A 3-TIER INFRASTRUCTURE: VIRTUAL-, MINI-, ONLINE-HUBO STAIR CLIMBING AS A CASE STUDY

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1 3-TIER INFRSTRUCTURE: VIRTUL-, MINI-, ONLINE-HUBO STIR CLIMBING S CSE STUDY Youngbum Jun Mechanical Engineering and Mechanics Drexel University Philadelphia, P, US yj55@drexel.edu Paul Oh Mechanical Engineering and Mechanics Drexel University Philadelphia, P, US paul@coe.drexel.edu BSTRCT This paper introduces a 3-tier infrastructure for humanoid research. Using the KIST humanoid Hubo-, virtual-, mini-, and online-hubo comprise an infrastructure to respectively prototype, test-and-evaluate, and verify-andvalidate algorithms. The resulting closed-loop design cycle promotes research that can reproduced and verified by the humanoid research community. This paper presents stair-climbing as a case study, thus demonstrating the efficacy of the 3-tier approach. Beyond the 3-tier infrastructure, the paper presents an effective climbing pattern generation and analytic inverse kinematics. This stairclimbing approach is prototyped in virtual-hubo, experimentally tested-and-evaluated on mini-hubo, and verifiedand-validated on online-hubo. KEY WORDS Virtual-Hubo, Mini-Hubo, Hubo, Stair Climbing, 3-tier infrastructure 1 Introduction In past two decades a lot of humanoid research papers have been published. Many researchers have simulated or built their own humanoid robots to verify and validate algorithms and control techinuqes. However, the current actual humanoid technology has not caught up with the achievements in such papers since there was a critical gap; platforms were not easily available, and mechanically and systematically different, and hence research was difficult to validate and hence results were hard to reproduce. In 7 the National Science Foundation in the United States awarded a grant that partnered merican and Korean roboticists to create a 3-tier infrastructure to stimulate and advance humanoid research 1. This infrastructure served to fill such critical gaps. To overcome this challenge, virtual-, mini- and online-hubo were constructed to respectively prototype, test-and-evaluate, and verify-and-validate humanoid-based research. Based on the full-sized KIST Hubo humanoid, virtual-hubo is a zero-to-low cost simulator, mini-hubo is a 17-inch scaled open-source robot that one can construct for less than 1, USD and online- 1 This project was supported by a US NSF Grant 736 Figure 1. 3-tier infrastructure: virtual-, mini-, online-hubo stair climbing Hubo is the full-sized robot (called Jaemi Hubo) that is tethered to a gantry and can be programmed and monitored using the Internet in order to be world-widely accessed (see Figure. 1). n integrated software called Conductor [1] was developed to access 3-tier infrastructure and enabled a wide range of investigators to gain entry into humanoid research without being overly hindered by cost or maintanence. This paper serves to demonstrate the efficacy of the 3-tier infrastructure in humanoid research. Firstly, one s algorithms are prototyped in virtual-hubo and then secondly, tested and evaluated on mini-hubo. Thirdly, the algorithms modified and tuned in cycling between these two steps are ultimately verified and validated with online- Hubo. Through testing on 3-tier infrastructure, one s ideas are strongly supported and totally reproducible on many humanoid research environments since that is proved on simulation, miniature humanoid, and full sized humanoid platform. Stair-climbing was selected as a case study because there is wealth of humanoid literature on the subject. However, it was not clear to the authors if particular approaches could be universally applied to other humanoids and stair setups. Virtual-, mini-, and online-hubo provided the tools to quickly decide what could work and if any customization of the algorithms would be needed. There are generally two approaches to humanoid stair-climbing literature. The first focuses on trajectory

