IROS2019国际学术会议论文集2175

Whole-Body Locomotion and Posture Control on a Torque-Controlled Hydraulic Rover Sang-Ho Hyon1, Yusuke Ida1, Junichi Ishikawa2and Minoru Hiraoka2 AbstractThis paper presents the control method and sys- tem of a four-legged, four-wheel-drive hydraulic powered rover that can traverse irregular terrain such as agricultural or forest landscapes while carrying manipulators and other tools to do heavy-duty work. The rover is equipped with driving wheels at the tip of its legs and passive wheels at its knees or the bottom of its belly. By directly controlling the whole-body joint torque using hydraulic actuators, the multiple contact forces at its rolling contact points can be distributed optimally according to the rover state. This allows the acceleration of the rovers center of gravity and posture to be controlled while the active/passive wheels accommodate the terrain. The proposed control method is applied to our new fully torque-controlled rovers produced from low-cost hydraulic components. The simulation and experiments on balancing on moving ground, or running over slopes validates the proposed algorithm and the system. I. INTRODUCTION A. Background The aim of this study is to realize a general purpose mobile platform that can traverse irregular terrains such as agricultural or forest landscapes while carrying manipulators and other tools for heavy-duty operations. The following features are particularly important for this type of robot: (F1) Terrain adaptability: Able to adapt to even the extreme irregular surfaces and steep slopes, which are common in agricultural or forest landscapes. (F2) Base stability and mobility: Providing a stable platform that directly supports the operability of the working tools (such as manipulators) to be mounted on the base, or the comfort of the operator. Safety (fall stability) is also a fundamentally important concern. (F3) Impact resistance: Able to withstand impact from the ground because of a sudden change of the terrain geometry. Numerous and diverse design methods of these mobile robots satisfy these features, ranging from existing all- terrain-vehicles to unmanned planetary exploration rovers 1. We are investigating the possibility of a four-legged, Manuscript received: February, 25, 2019; Revised May, 17, 2019; Ac- cepted June, 11, 2019. This paper was recommended for publication by Editor Youngjin Choi upon evaluation of the Associate Editor and Reviewers comments. 1S.H. and Y.I. are with Humanoid Systems Laboratory, Department of Robotics, Ritsumeikan University (Noji-Higashi 1-1-1, Kusatsu, Shiga 525- 8577, Japan). 2J.I. and M.H. are Kubota Corporation (Shikitsuhigashi 1-2-47, Naniwa- ku, Osaka 556-8601, Japan). The authors have provided supplementary downloadable material avail- able at . It includes a single MPEG4 format video that shows the experimental results. 1.12 2.40 (m) 1.80 3.28 (m) 0.56 1.40 (m) Fig. 1.Hydraulic wheel-on-leg rover: Hydrover-II. four-wheeled-drive rover built from low-cost hydraulic com- ponents (Fig. 1). Legwheel hybrid mechanisms take advantage of features of a leg 2 (ability to discrete ground contact point selec- tivity and various operating confi guration) and of a wheel (simple, high effi ciency, and high speed). Many studies have examined position-controlled rovers (e.g., 37). In this study, we are particularly interested in large- scale wheel-on-leg rover, which is useful for heavy-duty tasks for agricultural or forest landscapes. Wilcox et al. 8 developed the Athlete rover (850 kg weight for the earth testing model). This rover has six identical 6-degrees-of- freedom (DoF) limbs that form a hexagon shape. The rover is position-controlled, but the joint torque estimates (from the difference between the motor angle and joint angle) are used to distribute the ground force evenly or resolve undesired internal force between the limbs. Cordes et al. 9 studied the SherpaTT rover (150 kg weight) having a leg-wheel mechanism with 5 DoF. They showed the performance of positioning the tip of the leg for base attitude stabilization and for force leveling. Reid et al. 10 developed the MAM- MOTH rover (80 kg weight) to study position-based rough terrain adaptation by way of recursive kinematics algorithms combined with terrain mapping. Technically, the research most resembling ours is work reported recently by