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Simulation and Modeling of 6-DOF Biped Mechanism

Roopa Nadgiri, Ayesha Saha, Avirup Ghosh and Vivekanada Shangmuganathan*

Mechatronic Division, VIT University, Vellore, India; viveks@vit.ac.in

Abstract

mechatronic architecture describing mechanical to software issues related to designing and execution of locomotion.

Keywords:

1. Introduction

Mechanical biped locomotion has been subject to rigorous

study and research for the last three decades. e available

literature lie on a wide range of information, from ecient

means of guring the dynamical equations, model for-

mulation, relations between mechanical limb locomotion

and biological limb locomotion, methods of harmoniz-

ing gaits, the automated recognition of biped robots, and

control as well as manipulation. Human walking is the

motivation, furthermore the catalyst for walking robot.

In the initial stage of this paper, by the help of motion

apprehension of subject’s walking on stairs, the scruti-

nizing of human walking data is achieved. Biped robots

can act and change its position more freely than wheeled

robots in a candid manner. Empowering a robot to climb

stairs or step over snag autonomously, appropriate per-

ception capabilities, together with close coordination

between consciousness and locomotion are required. Our

exploration focuses on the synergy between mechanized

actuation and biped walking in an automated fashion.

1.1 Background Study

e idiosyncratic feature of full-body humanoids is

mainly based on bipedal locomotion. On two legs, walk-

ing, as well as running may be uncomplicated but at the

same time humanoid robots still have deliberate dicul-

ties in it. Among the two conicting wings approaches to

bipedal walking, the rst one is based on zero-moment-

point theory (ZMP), introduced by Vukobratovic. e

ZMP is interpreted the addition of all the moments of all

active forces on a particular point in the ground, as equal

to zero. A biped robot will be dynamically stable if the

zero-moment-point lies within the convex hull (support

polygon) of all contact points between the ground and

the feet. One of the major use of ZMP is to gure out the

stability is a large-scale advance over the center-of-mass

projection criterion, that chronicles static stability.

1.2 Past Research Work

e approach of human-like automatons is nothing

modern. Leonardo da Vinci (in 1495) designed an

armored knight using a mechanical gadget which waves

its arms and moves its head via a tensile neck while open-

ing and shutting its jaw. Illustration of humanoid robot

appeared in the movies A.I. (Steven Spielberg, 2001),

Indian Journal of Science and Technology, Vol 8(S2), 185–188, January 2015

*Author for correspondence

ISSN (Online) : 0974-5645

ISSN (Print) : 0974-6846

DOI: 10.17485/ijst/2015/v8iS2/60295

Simulation and Modeling of 6-DOF Biped Mechanism

Indian Journal of Science and Technology

Vol 8 (S2) | January 2015 | www.indjst.org

186

and I, robot (Alex Proyas, 2004). Minetti and Alexander1

recommended a rened structure of limb dynamics which

is capable of anticipating functions of walking and run-

ning2. Alexander used a simple point mass model to

spectacle that positive work in walking is unavoidable

to build up energy lost during heel strike3,4. Mochon and

McMahon5 demonstrated the ballistic motion of the swing

leg resembling humans, and McGeer6 revealed that the

entire step cycle can be interpreted by passive dynamics

with energy yielded by a slight downhill slope or by active

power aorded by a hip torque or an impulse at toe-o7.

2. Mathematical Modeling

2.1 Forward Kinematics

In Forward kinematics the position and orientation of

the end‐eector can be determined by conguring the

dynamic joints. is study concentrates on the lower part

of the biped. Model has 6 DOF namely a 1 DOF thigh, a 1

Degree of freedom knee, a 1 Degree of freedom ankle for

each leg. Individual legs can be modeled as a kinematic

chain with 3 links connected by three revolute joints.

e local frames (Xi, Yi, Zi) are allocate to each joint

agreeing to the Denavit‐Hartenberg (DH) convention in

the Figure 1. Assume the base frame (X0, Y0, Z0) at the

middle of the hip as the global reference frame. e kine-

matic structural arrangement of the le leg of the biped is

similar as that of right leg. Hence we assign co-ordinate

frames of both the legs same.

Considering local co-ordinate frames Li denotes the

length of link i and Ѳi is the angle between the Xi-1 and

Xi axes measured about the Zi-1 axis; di is the length from

the Xi-1 to the Xi axis as measured about the Zi axis; ai is

the distance from the Zi-1 to Zi axis measured along the

Xi-1 axis; and ai is the angle between the Zi-1 and Zi axes

measured along the Xi-1 axis. Anti-clockwise rotation is

assumed positive. DH parameters can be given as:

2.2 Trajectory Planning

For following a desired trajectory it is necessary to control

the biped. Hence it is important to generate Joint space

trajectory given by the Cartesian space trajectory. Hence

walking produces a xed periodic function which used to

calculate rotational angles and torque in the Figure 2.

X0(t) = s/2pi((2pi t/P)-sin(2 pi t/P)) (1)

Y0(t) = sh/2pi((2 pi t/P)-sin(2 pi t/P)) (2)

X1(t) = s/2pi((2 pi t/P)-sin(2 pi t/P)) (3)

Y1(t) = sh/2pi((2 pi t/P)-sin(2 pi t/P)) (4)

X3(t) = d/2pi((2 pi t/P)-sin(2 pi t/P)) (5)

Y3(t) = h (6)

Where s = the range covered in one step, sh = the

height between the sole of the foot and ground, d = the

hip moving distance, h = the height of hip joint, P = the

period of single step, and t denotes time.

