Proceedings o the 6 IEEE International Conerence on Robotics and Automation Orlando, Florida - May 6 Compensation or the Landing Impact Force o a Humanoid Robot by Time Domain Passivity Approach Yong-Duk Kim, Bum-Joo Lee, Jeong-Ki Yoo, Jong-Hwan Kim, and Jee-Hwan Ryu Robot Intelligence Technology Laboratory, Dept. o EECS, KAIST, Guseong-dong, Yuseong-gu, Daejeon, -7, Republic o Korea Email: {ydkim,bjlee,jkyoo,johkim}@rit.kaist.ac.kr School o Mechanical Engineering, Korea University o Technology and Education, Cheoan-city, -78, Republic o Korea Email: jhryu@kut.ac.kr Abstract In this paper, a method to reduce the landing impact orce is proposed or a stable dynamic walking o a humanoid robot. To measure the meaningul landing impact orce, a novel oot mechanism, which uses FSRs (Force Sensing Resistors), is introduced as well. Humanoid robot might become unstable during the walking due to the impulsive contact orce rom the sudden landing o its oot. Thereore a new control method to decrease the landing impact orce has been required. In this paper, time domain passivity control approach is applied or this purpose. Ground and the oot o the robot are modeled as two one-port network systems which are connected and exchanging energy each other. And, the time domain passivity controller which has the landing impact orce as input and oot s position to trim o the orce as output, is implemented. Unlike previous works, the proposed controller can guarantee the stability o the robot system without any dynamic model inormation at all. The small sized humanoid robot, HanSaRam-VI which has DOFs, with the proposed oot mechanism is developed to veriy the proposed approach through dynamic walking experiments. I. INTRODUCTION A humanoid robot is a bipedal (i.e., two-legged) intelligent robot, and is expected to eventually evolve into one with a human-like body. Recently, many researches have been ocused on a development o humanoid robot which is similar to human beings. Honda R&D s humanoid robots [], WABIAN o Waseda University [], H6 [], and HanSaRam [] are well known humanoid robots. Humanoid robots have been developed to resemble human beings, both morphologically and unctionally. Current research being conducted in collaborating operations with human beings [][6], has progressed ar beyond studies in walking pattern generation [7][8] and an online (realtime) balance control [9][] during walking. But the standard and most important unction o the humanoid robot is the ability to walk saely in the real environment. Since a legged robot can be unstable while walking ast, one o the essential research topics is to reduce the contact impact orce that is created between the oot and the surace during walking. So ar several approaches have been established to reduce impact/contact orce, which is created rom the ground surace. By using heuristic approach, a method has been introduced by Huang [] and Silva [] to shit the oot position once it reaches the surace. However, there are problems in changing the oot position and PID coeicients voluntarily. Several researchers have studied the hybrid impedance and computed torque control, and the hybrid position and orce control or the impedance adjustment o the leg [][]. However in this situation, the complex dynamics o the robot must be known, besides it being diicult to ind control parameters. In addition to these, there is a study which tries to decrease the orce using special oot structure []. This paper propose a method to reduce the landing impact orce o a humanoid robot. Time domain passivity approach [6][7] is implemented or this purpose. The robot s oot is modeled as a one-port network system with admittance causality (the landing impact orce is an input, and oot s position is an output). By calculating the energy input into the one-port network based on the landing orce and the oot position, the oot o the robot is controlled to be passive. Unlike previous works, the proposed control method can guarantee the stable dynamic walking without any model inormation, and requires very little additional computation. In this paper, the novel oot mechanism which uses our FSRs (Force Sensing Resistors on each oot) is introduced as well or measuring the landing orce eiciently. Force torque (F/T) sensor has been generally used to measure the orce that is applied to the oot due to the good accuracy. However, the F/T sensor usually has relatively large volume and heavy weight. Thereore, a small-sized humanoid robot mainly uses FSR sensors. They are usually attached to the sole o the oot, while the F/T sensor is usually attached to the ankle o the robot. Thus, when we use FSR sensors, the accuracy o the sensor system depends on the structure o the sole o the oot. In this paper, a new oot structure is proposed. It contains our FSR sensors on the sole o the oot that are independently movable and perceiving the orce accurately. The small-sized humanoid robot, HanSaRam-VI, which has DOFs and uses the proposed oot mechanism, is developed -78-9-/6/$. 6 IEEE
