Control of a humanoid robot walking with dynamic balance*

Proceeding of the IEEE International Conference on Robotics and Biomimetics (ROBIO) Shenzhen, China, December 213 Control of a humanoid robot walking with dynamic balance* Guocai Liu 1,2, Fusheng Zha 1, Mantian Li 1,WeiGuo 1, Pengfei Wang 1,andHegaoCai 1 Abstract In this paper, we proposed a simple algorithm for controlling humanoid walking. We take the body as control target and the legs as control tool. The passie dynamic of robot is used as much as possible, and the legs will execute necessary actions for adjusting body states through sensors feedback. The hip actuators are used to aoid body from falling down including position and orientation which is the key for dynamic balance; the knee actuators are used to generate necessary spacing from ground when leg swinging; the ankle actuators are used to control walking elocity. Our control algorithm is test by simulation, the test shown that the robot can follow a gien elocity and its maximum walking elocity is near to human, the robot won t fall down or deiate its destination when suffering a relatie large disturbance. So our control algorithm is efficient and can be used to control humanoid robot walking. I. INTRODUCTION Using humanoid robot to sere for us is a dream of scientists, but humanoid walking is the key problem to build an agile humanoid robot. Although a lot of humanoid walking robots were built as yet, but there exist many deficiencies, such as walking slowly, falling down easily when suffering disturbance, control method intricately and so on. We argue that humanoid walking isn t a complex process, Using simple control algorithm can realize agile humanoid walking. Before addressing our control idea, we gie a simple reiew of humanoid walking robot nowadays firstly. When talking about humanoid walking, most of us will think about Honda humanoid robots [1 3], their loely appearance and moderate actions gie us deep impression. ASIMO which is a new type of Honda humanoid robots can walk up.44m/s with.61m length leg [1] and its nondimensionalized elocity (/ gl) is.18, but the walking elocity of human can easily up to 1.7m/s with 1m length leg and its nondimensionalized elocity is.54. So the walking elocity of ASIMO is much less than humans. Honda humanoid robots are based on zero moment point (shorted as ZMP) theory [4] which is the main reason for restricting their performance. ZMP theory requires the zero moment point should be in supporting area and far from the supporting edge as much as possible. For maintaining necessary supporting area, Honda humanoid robots use whole foot gait(whole foot touchdown and whole foot liftoff). Correspondingly, human usually use heel-toe gait(heel touchdown and toe liftoff). The process between *This work was supported by the Issue (No. SKLRS216B) of State Key Laboratory of robotics and systems(harbin institute of Technology), the project(no. 6117517,61576) of National Natural Science Foundation, and the National Hi-tech Research and Deelopment Program of China (863 Program, Grant No. 211AA438372). 1 State Key Laboratory of Robotics and System, Harbin Institute of Technology, Harbin, CO 158 CHINA 2 lgc@hit.edu.cn touchdown and liftoff, whole foot gait makes stance foot fixed and heel-toe gait makes stance foot rolling from heel to toe, which leading to the step distance of whole foot gait is shorter than heel-toe gait, so Honda humanoid robots hae a lower walking elocity than human. ZMP theory also makes Honda humanoid robots haing a poor disturbance enduring ability. Based on ZMP theory, the gait is stable only when the zero moment point is within supporting area. but the foot size couldn t be too large, so Honda humanoid robot can only endure small disturbance and its disturbance enduring ability is much lower than human. In a word, slowly walking and poor disturbance enduring ability restrict their application to real life. Unlike ZMP theory, Tad McGeer proposed passie dynamic theory. The robot based on passie dynamic theory can walk down a ramp depending on inertia and without any actie control [5]. Collins built a three-dimensional passie dynamic walking robot based on this theory, its walking elocity can up to.51m/s with.85m length leg and its nondimensionalized elocity is.18 [6]. From the iew of ZMP theory, the passie dynamic walking is unstable all the time, but the robot can achiee stable walking only depending on graity. Passie dynamic theory enlightens us that using passie dynamic makes walking efficient and