Towards Active Actuated Natural Walking

Humanoid Robot Legs Ren C. Luo Chwan Hsen Chen Yi Hao Pu Jia Rong Chang

Department of Electrical

Engineering

Department of Mechanical

Engineering

Department of Electrical

Engineering

Department of Mechanical

Engineering

National Taiwan University Yuan Ze University National Taiwan University Yuan Ze University

Taipei, Taiwan Taoyuan, Taiwan Taipei, Taiwan Taoyuan, Taiwan

renluo@ntu.edu.tw mecch@saturn.yzu.edu.tw r98921008@ntu.edu.tw s975039@mail.yzu.edu.tw

Abstract - The objective of this paper is to investigate towards

active actuated natural walking humanoid robot legs.

Conventional humanoid robots suffer from problems like

artificial and unnatural motion, or low agility. To improve the

performance of the humanoid robot, this paper introduces the

idea which employs the active-actuated biped robot legs and

the passive dynamic walkers with more naturally walking. The

approach is primarily based on the utilization of shock

absorber and parallel linkage mechanism and the walking

algorithm which combines “Series Elastic Actuation” and

“Limit Cycle Walking”. The shock absorbers mounted in

series way enable the implementation of the conventional

“Series Elastic Actuation”, and the shock absorbers mounted

in parallel way are added as the modification in order to store

the energy of the actuators like the human muscle. The

specifically designed mechanism provides better support and

lower load of the motor than traditional design. The hardware

prototype has been implemented.The simulation and analysis

demonstrate the high potential and possibilities of this concept

and provide the new direction towards the naturally walking

humanoid robot legs design.

Keywords- Humainoid Robot Legs; Series Elastic Actuation;

Limit Cycle Walking; Combined Natural Active Walking and

Passive Walking

I. INTRODUCTION

During the past few years, research about biped humanoid robot has been widely developed around the world. Among all the countries, Japan devote themselves in this area for the longest time, like the most famous and earliest Asimo from Honda [1]. From 1986 until now, including the early works that has no upper body, the latest model is their twelveth-generationed product. Wabian family from Waseda University is another cluster of Japanese researching highlight [4]. WABIAN-2R, the traditional ZMP-based biped robot which has an impressive result that it walks with stretched knee, heel-contact and toe-off motion [5]. Another example from wabian family, WL-16, employs the idea similar to stewart platform, using linear actuators and capable of carrying one person. They are all able to perform multiple tasks [4].

In German, Munich University of Technology is also continuously working on this domain; Johnnie and Lola are their very successive result. Lola is the successor of Johnnie,

they both combine the different methods of driving a joint, some joints are driven by rotary motor and harmonic drive, some joints are driven by linear actuators and parallel mechanism [6][7][8].

Petman is the biped humanoid robot being built by Boston Dynamics to test military suits used to protect soldiers in chemical warfare [9]. With the external power and elegant mechanism design that is totally different from Wabian and Lola, Petman easily achieves the speed of 3.2mph with the human gait of heel-toe walking pattern and packs enough balancing intelligence to remain upright even when given a shove from the side.

All the robots mentioned above are actively controlled, but passive walking robot has also been researched and developed for a long time, such as Stappo and Bob built by Delft University of Technology [10]. They usually take advantage of their own mechanism design, and exploit gravity force as their power source.

The problem of active controlled robot is that they are usually not humanoid enough, some of them are capable of running and walking very fast but with their knee bending, some of them are capable of walking with their knee stretched but their efficiency are too low compare to human muscle. Petman seems to be the solution of the above paradox, but its hydraulic actuator and external power from internal combustion engine are still not favorable.

On the other hand, the passive walking robots have really high efficiency, but most of the time, they can only walk straight on a ramp. In 2008, based on their original understanding in passive dynamic walker, Delft University of Technology presents an active-controlled humanoid walking robot called „Flame [11].‟ It utilizes the idea such as “Series Elastic Actuation” and “Limit Cycle Walking” and successfully achieves a stable and very human-like walking process [12]. But it can only walk straight because it has only three active joints in each leg.

Our goal is to exploit both the benefit of the active-actuated robots and the passive dynamic walkers, while active-actuated robots tend to have high versatility and thus are able to perform multiple tasks, and passive dynamic walkers have better performance in terms of efficiency and walk more human-like and natural.