to veriy the passivity control. The validity o the proposed control method is conirmed through dynamic walking experiments. The remainder o this paper is organized as ollows: Section II describes passivity concept and modeling o robot s oot system. Section III proposes the time domain passivity controller or reducing the landing impact orce. The novel oot structure or eicient sensing orce is presented in Section IV. Section V presents the experimental results with the proposed controller. Finally, conclusions ollow in Section VI. II. PASSIVITY AND SYSTEM MODELING In this section, we briely review the passivity o a sampled time system, and model the robot s oot and the ground in terms o network sense. x& + - F( k ) Fig.. k Fig.. N One-port network model. x&(t) F( k ) Sampled time notation. A. Passivity in Sampled Time System First, we deine the sign convention or all orces and velocities, so that their product is positive when power enters the system port. Also, the system is assumed to have initial stored energy at t =o E() (Fig. ). Several variables are deined or the sampled time system during one sample time (Fig. ). ) (t) =F (k ) is the orce, which is assumed to be constant. ) ẋ(t) is the system velocity. ) x(k) and x(k ) are the position at k and k sample times, respectively. The ollowing widely known deinition o passivity is then used [8]. k Deinition : The one-port network N with initial energy storage E() is sampled time passive i and only i E(k) = k F (j )(x(j) x(j )) + E() () j= where k =,,,..., or sampled orce F (j) and position x(j). IE(k) or every k, this means the system dissipates energy. I there is an instance that E(k) <, this means the system generates energy, and the amount o generated energy is E(k). B. Robot s oot system modeling Δx Foot Ground (a) Robot s oot and surace. Fig.. Δx Foot + - Ground (b) One-port network model o the system. Robot s oot system modeling. To implement the time domain passivity approach, the robot s oot and the ground are modeled as a network system. Both systems can be modeled as one-port network systems, which are connected to each other. The impedance o the ground is zero when the oot is in swing mode, and has a certain value when the oot is in contact with ground. Fig. shows the real and the modeled network system, respectively. The sign convention or orce and velocity is deined so that the energy is positive when the power enters the system port o the robot s oot. In ig. (b), the orce and the velocity are positive in the upper direction. Since the ground can be considered as an intrinsically passive system, the connected system (the robot s oot and the ground) can be passive i only the robot s oot, one port network, is passive. Once we prove the passivity, stability o the robot system can be guranteed because passivity is a suicient condition o stability. This is a situation where the oot is physically absorbing the contact orce and showing the motion o sitting down. On the other hand, when the robot s oot, one port network, is active (while the input energy is negative), the robot might be unstable. This is the case when the robot s oot kicks the surace, it causes a big landing impact orce between the oot and the ground. This orce is the main reason or the 6