simple. But it can only walk down a ramp for obtaining graity energy and we couldn t control its walking elocity and direction without any actie control, so passie dynamic walking robot couldn t be used in real life. Recently, Liu, et al proposed a noel control algorithm for planar biped walking [7]. In their control algorithm, the stance leg rotates like an inerted pendulum and will fall toward a direction depending on passie dynamic, and the swing leg will swing to the direction that the stance leg falling and supporting the body timely, then a new step will start and repeat the preious process. In the process of biped walking, passie dynamic is used as much as possible and actie control is used only when necessary such as aoiding falling down or adjusting walking elocity. But their control algorithm also has some deficiencies. For example, their control algorithm is used in two-dimensional space, but our real enironment is three-dimensional space; their biped robot has a telescopic knee, but all the legged animals in our world are joint knee; their biped robot has no feet, but humanoid robot should hae a pair of feet; their biped robot s body is located in hip, but humanoid robot should hae a upper body. Enlightened by human walking and combine the preious research of biped walking, we proposed a simple control algorithm for three-dimensional humanoid walking control. 978-1-4799-2744-9/13/$31. 213 IEEE 2357

We take the body as control target and the legs as control tool, and use sensors to monitor the robot s states. The stance leg is rotating by its passie dynamic and actie control is added when necessary through the sensors feedback. The dynamic math model of robot isn t required, the body states is our care and be kept in an allowed states by the adjusting robot s two legs. In this paper, a simulated humanoid robot is built. Its geometric characteristics and mass distribution are similar to humans. The hip actuators are used to aoid body from falling down including position and orientation; the knee actuators are used to generate necessary spacing from ground when leg swinging; the stance leg ankle actuator is used to adjust body walking elocity. The motions of different joints aren t related to each other and controlled separately, and this method makes the control simpler. We test our control algorithm by simulation and obtain good result. II. MODEL OF HUMANOID WALKING ROBOT The sketch model and solid model of our robot are shown in Fig.1. When building the solid model of our robot, the feature of humans is referenced [8]. Our robot is composed by seen parts, including one body, two thighs, two cruses and two feet. Body represents head, neck, arms and hands of humans for simple and takes 7% mass of the whole robot. Thigh, crus and foot take 1%,4% and 2% mass respectiely. The geometries of body, thighs and cruses are all built as frustums for simple, and these geometries can reflect human characters roughly. Foot will contact with ground intermittently when walking and its geometry has an eident effect to walking, so foot is built with more detail. The contour of foot is cured which is imitating humans and the heel of foot with a large rounded. The two feet aren t placed in parallel but with a 6 degree angle outwardly. This layout of feet is also similar to human and good for reducing impact force in forward direction and lateral direction together. The detail of feet has no effect to our control algorithm, but makes the walking relatiely smooth. For realizing three dimensional space walking, there are eight rotational joints in our robot in all. For each leg, there are two rotational joints at hip in forward direction and lateral direction respectiely, one rotational joint at knee in forward direction and one rotational joint at ankle in forward direction. Each joint has one drie. Joints at hip are droed by torque and joints at knee and ankle are droe by angular elocity. Torque control is soft for absorbing ibration in walking and angular elocity control is rigid for supporting body firmly. The states of robot including body pitch angle θ, body roll angle φ, body lateral elocity l, body forward elocity, swing pitch angle β, swing roll angle α, swing knee angle γ sw, stance knee angle γ st, swing ankle angle δ sw,stance ankle angle δ st and contact forces are all feedback to control system for use. III. CONTROL ALGORITHM In our control, we use a simple point of iew to obsere humanoid walking. Humanoid walking is treated as an Fig. 1. T lst l φ T α lsw Tfst β ω kst γ st