Hutter et al. 11. They introduced hydraulic torque control to a Walking Excavator (960 kg weight) by Menzi Muck. Thereby, they succeeded in travers- ing a slope by partially automating the control. They in- troduced high-performance servo-valve-based actuators in collaboration with MOOG, Inc. IEEE Robotics and Automation Letters (RAL) paper presented at the 2019 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) Macau, China, November 4-8, 2019 Copyright 2019 IEEE B. Paper subjects and scope The subjects of interest here is how to coordinate the motion of the legs and wheels to achieve good stability and mobility and overcome various irregularities. This paper particularly focus on a specifi c rover hardware Hydrover. Fig. 1 shows the second prototype. Each leg has four active DoF: the hip has yaw and pitch joints; the knee has a pitch joint; and the driving wheel attached to the end of the leg rotates around the pitch axis (see Fig. 2). The robot also has passive wheels at knee joints, which are used to support the body weight when necessary. In this paper we do not discuss turning motions (until we install additional yaw joints near the wheels), hence we do not use the hip yaw joint. Unlike many other rovers, we are aiming at active contact force control by directly manipulating the joint torque to achieve (F1)(F2). Because the whole body moves compli- antly, the robot is expected to be able to accommodate irregular terrain even if it is running “blind” (without camera or lidar). It also functions as an active suspension that fl exibly absorbs impact from unexpected irregular surfaces (F3). Although the method follows our earlier work on hydraulic humanoid robots 13, this paper specifi cally examines the optimal contact force control method while considering the rolling contact and auxiliary (passive) wheels for our new rover model. In the next section, we describe the control algorithm. Section III presents results of the dynamic simulation on balancing and locomotion control. High-level motion plan- ning is saved as a subject for future work. Section IV describes the experimental evaluation on terrain locomotion. The simulation and experiment results are supplemented in the video attachment, where optional movies are also included. II. CONTROLALGORITHM A. Model defi nition We consider an eight-wheel (including the passive wheels), four-legged robot model and coordinates defi ned in Fig. 2. However, the control method is applicable to any leg-wheeled robot. Let rC= xC, yC, zC R3be the position vector of CoM in the world (Cartesian) coordinate frame W. Also, let = R, P, Y R3be the orientation of the base, and let q Rnbe the joint coordinates. Let rP= xP, yP, zP R3be the position vector of the center of pressure (CoP) in W, and CrP be the same expressed in the CoM coordinate frame C. Let be the ground applied force (GAF) fP= fxP, fyP, fzP R3, the force with respect to Wthat the robot applies to the environment through CoP (Note: reaction of GAF is the ground reaction force (GRF). We assume a total of contact points defi ned as rS= rS1, rS2, , rS R3, where each vector com- ponent is rSi=xSi,ySi,zSiR3. Then, the associated applied contact forces are defi ned as fS= fS1, fS2, , fS R3, where each vector com- ponent is fSi= xSi, ySi, zSi R3. Note that CoP rP must lie within the supporting convex hull of rSj. CoM CoP rC g rSi( i =1,2,3,4 ) ( i =1,2,.,8 ) fSi X Z Y rP Hip yawBase link Driving wheel Hip pitch Knee pitch 4-wheel contact 8-wheel contact C ?W fP rP Fig. 2. Joint confi guration and defi nition of coordinates. Each ground contact point rSiis assigned a contact force fSi. The contact forces fSi are determined using a desired GAF fP. The CoP rPinvariably lies within the supporting convex hull of rSi. The hip yaw joint is locked in this work. B. Controller overview The overall structure of the controller is shown in the block diagram of Fig. 3. It consists of three control modules: C1, maneuver planning; C2, whole body motion control; and C3, local joint servo. C1 determines which wheel should be in contact with the ground, based on the measured ground information. It also determines whether the joints are to be locked or not. This setting corresponds to selecting “driving mode” for the robot. For example, on fl at ground, it is more energy-effi cient to transverse only with the driving wheels