unstable walking. Thereore, a control algorithm is required or reducing the big landing impact orce. III. COMPENSATION FOR THE LANDING IMPACT FORCE USING TIME DOMAIN PASSIVITY CONTROL Δx + - Foot mechanism Fig.. Robot α δx pc Δx + Δx + One-port network with PO/PC. Planner We can divide the one-port network o the robot s oot system into two parts, mechanism part with low-level position controller and planner part with high-level controller. Fig. shows the separated network system o robot s oot. (= = ) is the landing impact orce, which can be measured by the FSR sensors on the robot s oot. x is the actual height position o the robot s oot, and Δx is the dierence between two consecutive sampled data o x. The modiied position x is obtained rom the originally planned trajectory (x ) and the output o the passivity controller (δx pc ). x is a planned height position o walking trajectory rom the planner, which did not consider the landing impact orce rom the ground. I we use the originally planned walking trajectory, the robot s oot might get a big landing impact orce rom the ground in a very short time, and it makes the one-port o the robot s oot active. For reducing the landing impact orce, the passivity controller is attached to modiy the original walking trajectory (x ) to x by adding δx pc. Thereore, the robot takes the ground reaction orce into account and it can make a contact with the ground more securely. The proposed time-domain passivity control system consists o a passivity controller (PC) and passivity observer (PO), which controls and monitors the input/output energy low between the robot s oot and the ground. Passivity observer computes the energy low using the landing orce and the oot position as ollows: W (k) =W (k ) + (k )(x (k) x (k )) () W o (k +)=W (k)+ (k)(x (k +) x (k)) () where W (k) is the total energy output rom to k, and W o (k+ ) is the prediction o the one-step-ahead energy output. The last term o Eq. () is the estimation o the one-step-ahead energy output, which is the output energy rom k to k +. Note that we know the planned position x (k +) at step k. I the PO can predict whether the system at the next step will be passive or not at the current step k, the PC can modiy the desired position at the next step (k +) to make the system passive. The PC absorbs exactly the net energy output (i any) measured by the passivity observer at each time sample. Based on the PO and steps and below, the PC algorithm (steps 6 and 7 below) or the one-port robot s oot with admittance causality is developed as ollows: ) (k) = (k) is the input; ) Δx (k) =x (k) x (k ) Δx (k +)=x (k +) x (k); ) Δx (k) is the output o the one-port network; ) W (k) =W (k ) + (k )Δx (k) is the energy output at step k ) W c (k +) = W (k)+ (k)δx (k +) is the prediction o the energy level at step k + 6) The PC output or making the system passive is calculated as ollows: { Wc(k+) δx pc = (k), i W c (k +)<, i W c (k +) 7) The modiied desired height position can be calculated rom Δx (k +)=Δx (k +)+δx pc (k). Please note that the PO/PC is or achieving the stable landing o humanoid robot. Once the stable landing is achieved (maintaining N steps with positive energy, and N is constant.), the robot s walking path should be modiied to ollow the initially planned walking path. The walking pattern, changed by the passivity controller, is interpolated to the initially planned walking trajectory by using the polynomial method. In this stage, passivity observer is also reset to prepare the next observation. IV. FOOT MECHANISM FOR FORCE MEASUREMENT In a design aspect, the proposed oot structure, as shown in Fig., is unique when it is compared to other humanoid robots [9]. The FSR sensors are added to the end-tip sensor stages (Fig. (b)). I a oot hits the ground, the tip point o a ball joint will push sensors through a round shaped lat panel. This sensing mechanism can measure not only perpendicular contact orce, but also diagonal ground contact orce. Since the end-tip sensor can rotates toward the ground according to the movement o oot plate, the sensor stages enable the FSRs to measure the landing impact orce or the ground reaction orce even though the oot hits the ground in non-perpendicular direction. Moreover, the sequence o the landing o each our FSRs can be known because each sensor stage is independently connected to the oot plate. V. EXPERIMENTS In this section, the proposed time-domain passivity control approach is veriied through real experiments with a smallsized humanoid robot platorm. 7