δ sw ω ast δ st f θ Tfsw ω ksw γ sw ω asw The model of our simulated humanoid robot. inerted pendulum rotating depending on passie dynamic and the actie input is used as adjustment when necessary. Actie input adjusts three aspects when walking including body orientation, body height and body elocity. Adjusting body orientation and body height make robot keeping stance, adjusting body elocity makes robot starting to go. Because the main motion of human walking is depending on passie dynamic, we needn t to pay attention to the walking process and only need to monitor and adjust some states of the robot, so our control algorithm is efficient and simple. Although humanoid walking is a multi-input and multioutput system, we use an input to adjust one state. In our control algorithm, hip torque of stance leg is used to adjust body orientation, hip torque of swing leg is used to adjust body height and ankle angular elocity of stance leg is used adjusts body elocity. This decouple control is seemed ery rude, but it is ery effectie in the control. One input will adjust one state and influence other states at the same time, but other states will be adjusted back to ideal condition when their own inputs are actiated. A finite state machine is used to track the walking behaior, we diide a whole walking process into six states and different state will hae different actuation input. In the following, we will introduce the finite state machine firstly and then illuminate control algorithm at hip, knee and ankle in detail. A. Using finite state machine tracks humanoid walking circle In the finite state machine, we diide a whole walking step into six states and eery state has a set of actuators input. Only one state is actiated at the same time and the state will switch to its neighboring state by trigger eent. When these six states are actiated in turn, a walking step is finished and a new waking step will start and repeat the just states circle. The finite state machine and its detail are shown in Fig.2 and Table.I. The main motion of humanoid waking is depending on passie dynamic and the actuators actions are only used for motion adjustment. For example, stance hips are used to sero body upright all the time, swing hips are used to sero swing leg to a suitable angle for supporting body when touchdown and stance ankle is extended when 2358

TABLE I DETAILS OF FINITE STANTE MACHINE FOR HUMANOID WALKING Fig. 2. A finite state machine tracks humanoid walking behaior to synchronize the control system. stance leg rotating oer halfway. The stance leg rotates liking an inerted pendulum by passie dynamic, but in the action of these simple control rules, the swing leg can support body timely and the stance ankle can drie the stance leg rotating toward the expected walking direction, then the humanoid walking is created finally. Because the passie dynamic is used mainly and this process is no need to control, so our control algorithm is ery effectie and simple. B. Hips control The humanoid walking based on our control algorithm can keep dynamic walking, but what s dynamic walking? Dynamic walking means the robot won t fall down when suffering a large disturbance. Hips control is the key for dynamic balance in our control algorithm. Hips control including stance hips control and swing hips control. Stance hips are used to control body orientation upright all the time and swing hips are used to control body height in an allowable scope by selecting suitable swing leg angles. These two control rules make the robot keeping stance een when suffering a large disturbance. 1) Stance hips control: The stance leg will rotate liking an inerted pendulum and body will moe correspondingly, but body shouldn t rotate with the stance leg. Body should be kept upright when walking, or the robot will fall down finally. The hips of stance leg can correct body orientation through ground contact force, so body orientation can be controlled by the following formulas T fst = k fp (θ θ d ) k f ( θ) (1) T lst = k lp (φ φ d ) k f ( φ) (2) Where, T fst and T lst are the forward stance hip torque and lateral stance hip torque. k fp and k lp are position feedback gains; k f and k l are elocity feedback gains. θ d and φ d are the ideal body pitch angle and roll angle, these data are usually set to zero. State Trigger Action Eent Right leg Left hips: sero body upright State 1: lift off or Right hips: sero leg swing Right leg Right leg Left knee: keep knee straightly swing and swing Right knee: contract knee contract before Left