similarly to a car while the other joints are locked. C1 also commands the traveling speed and postures of the robot, which dictates the position and velocity of the center of mass (CoM) (rC, rC), the target attitude of the robots base (t), and the target wheelbase (horizontal distance between the wheels). C2 computes the joint torque necessary to follow the target of the CoM, base attitude and wheelbase given by C1, while ensuring the terrain adaptability property, similarly to an active suspension. Specifi cally, the contact forces fS applied to the environment from each wheel are determined optimally as described in Section II-C. This problem includes C1 Maneuver plannerC2 Whole-body control C3 Local servo control Joint torque computation Applied force / moment Mode selection Motion command - Base position/attitude - CoM position/velocity - Wheelbase - No. of contact - Drive/passive wheel - Lock /free joints - Feedfoward - Feedback (e.g. PID) - Dynamic stability - Contact force distribution - Contact Jacobian - Torque servo - Position / velocity servo - Lock / free joints Auxiliary command Torque command Fig. 3.Control framework for torque-controlled rover. dynamic stabilization of CoM and base posture. C3isajointservosystemthatmakesthejoint torque/velocity/angle follow the target value with minimum error. C. Passivity-based whole-body motion control In this section, C2 details are explained. This work em- ploys a passivity-based whole-body motion control algorithm proposed in 13. However, because the drive wheels and the passive wheels are included in the robot model, modifi cation is necessary. Using the following procedure, C2 computes the joint torque: 1) Calculate the desired GAF fPand desired CoP. 2) For given active contact points rSi(i 1,2, ,) and active joints qj(j 1,2, ,n); then construct the contact Jacobian CJS from the CoM to the supporting contact points. 3) Compose desired forces to control the wheelbase and the base orientation. 4) Compute the desired contact forces fS. 5) Transform the contact forces fSto torque commands for the active joints. Related details are presented below. 1) Balance and locomotion control: This is achieved by setting: fP=MrC+ Mg0, 0, 1 KPC(rC rC) KDC( rCrC)(1) with M = diag(m,m,m) (where m represents total mass), desired CoM accelerationrC, velocityrC, position rC, and the PD-gains KPC,KDC 0. Considering the moment balance, the desired CoP rPin Cis set as xP= xC+ zPfxP fzP ,yP= yC+ zPfyP fzP .(2) If the desired CoP does not lie within the supporting convex hull, then we truncate the desired GAF accordingly. 2) Contact Jacobian: It is noteworthy that contact Jaco- bian CJS is computed by CJS(,q) =CrS q R3n, where CrS = rSrC, and contains not only joint coordinate q, but also the base orientation . Extension to rolling contact is given in Section II-D. The dimension of the contact is = 4 for four wheel drive mode and = 8 if the passive wheels are in contact with the ground. Inactive joints such as hydraulically locked joints are removed from the column of CJS. These are subject to change. 3) Wheelbase and base attitude control: We set the de- sired internal forces for X and Y direction for the i-th contact point as xSi= KSx(xSi xSk xik),i = k(3) where xik 0 is the desired wheelbase (e.g., some nominal value) between the position of the i-th wheel xSiand k-th wheel xSk, and KSxis the desired stiffness. This setting was achieved in our earlier experimental work 14, where a torque-controlled humanoid robot maintained the distance between the feet to balance stably on a slippery ground surface. Similarly, we set the vertical contact forces zSithat col- lectively generate the moment for the attitude stabilization: Tx= KPAx(R R) KDAxR, Ty= KPAy(P P) KDAyP, (4) where Rand Pare the desired roll and pitch attitudes, and K 0 are the PD gains. These are substituted to the moment equation Tx Ty = yB yS1yB yS xB xS1xB xS zS1 . . . zS (5) to solve for zSi, where xBand yBare the horizontal positions of the base center. 4) Optimal contact force distribution: We distribute GAF to each ground contact point as described below. First, from the defi nition, CoP can be expressed as xP= i=1xSifzSi i=1fzSi ,yP= i=1ySifzSi i=1fzSi ,(6) where GAF is the sum of the respective contact forces: fP= i=1 fSi.