Figure 1. Kinematic description of the biped. Figure 2. Parameters of trajectory planning.

Table 1. DH table for le leg

DH parameter Joint

ѲiѲ1Ѳ2Ѳ3

Di-l1 0 l3

Ai0 l2 0

aiΠ/2 0 Π

Roopa Nadgiri, Ayesha Saha, Avirup Ghosh and Vivekanada Shangmuganathan

Indian Journal of Science and Technology 187

Vol 8 (S2) | January 2015 | www.indjst.org

3. System Architecture

3.1 Specication

3.1.1 Arduino AT mega 2560

Arduino AT mega 2560, with 54 digital pins and 16 analog

input pins, is used as a hardware interfacing platform.

Operating voltage is maintained at 5 volts at 16 MHz

clock frequency. Out of 256KB ash memory 8KB is used

by boot loader.

3.1.2 Servo Motors

Nylon gear type Servo Actuators of dimensions 1.6” x

0.8” x 1.4”, 41gm with 5.5kg/cm variants is used at 4.8-6.0

Volts Operating voltage. For Pulse Width Modulation 3-5

Volt Peak to Peak Square Wave is required.

3.2 Mechanical Constraints

ere are multiple design considerations when designing

a Bipedal robot. e main components are Robot’s size

selection, Degrees of freedom (D.O.F) selection, Stability,

Link Design and Foot Pad design.

3.2.1 Robot Size Selection

Miniature size of the robot is elected in this project, so

a height of approx 29.5cm is decided followed by the

mounting of the controlling circuits, but the substantial

robot’s size is 26 cm excluding controlling circuits.

3.2.2 Degrees of Freedom

6 DOF.

3.2.3 Link Design

e bracket concludes of two parts. U-shaped bracket A is

employed for joints formation and Servo bracket B is used

for joint for the motors. Servomotors are hooked inside

the bracket A and the bracket B is used to disseminate

the output of the servomotor. Dimensions of Bracket A -

(51x24.6x49) mm, Bracket B - (66x37.10x24) mm.

3.2.4 Foot Pad Design

e stability of the robot is resolved by the foot pad.

Normally over sized and heavy foot pad will have more

contact area, causes more stability. But keeping in mind

the disadvantage of torque demand and liing the leg

against the gravity, an optimal sized foot pad was used.

4. Block Diagram

Figure 3 explains the basic illustration of the design.

Pro-E and Matlab is used for simulating the parameter of

the biped while Arduino IDE is used for connecting the

logic from the code to hardware level. Using the actuation

of motors liing of leg and walking is set up.

5. Preliminary Results

5.1 Pro-E Simulation

Pro-E design is a simple tool for animation design of

sequence mechanism. Following g.4 are the sequential

results for Pro-E simulation of biped.

5.2 Matlab-Simulink Simulation

Simulation has been done in MATLAB implementing the

Simulink model for PID control.

Figure 5 explains the GUI modeling of the Simulink

block of the biped for 10 seconds of motion. Simulation

for dierent speed and distance is observed and biped

parameters are computed.

Figure 3. Block diagram of the model.

Figure 4. Pro-E Animation.

Simulation and Modeling of 6-DOF Biped Mechanism

Indian Journal of Science and Technology

Vol 8 (S2) | January 2015 | www.indjst.org

188

5.3 Arduino Hardware

Depending in the result of Matlab simulation and Pro-E

design parameters for hardware implementation is

designed for motor actuation.

Arduino IDE is used for dumping code into Arduino

Mega microcontroller. Figure 6 depicts the hardware

implementation of biped robot to achieve 6-DOF.

6. Conclusion

In this project we integrated results of Matlab, Pro-E and

C coding in Arduino IDE to improve modeling capabili-

ties of biped. Howsoever, ease with which human works

are still not reected in Humanoid robots. e step time

was over 10 seconds per step in Matlab simulation and

the harmony control strategy was achieved through the

application of COG (Center Of Gravity).

7. References

1. Minetti AE, Alexander RM. A theory of metabolic costs for

bipedal gaits. J eor Biol. 1997; 186:467–76.

2. Alexander RM. A model of bipedal locomotion on

compliant legs. Philos. Trans. R Soc London Ser. B. 1992;

38:189–98.

3. Alexander. Mechanics of bipedal locomotion. Perspectives

in Experimental Biology 1. In: Davies PS, editor. Oxford:

Pergamon; 1976. p. 493–504.

4. Alexander. Simple models of human motion. Appl Mech

Rev. 1995; 48:461–9.

5. Mochon S, et al. Ballistic walking: an improved model.

Math Biosci. 1980; 52:241–60.

6. McGeer T. Passive dynamic walking. Int J Robot Res. 1990;

9:68–82.

7. Alexander RM. Optimization and gaits in the locomotion

of vertebrates. Physiol Rev. 1989; 69:1199–227.

8. Garcia M, Chatterjee A, Ruina A, Coleman M. e simplest

walking model: stability, complexity, and scaling. Asme J

Biomech Eng. 1998; 120:281–8.

9. Garcia M, et al. Eciency, speed, and scaling of passive

dynamic walking. Dyn. and Stab. Syst. 2000; 15:75–99.

Figure 5. Matlab GUI model.

Figure 6: Hardware Implementation