(a) Foot structure with our FSRs. Fig. 6. HanSaRam-VI. B. Experimental Results Dynamic walking experiments were perormed to veriy the proposed time-domain passivity control approach. The results are compared with those without PO/PC. In the experiments, the biped robot walked with a speed o cm/s and a step length o cm. Double and single support phases o a step were. s and.6 s, respectively. All experimental results are plotted ater the initial seconds o operation and then or seconds thereater. (b) End-tip sensor stage. Let oot position without PC Fig.. A. System Description Foot structure or orce measurement. Fig. 6 shows small-sized humanoid robot, HanSaRam-VI. It has DOFs, and consists o DC motors in lower body and RC servo motors in upper body. Its height and weight are cm and. kg, respectively. This biped robot s structure is mainly composed o Duralumin. Even though HanSaRam-VI is a small humanoid robot, the design o the lower body is ocused on generating suicient power and accurate control, and consists o DC motors and Harmonic drives. In the design o the upper body, RC servo motors are used, since RC servo is light in weight and easy to control. The on-board Pentium-III compatible PC, running RT- Linux, calculates the walking pattern in real time. The walking pattern is generated on-line through three-dimensional inverted pendulum mode []. The stand-alone vision system using PDA is equipped to ind out three colors in real time. To measure orces on the oot, FSRs with the proposed oot mechanism are equipped on each oot. With the help o all the computational and power parts, HanSaRam-VI has the ability or ully independent locomotion, sensing, and processing. Right oot position without PC Fig. 7. Foot s height position without PO/PC. First, the experiments were perormed without PO/PC. Fig. 7 shows the walking trajectory without considering landing impact orce. When robot s oot was landing, there was a big landing orce as shown in Fig. 8. This orce caused double contacts o the oot. Even ater the robot s oot was landed on the ground, it was bounced back rom the ground instantaneously due to the big landing orce such that it disturbed stable dynamic walking. It should be noted that two orce plots are dierent because the mass distribution was 8
Force (Kg) Force (Kg) Let oot orce without PC Right oot orce without PC Let oot position with PC Right oot position with PC Fig. 8. Force without PO/PC. Fig.. Foot s height position with PO/PC. Energy (Nmm) Energy (Nmm) Let oot Energy without PC. -. -. Right oot Energy without PC. -. -. Force (Kg) Force (Kg) Let oot orce with PC Right oot orce with PC Fig. 9. Energy without PO/PC. Fig.. Force with PO/PC. asymmetry in the real robot. Fig. 9 shows the input energy rom the one-port robot s oot. When the oot kicks the surace, the energy becomes negative, and the robot s oot is no longer passive. It means that the robot might be unstable due to this active energy output rom the oot. Fig. - Fig. show the results when the proposed time-domain passivity approach implemented. The modiied walking trajectory is plotted in Fig.. Foot is slightly moved upward on each landing time, since the passivity controller modiied the desired oot trajectory to satisy the passivity condition. Ater steps in which the energy stays positive, it was shited to its original position by cubic spline interpolation. As shown in Fig., the impact orce was reduced, because the passivity controller immediately reduced the impact orce. There was no double contact any more. Fig. shows that energy was also positive with the passivity control. It means that the robot system does not give o the active energy which could make the system unstable. The results o the overall experiments indicate that the proposed passivity controller decreases the impulsive landing impact orce at the ground surace and makes stable oot landings passible. It is important to remember that system dynamic equations are not used any more in the proposed method. Moreover, control parameters are not required. VI. CONCLUSION This paper proposed a new method to compensate or the landing impact orce or the ground reaction orce o a humanoid robot. For the use o the time-domain passivity approach, the ground and the robot s oot were modeled as two one-port network systems, which were connected and exchanging energy each other. Admittance type time-domain passivity controller, which has the landing impact orce as 9