2011 IEEE/ASME International Conference onAdvanced Intelligent Mechatronics (AIM2011)Budapest, Hungary, July 3-7, 2011

978-1-4577-0839-8/11/$26.00 ©2011 IEEE 886

II. SYSTEM OVERVIEW

The requirement of our robot is to walk and turn smoothly as well as maintain high lateral stability simultaneously. Therefore the robot should possess all the functions of the conventional humanoid walking robot. An overview of robot configuration is given in Fig. 1. Each of the robot‟s leg has seven degrees of freedom, active joints include roll, and yaw joints of the hip. Considered that the lateral stability is mainly maintained by the roll joint of hip, the robot possesses only a passive roll joint at ankle. A passive movable ”toe” mechanism is also designed to make the robot walk more human-like, and able to perform toe-off motion. The ranges of all the joints are given in Table I.

TABLE I

THE RANGE OF SEVEN DOFs OF THE ROBOT

Joints Range(degree)

Hip Pitch -10~58

Roll -9~12

Yaw -7~12

Knee Pitch 0~85

Ankle Pitch -23~35

Roll -25~25

Toe Pitch 0~40

The entire mechanism height is 886mm, and total weight is about 25kg. The detailed dimension and weights of each section are given respectively in Fig. 2, and Table II.

TABLE II

THE WEIGHT OF EACH SECTION OF THE ROBOT

Section Weight(kg)

Pelvis 5

Thigh(one leg) 5.2

Shank(one leg) 4.2

Foot(one leg) 0.6

III. MECHANISM DESIGN

A. Hybrid Joints

Pitch joint of hip, knee, and ankle are very crucial for humanoid walking robot. To fulfill the idea aforementioned,

the shock absorbers linked to these crucial joints of humanoid robot leg are utilized. Because the shock absorber added makes these joint possess not only the controllable active characteristic but also passive compliance. We call these joints “Hybrid joint”.

The shock absorbers are connected to those joints in both parallel way and series way, the series shock absorber act with the concept of “Series Elastic Actuation”, it not only stores the actuator‟s energy like the human muscle but also sustains the weight of the robot, therefore decreases the load of actuator shaft and improves the shock tolerance of robot. The parallel shock absorber is the modification and improvement we made to traditional “Series Elastic Actuation”. Because of the high motor output requirement for humanoid walking robot, the parallel shock absorbers are applied to assist the motor, taking advantage from the natural dynamic of the shock absorber and reduce the motor output load.

B. Parallel Linkage Mechanism

All the joints of the robot are driven by linear actuators with parallel linkage mechanism. Combined with the shock absorbers, the parallel linkage mechanism works like the suspension system of vehicle. The biggest advantage is that the shock the robot confronted can be easily spread into structure, hence lower the possibility to cause harm to the vulnerable parts of the robot such as motor shaft. The mechanism of this kind transports the force more directly and will barely suffer from the backlash problem. The relatively low tolerance for manufacturing precision is also a desirable characteristic of parallel linkage mechanism.

Though the hybrid joint and parallel linkage mechanism design can effectively lower the output torque requirement, the output speed for the walking motion in pitch joints of hip, knee, and ankle are still critical. Therefore, in each of

Fig. 1. The configuration of the degrees of freedom of the humanoid robot

leg. Each robot leg possesses 7 degrees of freedom. Two of them are passive,

including the roll of angle joint and the toe joint.

Fig. 2. The front and side view of the mechanism. Red words denote the dimension of the mechanism.

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these particular sections, two linear actuators with high output speed and low output torque are employed.

Fig. 3 shows the overview of entire leg mechanism design. Hip actuators move in common to give sufficient torque for driving a pitch motion in hip, while differential movement drives roll motion in hip. Knee actuators move in common to give sufficient torque for driving a pitch motion in knee, while differential movement drives yaw motion in hip. Ankle actuators can only give common movement that drives pitch motion in ankle. With the design, the required motor peak force can be reduced and it provides better support of the robot[13].