2 generation. To overcome unmodeled dynamics Kajita s 3D linear inverted pendulum (3D-LIPM) is often employed []. For example, Huang et al in Singapore employ the 3D- LIMP and Webots to simulate a full-sized humanoid and use zero-moment point (ZMP [3]) preview control [4] to generate trajectories to walk forward on slopes [5]. Purdue University roboticists also employ Webots to simulate a HOP- humanoid. Similar to preview control, they employ a convolution sum and set stable region bounds by taking the third derivative of hip position modeled by a 3D- LIPM [6]. Researchers at Tsukuba use captured motion data to generate trajectories and simulate stair-climbing. Here, they decomposed the data into six phases, generate trajectories for each phase and then re-assemble the data for stair-climbing [7]. The second approach focuses on control techniques. KIST for example also employ a 3D-LIPM with cycloid algorithms. Using force/torque ankle sensor data, they employ an observer to compensate for errors between actual and desired ZMP. Only ankle joints are controlled and they experimentally demonstrate stair-climbing on Hubo [8]. In China, Fu et al experimentally demonstrate stair climbing on the THBIP-1 humanoid. Trajectories are manually designed and define stable regions. Instead of controlling the position of the center-of-mass, force sensors, gyros and accelerometers provide data to control hip and ankle joints [9]. Taiwanese researchers apply a fuzzy controller on a custom-built miniature humanoid. Here, foot placement phases are defined to climb stairs [1]. The authors of this paper are particularly interested in analytic solutions for trajectory-based approaches. The authors reproduced ZMP preview control [4] and real-time ankle controller for ZMP compensation [8] with Jacobian Pseudo-inverse Kinematics (IK) [11]. Based on insight gained from virtual-hubo prototyping, mini-hubo evaluation, and online-hubo verification the authors observed three main issues; Since unmodelled dynamics, ZMP preview control results in large forward momentum for long strides during the double-support phase. Phase for climbing motion is ambiguous in ZMP preview control. Jacobian pseudo-inverse IK is computationally poor that does not fit in the miniature humanoid. To resolve, cycloid velocity profiles [8] are combined with ZMP preview control and single-support phase () is decomposed into upward-single-support phase (U) and described in Section. n analytic IK solver is developed to improve computation efficiency in Section 3, that resolves the second issue. The experimental results with the algorithms finalized through 3-tier infrastructure are demonstrated in Section 4, that strongly support the author s proposal. The conclusion and future work are described in Section 5. Figure. Simplified humanoid model: 3D linear inverted pendulum Stair Climbing Pattern Generation.1 Center Of Mass Trajectory Since unmodelled dynamics in 3D-LIPM depicted in Figure., ZMP preview control results in large forward momentum for long strides during the double-support phase. That yields a robot falling down to the forward direction. To minimize the momentum in forward direction, cycloid function is used. First, one begins with the 3D-LIPM to yield a simple humanoid dynamics model []. Here, the robot is modeled as a point mass m of length l located at the humanoid s center-of-mass (COM). This results in an equation of motion in the X-direction ml θ = mglθ τ y (1) where g is the gravitational constant and τ y is the torque around Y -axis. ssuming that the height of the COM remains constant, then let z c = l where lθ is the X position of COM. Equation (1) then becomes z c g ẍ=x τ y mg The relationship between the X- and Y -directions for the COM (x com,y com ) and ZMP (x zmp,y zmp ) are given by and the ZMP in X- and Y -directions can be respectively defined as () x zmp = x com z c g ẍcom (3) y zmp = y com z c g ÿcom (4) Second, reference trajectories must be generated and a ZMP preview control [4] is used with optimal previewable control theory [1]. The result yields hip trajectories based on a given ZMP reference trajectory and the humanoid s dynamics. For this paper, only lateral hip trajectories are generated for reasons described in Section 1.

