed stiffness can cause a lack of controllability for precise tracking and be involved in serious latency for compliance control Also the extra fixtures will increase the size weight and moment of the inertia of the robot joints Compliance of rigid leg with variable stiffness control by means of torque controlled joints is becoming more and more interesting for legged robots 7 9 First of all the force feedback can be directly measured from force sensors For example hydraulic quadruped robot BigDog demonstrates excellent dynamic performance on rough terrains using the feedback control from load cells at end of cylinder rod 10 and torque sensors are also equipped on the output of harmonic gear for compliance control of motor actuated HAA joints in HyQ quadruped robot 11 The humanoid robot TORO 12 uses torque controlled joints with a torque sensor for multi contact balancing However torque sensors are too bulky for over 100 Nm torque measurement in strictly compact joints of large legged robots Moreover the joint torque can be approximated as torque constant multiplied by the current observed from the motor directly when using gearing systems of very low reduction and high efficiency and the compliance control achieved by direct Joint Torque Estimation toward Dynamic and Compliant Control for Gear Driven Torque Sensorless Quadruped Robot Bingchen Jin Caiming Sun Aidong Zhang Ning Ding Jing Lin Ganyu Deng Zuwen Zhu and Zhenglong Sun 2019 IEEE RSJ International Conference on Intelligent Robots and Systems IROS Macau China November 4 8 2019 978 1 7281 4003 2 19 31 00 2019 IEEE4630 b Fig 2 Structure and transmission of the leg of the robot a the meanings of the parameters used in compliance control b virtual leg compliance realization with programmable stiffness of each leg motor current control in each joint provides the artificial elasticity 13 This virtual compliance has been used for long in rehabilitation applications and for haptic systems Recently MIT Cheetah 3 14 the most dynamic quadruped robot introduced direct motor current control to its controller to provide virtual compliance This method is very effective in the joint where the motor drives directly or with small reduction ratio gear the gear ratio of Cheetah is 5 8 1 15 because the friction of gears can be ignored However the gear reduction is too low to provide enough load capacity for these quasi direct drive systems Harmonic gears have been extensively used for legged robots due to compact size high reduction ratio and low weight Up to now many electrically actuated legged robots have been relying on harmonic gear to increase the output torque of motor including the biped group of AIST Humanoid Robot Platform 16 Toyota humanoid robot 17 Asimo 18 and UBTECH s Walker and the quadruped robot group of TITAN series 19 AIBO 20 and Little Dog 21 Using high gain position control these robots demonstrated quasi statically stable walking and sometimes with the help of accurate perception of environment and intelligent learning showed a little bit dynamic performance like Asimo and Little Dog However it is nearly impossible for harmonic gear Fig 3 Electrical controller system of the quadruped robot driven legged robots to obtain compliance due to lack of active control of joint torque which leads to high instantaneous torque peaks each time the robot s feet hit the ground Many researchers have spent plenty of attention on modeling of harmonic gear with high reduction to get better torque estimation on each joint Zhang 22 develops a joint torque estimation method based on a proposed harmonic drive compliance model However the behavior of the harmonic drive has nonlinear relationship with transmission friction and kinematic error 23 Nagamatsu 24 proposed a joint torque estimation method using the simplified Coulomb and viscous friction model which is difficult to be applied to the dynamic walking In dynamic locomotion of legged robot velocity and acceleration of joint motion varied in a quite wide range the friction of harmonic gear will become very complicated which means the Coulomb and viscous friction model will not work 25 In our laboratory a highly compact and robust quadruped robot Pegasus has been built as shown in Fig 1 We implement torque estimation to equip our robot with virtual elasticity using dynamic and compliant control for the absorption of foot impact on the ground and the joint torque is directly correlated with motor current and rotation velocity detected on each joint based on a proper friction model of harmonic gear instead of using torque sensor This paper is organized as follows Section II illustrates the mechanical and electronic design of the quadruped robot The joint torque estimation method is introduced in Section III 1 1 4 2 5 3 4 HAA HFE KFE Motor driver Data acquisition card Hip roll Hip pitch Knee pitch 4 Operator PC Wifi Ethernet Host PC NETCAN CAN Knee pitch Hip roll Hip pitch 4 a 4631 The locomotion control framework of the hybrid force and