IV. MOTION CONTROLLER DESIGN

A. Limit Cycle Walking

Conventional control algorithms for biped robot including “static stability” and “ZMP criterion” are applied throughout the world, and have quite impressive results, but they still suffered from too many artificial stability constraints, and consequently are suffered in terms of efficiency, disturbance handling, and natural appearance compared to human walking.

Because of some of the shortcoming of the conventional algorithm, the newly introduced stability paradigm of “Limit Cycle Walking,” are experimented, which has fewer artificial constraints and thus more freedom for finding more efficient, natural, fast and robust walking motions.

The essence of “Limit Cycle Walking” is that it is possible to obtain stable periodic walking without locally stabilizing the walking motion at every instant during gait, which means it doesn‟t require the stability in continuous-

time for the direct neighborhood of a state along a walking motion trajectory [14].

“Limit Cycle Walking” is first developed by Delft University of Technology for their passive walkers without actuator or only a few joints are controllable. Though, by the latest work of Delft University of Technology, it was shown that “Limit Cycle Walking” can also be implemented well on an active control robot with multi degree of freedom. But “Limit Cycle Walking” still maintains many properties related to passive biped walker. Therefore the “Limit Cycle Walker” moves mostly according to their natural dynamic to achieve r highly efficient and human-liked walking motion. In other words, it is very important to design the mechanism with high compliance.

B. Series Elastic Actuation

In order to meet the requirement, the actuators must have low impedance and high controllability. Combined the actuators and the shock absorbers in our design, we can implement the “Series Elastic Actuation”, which is perfect for “Limit Cycle Walking”. Because the natural dynamics of the walker intact is able to properly apply the concept of Limit Cycle Walking.

Fig. 4 shows the basic and simplified control architecture of our design. The plant signifies one single hybrid joint, which is a linear actuator with one parallel shock absorber and one series shock absorber as depicted in Fig. 5. The main controller will send a desired force command to the local controller, such as a PD controller in the Fig. 4. The feedforward path of desired force and feedback path of output torque is the fundamental configuration of “Series Elastic Actuation[15].”

Fig. 3. The architecture of the entire design of humanoid robot leg

mechanism.

a:Hip Serial Spring, b:Hip Actuator, c:Knee Actuator,

d:Hip Parallel Spring, e:Knee Parallel Spring, f:Knee Serial Spring,

g:Ankle Actuator, h:Ankle Parallel Spring, i:Ankle Serial Spring.

Fig. 4.The simple block diagram of the control architecture of one single

hybrid joint. Utilizing the concept of “Series Elastic Actuation,” the data

acquired by sensor is sent back to main controller in order to learn the current state and thus be able to perform Limit Cycle Walking

Fig. 5.The basic diagram of the plant in Fig. 4. .The greatest difference

between conventional “Series Elastic Actuation” and our design is the

shock absorber mounted parallel to actuator.

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C. Control Algorithm

The only difference between our design and conventional “Series Elastic Actuation” architecture is that we have to mount sensors on both shock absorbers to acquire the compression quantities of both shock absorbers, and then get the output force information. All the information of a certain time point during a motion of step will be sent to main controller, and through the program inside the main controller, map to the next state, which is the same time point in the next motion of step. This mapping function is termed “stride function” by McGeer[16],

If the two successive states yield the exactly same value, then it is a periodic motion. Through the analysis of the following relation,

the cyclic stability of this periodic motion can be established when the eigenvalues of the linearization matrix A, which are the partial derivative of the mapping inside the main controller to the state aforementioned, all lie within the unit circle of the complex plane.

V. EXPERIMENTAL RESULTS

A. Parallel Spring Verification

The motor load with parallel shock absorbers of different spring constant is analyzed. The result is given in Fig. 6. Blue line is a reference, represents no parallel absorber attached. It can be seen that the motor force increases with joint angle, and reaches 200N when the angle is 20 degrees. When parallel shock absorber is added, the motor force drops drastically, but the relationship between spring constant and peak motor force is not linear. When the shock absorber with too big the spring constant is chosen, the force of absorber is greater than the load, so motor have to offer additional effort to balance the overload situation. An intermediate spring constant value such as 55N/mm keeps the motor output force around 10N, which is 20 times smaller than one without parallel shock absorber, accordingly verify that the parallel shock absorber can effectively reduce the motor output load.