3 Hip Trajectory in Y direction from ZMP preview Hip trajectory in X direction by Cycloid lgorithm Yzmp Hipy 3 Hip in X from Cycloid lgorithm Hipx C Xzmp Distance between Foot B/ Step Distance, Forward ZMP trajectory B/ Walking Period, T = + T T1 T T3 T4 T5 T6 T7 Time Figure 3. ZMP previewer yields hip trajectory in Y - direction T T1 T T3 T4 Figure 5. Hip trajectory in forward direction using cycloid function Cycloid Function Comparison of the forward hip trajectory from ZMP preview and Cycloid when 1/3 stride of leg length 3 Hip in X from Cycloid lgorithm Hipx C Hipx P Xzmp mplitude, Step Distance, Foward ZMP trajectory Hip in X from ZMP preview T Period, T T T1 T T3 T4 Figure 4. Cycloid function: πt sin(πt) Figure 6. Hip trajectories generated by ZMP preview and cycloid algorithms For the Y -direction, Figure. 3 shows the hip trajectory for a given ZMP trajectory specified by the Double-Support Phase (), Single-Support Phase (), and the distance between each foot B. cycloid hip generation algorithm developed in [8] allows tuning velocity and hip positions. cycloid is a curve defined by the path of a point on the edge of a rolling wheel (Figure. 4). x cyc (t) represents this path over time x cyc = (π ft sin(π ft)) (5) π where is the amplitude and f is the frequency defined as 1 T when T is the period. To combine (5) with the ZMP equation in (3) for the X-direction, the second derivative of the cycloid function is needed ẍ cyc = π ((π f) sin(π ft)) (6) Equations (5) and (6) are combined x zmp = Wπ (Wπ ft (1+ z c g (π f) sin(π ft))) (7) where W is the weight value to control the acceleration of the hip in the double-support phase (), is the step distance, and f is T 1 when T = + and is the single-support phase. Figure. 5 shows the hip trajectory in X-direction using a cycloid algorithm for a given ZMP trajectory. The hip trajectories from the ZMP preview control and cycloid algorithm for X-direction are compared in Figure. 6. Here, is set to one-third of the leg length. Figure. 7 shows the velocity changes for the trajectories given in Figure. 6 thus illustrating the reduction in hip momentum when one employs cycloids versus ZMP preview control.. Climbing Motion of Hip For a given ZMP trajectory, the previous section derived hip trajectories in both the X- and Y -directions. For the stair climbing the vertical motion of hip should be defined and foot motion should be also derived from ZMP trajectory for stability. Different phases associated with human stair climbing are notionally depicted in Figure. 8. From this figure, one observes that person s body moves vertically between

4 Change of linear velocity in ZMP preview and Cycloid lgorithm Hip trajectory in upward direction (Z direction) 3 Hip Velocity in X from Cycloid lgorithm Xzmp Vel C Vel P Hip trajectory in Z Hipz Yzmp Step Distance & Velocity Vp Vc Vc=approximately /3 of Vp Hip Velocity in X from ZMP preview Stair Height, H 3H H H Lateral ZMP trajectory T T1 T T3 T4 U Walking Period = +U+ T T1 T T3 T4 Figure 7. Hip trajectories generated by ZMP preview and cycloid algorithms Figure 9. Vertical hip motion (Z-direction) Figure 8. Human stair-climbing phases Figure 1. Foot motion in the human walking model and. To capture this phenomena the authors define an upward single-support phase (U). Hip vertical travel (Z-direction) is shown in Figure. 9 for a given ZMP trajectory in the Y -direction for a climbing period T and stair height H. The U period can be determined from simulation or experimentally. In Figure. 9, the U period was set to half of the period. First-order linear interpolation was then applied to generate hip motions in the Z-direction..3 Foot Trajectory Humanoid feet are the only body part that contact the ground when walking and hence play an important role in stability. However, their role in biped walking are often neglected. Through virtual-hubo prototyping, incorporating foot trajectories also improves stair-climbing performance. Figure. 1 depicts the foot-motion sequence. Sinusoids can be applied to design vertical foot positions (Zdirection) as in [8] [13]. By contrast, applying cycloids would provide foot position and minimize foot reaction forces when making ground contact. Such an approach needs three parameters: the duration; step distance in the X-direction; and the foot s maximum height. The first two parameters are obtained from the ZMP trajectory. The third parameter is defined manually. From concepts described in Section.1, (8) yields foot trajectories in the X-direction. Foot x = S d π (wt sin(wt )) (8) Equation (9) and (1) yield foot trajectories in the Z- directions when t < U and U < t, respectively. Foot z = H (wt sin(wt)) (9) π Foot z = H+ H (sin(wt) wt) (1) π where S d is the step distance in X-direction, w denotes π f, f = t 1, t is the duration, and H is the maximum foot motion height. When climbing stairs, stair height should be added to H in (9) as an offset. When added, the left and right foot trajectories in X- and Z-directions derived from (8) and (9) yield plots given in Figure. 11 and Figure. 1 for step distance and stair height SH.