(7) Therefore, the equation related to the vertical contact force fzScan be written as xP yP 1 fzP |z bzR3 = xS1xS2xS yS1yS2yS 111 |z AzR3 fzS1 fzS2 . . . fzS . |z fzSR (8) Then, the optimal vertical contact force fzSthat mini- mizes the scalar cost function f zSWzfzSwith the weighting matrix Wz Ris obtained as fzS= A# zbz, (9) where A# z = W1 z A z(AzW 1 z A z)1. Similarly, we obtain the optimal horizontal contact forces fxS, fySby inverting the force/moment balance equations: yPfxP zPfxP fxP = AxfxS.(10) Finally, the internal force xS= xS1,xS2,.,xS and the base stabilization force zSto generate the desired moment Eq. (4) are merely superposed, respectively, to the contact forces fxSand fzS. Note that we do not use fyS, nor ySiin this paper because we disabled the hip yaw axis. But, q1F q2F q3F Z CoM Fore Leg Hind Leg Base ? q1H q2H ? ? ? ? X rSH q3H rSF ?P ? ?W rC rP rP C CoP H Fig. 4. Defi nition of coordinates of the model projected onto the XZ plane. fyPin Eq. (2) is used to determine fzSthrough CoP yP. Also note that we can combine Eq. (5) and Eq. (8) to obtain fzS simultaneously 13. There are almost no difference between them because two feedback controllers (CoM position and base attitude) can coexist. . Instead of least-square methods, one can apply nonlinear programming methods to enforce some hard constraints on the contact forces (positiveness, friction conditions, etc.) 15 and/or the joint torque limits 16, and so forth. 5) Joint torque computation: The fi nal commanded joint torques are computed as = CJS(,q)f S+ (q, q), (11) where represents the damping term. D. Extension to rolling contact force control for slant The algorithm above must be modifi ed for application to the rover to accommodate the rolling contact as follows. The terrain information (local inclination of the ground at each contact point) must be incorporated as well. 1) Rolling contact Jacobian for irregular terrain: Contact Jacobian CJS(,q) must represent the rolling constraint between the ground surface and the wheel. We can apply the kinematic model for the 3D rover 37. However, in this study, we consider the planar model presented in Fig. 4, where the robot is contacting the slant surface. We do not take steering and slip into consideration. Here we assume only three joints per leg, but the number of joints is not limited in general. Now, let ibe the wheel radius, ibe the local slant of the i-th contact point rSi between the ground and wheel. For the simple model in Fig. 4, we have only two contact points with the index i =F, H, i.e., front and hind wheel, respectively. In the latter simulation and experiment, we use i =FR, FL, HR, HL for all four wheels. The additional letters R and L respectively represent Right and Left. For the slanted surface, we set the desired CoP on the virtual ground plane depicted as the dashed line in Fig. 4. If we assume ideal rolling without slip, then the tangential velocity of the contact point and the wheel rotation rate j, both expressed in W, meet the following non-holonomic relation: xSi icosii= 0(12) zSi isinii= 0.(13) The angular rate of the wheels is expressed as i= P+ q(i) 1 + q(i) 2 + q(i) 3 ,(14) where q(i)= q(i) 1 , q(i) 2 , q(i) 3 is the joint angle of the active joints in the i-th limb. Therefore, the contact Jacobian CJSi in Eq. (11) is re- placed by CJSi(,q) = q(i) xSi xC icosii zSi zC isinii R23(15) Note that: (1) If the Jacobian is set up to the wheel axles (not the contact points), then the joint torque is not allocated to the wheels. (2) This method requires j, i.e. information on the ground shape. Its measurement or estimation are already pro- posed in some literatures 17. In this paper, we do not consider this problem. Instead, they are prescribed in terms of the horizontal position of the ground. 2) Damping injection: Damping injection in Eq. (11) is indispensable in passivity-based redundancy resolution 18. Otherwise, undesired internal motions (self motions) will appear 19. In this work, the simplest form of damping of = D q was taken, where D is a diagonal constant matrix. The best value for damping coeffi cient D depends on the motion. If we want the driving wheels to move quickly, then it is better not to give any damping to the wheel joints. In our robots, because the internal friction of the hydraulic motor is large, little room exists for damping in all joints. One can also employ any priority-based redundancy resolutions (e.g. 20, 21).