Fig. 6. Motor load versus joint angle under different spring constant of the

shock absorber. It can be clearly seen that with the appropriate chosen spring

constant value, the motor load can be maintain within 10N. The unit of spring

constant is N/mm.

Fig. 7. the motor forces of each pitch joint versus each joint angle during the

crouching process. Blue lines denote the load without parallel shock absorber,

whereas red lines denote the load with parallel shock absorber.

Fig. 8. This figure depicts the process of crouching motion of humanoid robot, the upper body is added to simulate the situation under heavy load.

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B. Linear Actuator Verification

To verify that the mechanism designed and the component chosen are capable of performing certain movement of human being, two motion scripts are set. One is the most crucial motion of humanoid robot, walking. The other is the most struggling motion, crouching.Fig 7 gives the motor forces of each pitch joint versus each joint angle during the crouching process. Fig. 8 shows the dynamic simulation result of crouching motion. Blue lines denote the load without parallel shock absorber, whereas red lines denote the load with parallel shock absorber. The effect that parallel shock absorber divides the burden of actuator is obvious. With the assistance of parallel shock absorber, the average required load force is about 40N, lower than the rated output force of the linear actuator chosen, and the maximum required load force is limited to 100N, lower than the maximum output of the linear actuator chosen.

Fig. 9 shows the dynamic simulation result of walking motion. The motor force of hip pitch joint versus time and the motor force of knee pitch joint versus time are given in Fig. 10. The motor velocity of hip pitch joint versus time and the motor velocity of knee pitch joint versus time are given in Fig. 11.

Fig. 12 shows the prototype of the robot leg mechanism. It is fabricated through CNC process. The shock absorbers inside the structure can be clearly seen before the motors mounted on..

Fig. 9. This figure depicts the process of walking motion of humanoid robot, the upper body is added to simulate the situation under heavy load.

Fig. 10. The motor force of hip pitch joint versus time and the motor force of knee pitch joint versus time.

Fig. 11. The motor velocity of hip pitch joint versus time and the motor

velocity of knee pitch joint versus time.

Fig. 12. The prototype of the robot leg mechanism.

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To perform the walking motion, the maximum load required is about 60N, lower than the maximum output force of the linear actuator. The maximum motor velocity required is about 80mm/s, which is also lower than the maximum output speed of the linear actuator chosen. The period of each step is about 1.3 second, and the step size is about 44cm, which leads to the approximate walking speed 2.4km/h.

VI. CONCLUSIONS

The specifically designed mechanism for humanoid robot leg is proposed in this paper. It features the parallel and series shock absorbers and parallel linkage mechanism design. The stretching and compression motion of linear actuator and the shock absorber completely mimic the function of human muscle, along with the parallel linkage mechanism, the energy efficiency is also elevated to a level closer to human muscle.

The compliant mechanism with shock absorbers also wisely adopt the concept of suspension from street vehicle and thus has the ability to support the whole structure that weighs much more than the maximum output force of actuators. In other words, the lighter actuators of lower output force can be chosen, correspond to the aforementioned idea of higher efficiency. Furthermore, the mechanism also offers more capability to tolerate the impact comes from ground.

Due to the totally different concept of the mechanism design, the algorithm adopted should also vary from traditional approach such as “ZMP criterion.” “Limit Cycle Walking” is a newly developed idea of humanoid robot by Delft University of Technology. It has been proven that this paradigm works well with all the passive dynamic walkers proposed by Delft University of Technology. In addition, “Limit Cycle Walking” also operates successively on their active-actuated robot, “Flame,” which makes it the most suitable algorithm for our design.

The simulation result indicates that the robot leg can achieve the walking speed around 2.4km/h, about the same velocity as averaged children walk.

The linear actuators utilized so far are chosen under economical concern, and thus the performance is rather plain. The walking speed can be significantly increased by choosing the faster linear actuators.

In addition to improve the walking velocity, to broaden the versatility is also a primary goal of our future research. Through programmable shock absorbers, the spring constant and damping constant of shock absorber can be adjusted in real-time, and the support force shock absorbers contribution can vary simultaneously with the much more complicated motion of robot, such as jump or sprint.

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