ankle: keep ankle normal halfway Right ankle: foot parallel to ground Left hips: sero body upright State 2: Right leg Right hips: sero leg swing Right leg swing oer Left knee: keep knee straightly swing and halfway Right knee: extend knee extend Left ankle: extend ankle Left hips: sero body upright State 3: Right hips: sero body upright Double legs Right leg Left knee: keep knee straightly phase A touchdown Right knee: keep knee straightly Left ankle: keep ankle normal Left leg Left hips: sero leg swing State 4: lift off Or Right hips: sero body upright Left leg Left leg Left knee: contract knee swing and swing Right knee: keep knee straightly contract before Left ankle: foot parallel to ground halfway Left hips: sero leg swing State 5: Left leg Right hips: sero body upright Left leg swing oer Left knee: extend knee swing and halfway Right knee: keep knee straightly extend Left ankle: keep ankle normal Right ankle: extend ankle Left hips: sero body upright State 6: Right hips: sero body upright Double legs Left leg Left knee: keep knee straightly phase B touchdown Right knee: keep knee straightly Left ankle: keep ankle normal 2) Swing hips control: Body height should ary in a limited scope when waking. If body height is too low, the robot will fall down finally. When body height is lower than a height, swing leg should touchdown and preents body from continued descending. So body height can be controlled by the following formulas H = L 1+tan 2 α +tan 2 β (3) Where, H is lower limit of body height, the swing leg should touchdown when body height is around its lower limit. L is the swing leg length. The knee will unbend and the ankle will in the normal position before touchdown, so L is a constant alue. α is swing roll leg angle and β is swing pitch angle. If α and β satisfy the relation of (3), the body touchdown height will be controlled. Swing roll angle α isn t set arbitrarily, but it should balance the body lateral elocity l rightly. In other words, the body in lateral direction should rotate near to halfway and not oer halfway. If the body in lateral direction rotates oer halfway, the robot will occur side walking which isn t normal gait. If the body in lateral direction rotates far away 2359

from halfway, the touchdown impact force will increase and the body height couldn t rise enough. Here, we simplify humanoid robot to a point mass with massless leg and calculate the swing roll angle when rotating just to half in lateral direction, then gie a proportionality coefficient for adjustment. So, swing roll angle can be controlled by the following formulas ( ) 2gH cos α = k 2gH + l 2 (4) Where, k is a proportionality coefficient, usually we set k equal to 1, the larger of k, the more difficult for occurring side walking, but bring larger touchdown impact force. The direction of swing roll angle α is the same with the direction of l,soα can be expressed as following ( ) 2gH α = k 1 sign( l ) arccos 2gH + l 2 (5) If the robot is suffering a disturbance, it deiates from the original position. The swing roll leg angle α can be used to adjust the robot s side moement, so we can refine α as following ( ) 2gH α = k 1 sign( l ) arccos 2gH + l 2 + k 2 (s d s) (6) Where, k 2 is a proportionality coefficient. s d is the expected position in lateral direction and s is the actual position in lateral direction. Using formula (3) and (4), the absolute alue of swing pitch angle β can be obtainedβ can be expressed as following tan 2 β =1 L2 H 2 tan2 α (7) The direction of β is critical to dynamic balance. If the leg swings to a wrong direction, the body will not support timely and the robot will fall down. We simplify the robot model as an inerted pendulum, and calculate the kinetic energy T and potential energy U as following T = 1 2 2 f (8) U = g(1 cos ) (9) Where, f is the forward elocity and ς is the stance pitch angle. There are four states of T and U shown in Fig.3. We can express the four states in one expression as following SF = sign( f ) 1 2 2 f + sign()g (1 cos ) (1) Where, is the stance leg length in forward direction. The expression of swing pitch leg angle β can be expressed as following β = sign(sf) arctan 1 L2 H 2 tan2 α (11) The expressions (6) and (11) are used to calculated swing leg angles. The touchdown height will be guaranteed een suffering a large disturbance. Fig. 3. > < < U II I III IV > The signs of T and U in four states. C. Knee control When leg swing, the knee joint should contract in adance and extend before touchdown, the knee joint is controlled by angular