Energy (Nmm) Energy (Nmm).... Let oot energy with PC Right oot energy with PC Fig.. Energy with PO/PC. an input and oot s height position as an output, was implemented. The proposed controller could guarantee the stable dynamic walking without any system model inormation at all. In this paper, the novel oot mechanism which used FSRs (Force Sensing Resistors) was also introduced or measuring landing impact orce eiciently. The proposed time-domain passivity controller was veriied with the developed smallsized humanoid robot, HanSaRam-VI. The proposed control method could stabilize the landing motion o the biped robot. ACKNOWLEDGMENT This work was supported by the Ministry o inormation & Communications, Korea, under the Inormation Technology Research Center (ITRC) Support Program. REFERENCES [] K. Hirai, M. Hirose, Y. Haikawa, and T. Takenaka, The development o honda humanoid robot, in Proc. o IEEE Int. Con. on Robotics and Automations, Leuven, Belgium, May 998, pp. 6. [] J. Yamaguchi, A. Takanishi, and I. Kato, Development o a biped walking robot compensating or three-axis moment by trunk motion, in Proc. o IEEE/RSJ Int. Con. on Intelligent Robots and Systems, vol., Yokohama, Japan, July 99, pp. 6 66. [] K. Nishiwaki, T. Sugihara, S. Kagami, F. Sanehiro, and M. Inaba, Design and development o research platorm or perception-action integration in humanoid robot: H6, in Proc. o IEEE/RSJ Int. Con. on Intelligent Robots and Systems, vol., Takamatus, Japan, Oct., pp. 9 6. [] J.-H. Kim, D.-H. Kim, Y.-J. Kim, K.-H. Park, J.-H. Park, C.-K. Moon, K. T. Seow, and K.-C. Koh, Humanoid robot hansaram: Recent progress and development, J. o Advanced Computational Intelligence & Intelligent Inormatics, vol. 8, no., pp., Jan.. [] S. Setiawan, S. Hyon, J. Yamaguchi, and A. Takanish, Physical interaction between human and a bipedal humanoid robot, in Proc. o IEEE Int. Con. on Robotics and Automation, vol., Detroit, MI, May 999, pp. 6 67. [6] K. Harada, S. Kajita, F. Kanehiro, K. Fujiwara, K. Kaneko, K. Yokoi, and H. Hirukawa, Real-time planning o humanoid robot s gait or orce controlled manipulation, in Proc. o IEEE Int. Con. on Robotics and Automation, vol., New Orleans, LA, Apr., pp. 66 6. [7] S. Kajita, A. Kobayashi, and T. Yamamura, Dynamic walking control o a biped robot along a potential energy conserving orbit, IEEE Trans. on Robotics and Automation, vol. 8, pp. 8, Aug. 99. [8] Q. Huang, K. Yokoi, S. Kajit, K. Kaneko, H. Arai, N. Koyachi, and K. Tanie, Planning walking patterns or a biped robot, IEEE Trans. on Robotics and Automation, vol. 7, no., pp. 8 89, June. [9] J. Yamaguchi, E. Soga, S. Inoue,, and A. Takanishi, Development o a bipedal humanoid robot control method o whole body cooperative dynamic biped walking, in Proc. o IEEE Int. Con. on Robotics and Automation, vol., Detroit, MI, May 999, pp. 68 7. [] B.-J. Lee, Y.-D. Kim, and J.-H. Kim, Balance control o humanoid robot or hurosot, in Proc. o IFAC World Congress, Prague, Czech, July. [] Q. Huang, K. Kaneko, K. Yokoi, S. Kajita, T. Kotoku, N. Koyachi, H. Arai, N. Imamura, K. Komoriya, and K. Tanie, Balance control o a biped robot combining o-line pattern with real-teim modiication, in Proc. o IEEE Int. Con. on Robotics and Automation, vol., San Francisco, CA, Apr., pp. 6. [] F. Silva and J. Machado, Position/orce control o biped walking robots, in Proc. o IEEE Int. Con. on System, Man, and Cybernetics, vol., Nashville, TN, Oct., pp. 88 9. [] J.-H. Park, Impedance control or biped robot locomotion, IEEE Trans. on Robotics and Automation, vol. 7, no. 6, pp. 87 88, Dec.. [] H.-O. Lim, S. Setiawan, and A. Takanishi, Position-based impedance control o a biped humanoid robot, Advanced Robotics, vol. 8, no., pp.,. [] J. Yamaguchi, A. Takanishi, and I. Kato, Experimental development o a oot mechanism with shock absorbing material or acquisition o landing surace position inormation and stabilization o dynamic biped walking, in Proc. o IEEE Int. Con. on Robotics and Automation,vol., Nagoya, Japan, May 99, pp. 89 899. [6] B. Hannaord and J.-H. Ryu, Time-domain passivity control o haptic interaces, IEEE Trans. on Robotics and Automation, vol. 8, pp., Feb.. [7] J.-H. Ryu, D.-S. Kwon, and B. Hannaord, Stability guaranteed control: time domain passivity approach, IEEE Trans. on Control Systems Technology, vol., pp. 86 868, Nov.. [8] J.-H. Ryu, Y.-S. Kim, and B. Hannaord, Sampled- and continuoustime passivity and stability o virtual environments, IEEE Trans. on Robotics, vol., no., pp. 77 776, Aug.. [9] K. Erbatur, A. Okazaki, T. Takahashi, and A. Kawamura, A study on the zero moment point measurement or biped walking robots, in Proc. o IEEE Int. Workshop on Advanced Motion Control, Maribor, Slovenia, July, pp. 6. [] S. Kajita, F. Kanehiro, K. Kaneko, K. Fujiwara, K. Yokoi, and H. Hirukawa, Biped walking pattern generation by a simple threedimentional inverted pendulum model, Advanced Robotics, vol. 7, no., pp. 7,.