5 The left and right foot trajectories in forward direction Xzmp Right Foot x Left Foot x 6 7 Torso Step Distance, Thigh Knee Yaw nkle 1 Pitch Roll T T1 T T3 Figure 11. Forward walking foot trajectories based on ZMP trajectory Figure 13. Joint configurations in legs of a humanoid Stair Height, SH SH SH The left and right foot trajectories in Z direction based on Hip motion in Z U Left foot in Z Right foot in Z Hip motion in Z Hip in Z Right Foot z Left Foot z Yaw Roll 4 (Back View) COM Thigh Roll Zc Pitch d Yt l leg Knee 1 l1 Ya nkle Roll Y Z Za T T1 T T3 Figure 1. Vertical left and right foot trajectories when stair climbing Figure 14. Joint configurations on walking in back-plane view 3 Vector Inverse Kinematics sketched in Figure. 13, a pair of humanoid legs typically consists of at least 13 degrees-of-freedom (DOF). Pattern generators typically solve the inverse kinematics (IK) for each leg (six DOF) and treat the hip as an end effector and foot as the origin. Computational costs often prevent direct control of hip position [8]-[1] [14]. One casually observes that people typically do not yaw their torso when walking straight. One explanation is perhaps the conserve angular momentum except when turning or intentionally taking long strides. Taking advantage of this zero yaw observation prescribes four constraints on the thighs: the angular momentum of yaw is zero; the upper body is always perpendicular to the ground; the bottom of foot is always parallel to the ground; and the height of COM is constant. With these contraints the three pitch angles and two roll axes in each leg can be analytically calculated in the vector space. This is important because these constraints allow real-time hip-position control without demanding extensive processing power. Figure. 14 shows the roll angles for the ankle θ 1 and thigh θ 4 in the back plane of the humanoid. Z a is the ankle height and equals Z f + l 1 where Z f is the foot height and l 1 is the ankle-to-foot length. The Y positions for the thigh Y t and hip Y h are related by Y t = Y h d. l leg denotes the D vector between the thigh and ankle joints. Through trigonometry θ 1 and θ 4 can be determined as θ 1 = 9 arccos((y t Y a )/ l leg )θ 4 = θ 1 (11) where l leg = (Z c Z a ) +(Y t Y a ) ll pitch angles can be calculated using the same approach. Figure. 15 shows the ankle θ, knee θ 3 and thigh θ 5 pitch angles. Let X, Y and Z symbols respectively denote joint positions X-, Y -, and Z-directions. Further, let the upper and lower leg link lengths be respectively denoted by l up and l low. l leg is the 3D vector between the thigh and ankle. pplying the law of cosines yields θ 3 = 18 arccos((l up+ l low l leg )/(lup l low )) (1)

6 5 COM (Xh,Yh,Zh) (Lateral View) Stair Climbing Trajectories for virtual, mini, online Hubo 3 Pitch Yaw Thigh (Xt,Yt,Zt) Roll l leg l up l Knee (Xk,Yk,Zk) llow l1 Distance Forward ZMP Trajectory Forward Hip Trajectory Forward foot Trajectory Lateral Hip Trajectory Foot Trajectory in Z Hip Motion in Z SD LD SH Lateral ZMP Trajectory nkle Z (Xa,Ya,Za) Y X LD Time (second) Figure 15. Joint configurations on walking in lateral-plane view Figure 16. Experimental results: Hip and foot trajectories θ 5 = 9 θ arccos((l up+ l leg l low )/(l up l leg )) (13) θ = 9 θ + arccos((l low + l leg l up )/(l low l leg ) (14) where l leg = (Z t Z a ) +(Y t Y a ) + X t X a ) θ = arccos((x t X a )/ l leg ) To compare computational times, calculations were performed on a dual core 3.37 GHz Pentium 4 running Matlab. Traditional Jacobian pseudo IK using damped least squares yielded joint angle calculations for 61 trajectory samples in.95 seconds. By contrast, calculation time was reduced more than 5% (.4 seconds) when yaw motions were constrained to zero. 4 Experimental Result from 3-tier Infrastructure tier Infrastructure Under the NSF grant that supports work in this project, the authors collaborator (Virgina Tech s RoMeLa Lab) designed mini-hubo, a DOF scaled version of the KIST Hubo, which stands.5 m tall and weighs 3 kg. The pair of legs consists of 13 DOF. The robot is equipped with an Intel tom 1.6 GHz processor and constructed with RX-8 Dynamixel servos, force/torque sensors at each ankle and communicates via USB and serial ports [13]. mini-hubo was designed to be open-sourced; plans for anyone to construct this robot are freely available on the web. Estimated construction costs are under 1, USD with less than 4 person-hours of machining and assembly time. Virtual-Hubo is the emulator component for the 3- tier infrastructure. Open Dynamics Engine (ODE)-based software allows one to better visualize how motion algorithms