elocity and the knee angular position can be controlled as following ω k = k(γ d γ) (12) Where, ω k is the angular elocity of knee, γ is the actual angular position of knee, and γ d is the expected angular position of knee. In our simulation, γ d is set to zero all the time for stance leg; γ d is set to -.7 rad when before halfway and set to zero oer halfway for swing leg. D. Ankle control The robot energy is fluctuating when walking. For example, some energy loses when swing leg touchdown, some energy increases when suffering a forward direction push and some energy changes when walking in an uneen ground. When robot energy changing, the walking elocity will change correspondingly. So the robot energy should be regulated in eery step for obtaining an expected walking elocity. Because the whole robot system is ery complex, it s difficult for us to calculate how much energy increases when stance leg lengthening and how much walking elocity increases when the robot energy enhancing. But we know that walking elocity will increase when lengthen stance leg and decrease when shorten stance leg. So we can establish the relation between stance ankle angle increment and walking elocity directly as following Δδ std = k p ( fd f )+k d n i=1 ( fd f )t i (13) Where, Δδ st is the expected ankle angle incensement. In our control algorithm, the knee joint is locked and unchanged in stance states and the ankle is used to change stance leg 236

length. k p and k d are proportional coefficient and integral coefficient respectiely, fd is the expected forward elocity, f is the actual aerage forward elocity, t i is the last time of i th step. The formula establishes the relation between stance ankle angle and walking elocity. We can select suitable stance ankle angle based on walking elocity feedback. Ankle control is the key for following an expected walking elocity. IV. SIMULATION AND RESULT We test our humanoid robot by simulation. We did two tests for our robot. The first test is following a gien elocity, and the robot will suffer a disturbing force on the road. The second test is the largest walking elocity test. A. Following a gien elocity with suffering disturbance The test scene is shown in Fig.4. The expected walking elocity is 1.1m/s and the initial state of robot is stand up with still. A rod is on the side of road and will push the robot when it passing. Fig.5 (a) is output cure of body forward elocity and body lateral elocity. We can see that body forward elocity is soon stable around 1.1m/s which is the expected walking elocity and body lateral elocity is swing about zero within the scope of.3m/s in one side. When the rod gies a disturbing push to the robot when it passing, the body lateral elocity is suddenly change to about 1.5m/s and the body forward elocity is also fluctuating, but this big disturbing push haen t knockdown the robot, it will soon recoer to the normal walking elocity in forward and lateral direction. When swing leg touchdown, the body suffering a large impact force and the stance leg torque seros the body upright, so an instantaneous forward elocity change is generated, this lead to the body forward elocity cure has a long downward peak in eery step. Fig.5 (b) is the input cures. Swing leg roll angle cure is ery similar to body lateral elocity cure. It s because the swing roll angle is used to balance the body lateral elocity, so the body lateral elocity has decisie effect to the swing roll angle. But they aren t the complete proportional relationship, the swing roll angle is decided by equation (6). The swing pitch angle control cure is also has a downward peak similar to body forward elocity cure s and It s because when body elocity reerse, the expected swing roll angle is reersed correspondingly for supporting body. The stance ankle angle is also has some fluctuating for adjusting energy leel when the disturbing push is added. This test show that the robot based on our control algorithm can follow the expected elocity and keep dynamic balance when suffering disturbance. B. Maximum forward elocity test Maximum forward elocity is a ital index for ealuating a control algorithm. To test the maximum forward elocity of humanoid walking, the expected forward elocity is gien to 1m/s in the first two seconds, and then increasing expected forward elocity gradually until the robot is falling down. The result is shown in Fig.6. With the increasing of actual Fig. 4. Fig. 5. 1.5 1.5 -.5-1 -1.5.4.2 -.2 -.4 The test scene of following a gien elocity with disturbance. -.6 5 1 15 2.5 2 1.5 1.5 -.5-1 5 4 3 2 1 The walking elocity and control input of humanoid walking. Actual forward elocity Expected forward elocity 2 4 6 8 1 12 14 16 18 Time (m/s) Fig. 6. Result of aximum forward elocity test. (a) (b) 2361