position control is explained in details in Section IV Section V shows the experimental results Some conclusions are drawn in the last section II MECHANICAL AND ELECTRONIC DESIGN The robust quadruped robot shown in Fig 1 is a 12 degrees of freedom DOF harmonic gear driven robot weighing about 30 kg The leg structure is shown in Fig 2 There are three actuators corresponding to 3 DOF in each leg The two joints in the leg sagittal plane are called hip flexion extension HFE joint and knee flexion extension KFE joint The third joint is called hip abduction adduction HAA joint Each joint comprises a brushless motor and a harmonic gearbox meanwhile the position encoders which servo the motor are mounted before the harmonic gear and the whole joint after the harmonic gear The knee joint is driven by a linkage between the knee motor and the crus We use Maxon EC 90 flat and harmonic gear with the reduction ratio of 50 to drive each joint With this structure the nominal torque of each joint is 27 Nm the stall torque can reach 228 Nm Fig 3 shows the electric and electronic design of the Pegasus quadruped robot Commands are sent to the robot via network from the operator PC An NVIDIA Jetson TX1 is used as a host PC to autonomously run the locomotion control algorithm The joint motors are regulated by 12 Maxon EPOS2 control modules that are connected through 4 parallel operating CAN buses with the host PC Also with the same communication interface 4 STM32F429 development boards are used as data acquisition card to provide the sensor signals of the additional joint encoders III JOINT TORQUE ESTIMATION In this paper a joint torque estimation method for motor with harmonic gear was developed The relationship between the joint output torque and the current of motor was obtained with the friction of the gear taken into account A Joint Model and Harmonic Drive Model Incorporating the moment of inertia of the wave generator into the moment of inertia of the motor and combining the moment of inertia of the flexspline and the load together a single joint can be considered as a two mass system consisting of a motor and a load as shown in Fig 4 All harmonic drives exhibit power loss due to transmission friction according to Taghirad s research 25 The bulk of energy dissipation can be blamed on the wave generator bearing friction 1 gear meshing friction 2 output bearing frictions 3 and the flexspline structural damping The torque relationships during the transmission are 1 1 2 3 1 Where represent the torque of the wave generator and the flexspline N represents the reduction ratio It has been Fig 4 The joint model and the transmission of the harmonic drive with friction shown that among all these frictions most of the frictional dissipation results from gear meshing 2 Also compared with output bearing frictions 3 wave generator bearing friction 1 is more important since it is acting on the high speed low torque port of transmission so the output bearing frictions 3 can be ignored The torque balance therefore can be written as 1 1 2 2 B Joint torque estimation If the reduction ratio of the robot s reducer is large it is necessary to estimate the relationship between the current of the motor and the torque of the joint because the effect of the friction of the reducer cannot be ignored Perform dynamic analysis on the two mass system 1 1 2 3 In which represents torque constant of the motor represents rotor inertia of the motor these two parameters can be obtained from motor data directly and represent the current value and angular acceleration of the motor and represent moment of inertia and angular acceleration of the load and represents the torque acting on the load in addition to the torque from the reducer The friction combination of is used to represent the nonlinear friction of the harmonic reducer 1 2 And also from equation 3 the nonlinear friction of the harmonic reducer is 1 4 Using equation 4 can calculate the friction of the robot s joint it still needs to choose appropriate friction model to describe it Many scientists have worked on this research topic and there are several kinds of friction model established 26 In this paper Coulomb Viscosity Stribeck friction model is utilized to estimate the friction of harmonic reducer because it can describe the friction with the reducer operating at both high speed and low speed The general mathematical expression for this friction model is sgn 5 Tf2 Tk N Tst Tf1 Tf3 Twg Tfs Motor Load Tnwg Tn Tc Harmonic drive 4632 Fig 5 Block diagram of the hybrid force and position control In which is the coulomb friction is the maximum static friction is the critical Stribeck speed is the viscous friction coefficient These parameters can be determined by experiment data and the details will be explained in section V Since 0 0 10 The experimental data are fitted to the friction model as shown in Fig 9 The R square of this fit is 0 9319 This model precisely reflects the variations of friction on harmonic gear driven