perform. graphical environment allows one to rapidly prototype and visualize algorithms that will be applied to mini- and online-hubo. This emulator can import CD models and employs the Webot ODE. The platform-independent architecture allows algorithms that run on virtual-hubo to port seamlessly to mini- and online- Hubo[1]. The platform-independent architecture, called Conductor [1], was developed by our group in order to allow algorithms that run on virtual-hubo to port seamlessly to mini- and online-hubo. This is accomplished by representing the control elements of the system in terms of a state variable approach, which is easily adjustable between the three architectures. The elements of control which are platform specific (motor drivers, calibration, etc) are left to lower level drivers that are easily interchangeable. Online-Hubo is built on top of the well-known full-sized humanoid, Hubo-, developed by HuboLab in KIST. The combination of remotely accessible and controllable software, and a powered safety harness allows the Hubo to be operated remotely. Researchers can access the robot anywhere, and monitor its motion via the Internet in realtime. With the Conductor, a program demonstated in Virtual-Hubo can be immediately loaded to online-hubo to verify its performance. 4. Virtual-, Mini-, online-hubo Experiments Based on the pattern generation algorithms with vector IK demonstrated in Section. and Section. 3, all trajectories applied to 3-tiers are generated in Figure. 16. The computational time in IK for each sample takes. miliseconds. That allows us to generate trajectories for and to control virtual-, mini-, and online-hubo on real time, that are run on 5Hz, 5Hz, and 1Hz respectively. It implies that the proposed algorithms overcome a limitation that Hubo- had in the previous stair climbing algorithms, which used joint trajectories generated on offline. The experiments run on 3-tiers are shown in Figure. 17, 18, and 19 as an image sequence. The stair height was set up as same as the ratio of dimension bewtween mini- and online-hubo. In the experiments, however, we tuned the momentum down for online-hubo since virtual-

7 Figure 17. Mini-Hubo simulation in Webots Figure 19. Hubo Experimental result: stair climbing of Mini- Figure 18. Hubo Experimental result: stair climbing of Mini- This paper presented stair-climbing as the authors first case study. lgorithms were rapidly prototyped in simulation, test-and-evaluated on mini-hubo, and then verified-and-validated on online-hubo. The results are promising and serve to demonstrate the efficacy of the 3- tier infrastructure and algorithms reproducible and reliable. Future work entails completion online-hubo ready to open to the public. The authors are currently working to post the simulator and open-source mini-hubo plans for free download. The team is also working to provide access to Jaemi Hubo (online-hubo) so roboticists can control the robot over the Internet. The net effect provides a universally accessible infrastructure; case studies like stair-climbing provide a context to begin analytical dialogs, reproduce experiments, identify best practices and ultimately lay foundational theory that vertical advances the state-of-the-art in humanoid research. and mini-hubo are one third in dimension but almost one fifteen in weight. 5 Conclusion and Future Work Until recently, the barrier to enter humanoid research was very high; full-sized humanoids were difficult to acquire and maintain. This made reproducing humanoid experiments and validating approaches by other roboticists next to impossible. In recent years, both simulators and miniature humanoids became widely available. Such platforms could serve as tools to rapidly prototype and test-andevaluate algorithms. Using such platforms to overcome barriers and benchmark humanoid research approaches embarked the authors on a 5-year project. The project develops a 3-tier infrastructure consisting of virtual-, mini- and online-hubo. References [1] Sherbert, R., Oh, P.Y., Conductor: Controller Development Framework for High Degree of Freedom System, IEEE Int. Conf. on Intelligent Robots and Systems (IROS11), San Francisco, US, Oct 11 (accepted to be published). [] Kajita, S., Kanehiro, F., Kaneko, K., Yokoi, K., Hirukawa, H., The 3D Linear Inverted Pendulum Model: Simple Modeling for a Biped Walking Pattern Generation, IEEE Int. Conf. on Intelligent Robots and Systems (IROS1), V1, pp.39-46, Oct. 1. [3] Vukobratovic, M., Borovac, B., Zero-Moment Point- Thirty five years of its life, Int.Journal of Humanoid Robotics, V1 N1, pp , 4

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