forward elocity, the contact force is increasing correspondingly and leads to the stance foot bouncing when forward elocity larger than 1.5m/s. The stance foot bouncing makes the program in disorder and the robot is falling down finally. So the maximum forward elocity of our humanoid robot is 1.5m/s with.9m length leg. V. DISCUSSION The walking elocity of our robot is up to 1.5m/s with.9m length leg, this elocity is near to the normal walking elocity of human. The nondimensionalized elocity of our robot is.51, and the ASIMO and Collins passie dynamic walking robot are all.18, so the robot based on our control algorithm has an eident adantage in walking elocity. Our robot can keep dynamic balance when walking. Although a larger disturbance makes the body lateral elocity changing suddenly, but the robot can place its leg in right position timely to support body and recoer to normal state in a few steps. This disturbance enduring ability is ery similar to humans. ASIMO robot doesn t discuss its disturbance enduring ability in the public papers, but it control algorithm is based on ZMP theory, so we can deduce that its disturbance enduring ability is small. Collins passie dynamic walking robot is also has ery little disturbance enduring ability. Because the continuous passie walking is based on a suitable initial elocity of eery step, if giing a disturbance, the initial elocity is changed and the robot will fall down directly. So, the robot based on our algorithm has an eident adantage in disturbance enduring ability. The characters of high walking elocity and excellent disturbance enduring ability will help humanoid robot waking out laboratory into real life. Although our algorithm can control humanoid walking with dynamic balance, the walking process isn t smooth. The impact force when swing leg touchdown is ery large and een more than four times of body weight which is shown in Fig.6(b), and it s leading to the body forward elocity haing a long downward peak. Larger impact force is increasing energy consumption, harm to mechanical structure and limited to achiee higher walking elocity. The humans walking are ery smooth, but our humanoid walking is ery bumpy. So additional control algorithm for smooth walking is needed and this is our research focus in the following time. REFERENCES [1] M. Hirose and K. Ogawa, Honda humanoid robots deelopment, Philosophical Transactions of the Royal Society a-mathematical Physical and Engineering Sciences, ol. 365, pp. 11-19, Jan 27. [2] T. Takenaka, The control system for the Honda humanoid robot, Age and Ageing, ol. 35, pp. 24-26, Sep 26. [3] K. Hirai, M.Hirose, Y.Haikawa and T.Takenaka, The deelopment of Honda humanoid robot, in 1998 Ieee International Conference on Robotics and Automation, Vols 1-4, ed, 1998, pp. 1321-1326. [4] M. Vukobratoic and B. Boroac, Zero-moment point thirty fie years of its life, International Journal of Humanoid Robotics, ol. 1, pp. 157-173, 24. [5] T. McGeer, Passie dynamic walking,international Journal of Robotics Research, ol. 9, pp. 62-82, Apr 199. [6] S. H. Collins,M.Wisse and A.Ruina, A three-dimensional passiedynamic walking robot with two legs and knees, International Journal of Robotics Research, ol. 2, pp. 67-615, Jul 21. [7] G. Liu, M.Li, W.Guo and H.Gai, Control of a biped walking with dynamic balance, in Mechatronics and Automation (ICMA), 212 International Conference on, 212, pp. 261-267. [8] W. S. Erdmann, Geometric and inertial data of the trunk in adult males, Journal of Biomechanics, ol. 3, pp. 679-688, Jul 1997. VI. CONCLUSION In this paper, a simple control algorithm is proposed for humanoid walking. In our control algorithm, stance hip torque is used to control body orientation, swing hip torque is used to control body height and stance ankle angular elocity is used to control body forward elocity. The walking process mainly depends on passie dynamic, and actie control is only used to adjust walking process. This makes walking process is ery efficient and the control algorithm is ery simple. A simulated humanoid robot is built and test by simulation, the result shown that the robot can follow an expected elocity with dynamic balance and its walking elocity is similar to human. This control algorithm can be used as a basic theory for controlling humanoid walking. 2362