joint A set of comparative experiments is implemented to evaluate the compliance performance of the leg with correct torque estimation on each joint In this experiment the whole robot is suspended in the air Then an external force with different values and directions is applied to left hind leg the leg in test to make it out of the foot end equilibrium position 0 0 5m The value of these predefined coefficients of the virtual spring and damper are 0 625 3 0 01 s N mm After the external force released the leg returns to its balance in a spring and damper way as shown in Fig 10 a indicating a good a HFE joint b KFE joint Fig 11 Joint torque responses in compliance control versus position control for robot pounded by external forces compliance with artificial elasticity We compare the position errors of the equilibrium position with and without the joint output torque estimation after the external force released The experiment results are shown in Fig 10 the red line and the blue line represent the maximum error and the minimum error respectively In the experiment without the joint torque estimation even though the leg can converge on a balance point but the maximum error is 12 4 mm and the minimum error is 5 2 mm as marked in Fig 10 b with the average error of 8 91 mm which means poor tracking performance of compliance control without torque estimation In contrast Fig 10 a shows better elasticity with joint output torque estimation and the maximum error of 7 1 mm and the minimum error of 1 8 mm with the average error is 3 88 mm means that the position accuracy of compliance control with joint torque estimation is increased by about 56 5 So our compliance control combines both position feedback and torque feedback together The joint torque estimation actually improves the compliance performance of the leg with better position accuracy of the foot end trajectory can give better tracking performance during dynamic walking and provide more ideal elasticity B Standing experiment The standing experiment exhibits the virtual compliance control performance under external forces In this experiment the robot stood on the ground and then it was pounded lifted up and pushed down The torque controlled joints demonstrated the effects of compliance control for the 510152025 0 10 20 30 40 50 60 Positin error mm Time s 101520253035 0 10 20 30 40 50 60 Position error mm Time s 05101520 0 20 40 60 80 100 Torque Nm Time s Compliance control Position control 05101520 0 20 40 60 80 100 Torque Nm Time s Compliance control Position control 4635 Fig 12 Summary of the foot end trajectory of the force control the hybrid force and position control with respect to the desired trajectory Fig 13 Tracking performance of different compliance controls whole body The predefined parameters of the virtual spring and damper are 0 625 3 0 01 s N mm Each leg s predefined foot end equilibrium position is 0 01m 0 5m The compliance provided artificial elasticity of each leg under external forces the robot shook a little and then restored the whole body balance with its legs acting like muscle driven animal legs The joint torque can be estimated by the motor current and rotation velocity detected in each joint The data of the four legs are similar to show the compliance control with precise feedbacks of position and torque ensures the robustness of the whole body balance control The torque of the hip joint and the knee joint of the left hind leg are represented in Fig 11 It shows that the joint torque in compliance control under external forces is much smaller than that in position control Also the torque estimation provides good elasticity for the compliance control The position control shows the behavior of rigid robot without any compliance triggering huge instantaneous torque peaks each time external forces executed C Walking experiment This experiment is to verify the tracking performance of the virtual compliance when the robot walks dynamically in the locomotion control framework based on hybrid force and position control High gain of the position control is used for desired precise trajectory in leg swing phase and compliance control based on torque estimation on each joint is involved in the stance phase in order to get better tracking performance The gain of the position control of 1779 leads to stiff joints In this experiment we setvs 0 1m s and Tst Tsw 1s so Lspan 200mm and the slow trotting is realized dynamically The control point of the desired foot end trajectory can be calculated P0 100 500 P1 117 500 P2 134 300 P3 0 300 P4 134 300 P5 117 500 P6 100 500 Fig 12 shows the summary of the foot end trajectory different compliance controls hybrid controls versus force control by torque feedbacks over the whole walking cycles with respect to the desired trajectory Let eh represents the difference between the highest point of the desired foot end trajectory and that of the actual foot end trajectory eL represents the difference between the end point of the d