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Simulation and Modeling of 6-DOF Biped Mechanism


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This is an approach of designing and implementing walking postures for bipedal robot. The project presents efficient mechatronic architecture describing mechanical to software issues related to designing and execution of locomotion. The aim is to simulate and exhibit the robustness and the efficiency of the controller architecture using PD controller in MATLAB. The mission is to develop a biped to walk using Arduino Mega 2560. PRO-E simulation is done to calculate motion parameters. Trajectory planning is accomplished using Matlab.
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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;
mechatronic architecture describing mechanical to software issues related to designing and execution of locomotion.
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 ecient
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 subjects 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 dicul-
ties in it. Among the two conicting 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 |
and I, robot (Alex Proyas, 2004). Minetti and Alexander1
recommended a rened 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 aorded by a hip torque or an impulse at toe-o7.
2. Mathematical Modeling
2.1 Forward Kinematics
In Forward kinematics the position and orientation of
the end‐eector can be determined by conguring 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
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 |
3. System Architecture
3.1 Specication
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 liing 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 liing 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 dierent 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 |
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 reected 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;
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;
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. Eciency, speed, and scaling of passive
dynamic walking. Dyn. and Stab. Syst. 2000; 15:75–99.
Figure 5. Matlab GUI model.
Figure 6: Hardware Implementation
... The mission is to develop a biped to walk using Arduino Mega 2560.PRO-E simulation is done to calculate motion parameters. Trajectory planning is accomplished using MATLAB [4]. It was previously believed that, among primates, only humans run bipedal. ...
Full-text available
We address performance limits and dynamic behaviours of the two dimensional passive-dynamic bipedal walking mechanisms of Tad McGeer. The results highlight the role of heelstrike in determining the mechanical efficiency of gait, and point to ways of improving efficiency. We analyse several kneed and straight-legged walker designs, with round feet and and point-feet. We present some necessary conditions on the walker mass distribution to achieve perfectly efficient (zero-slope-capable) walking for both kneed and straight-legged models. Our numerical investigations indicate, consistent with a previous study of a simpler model, that such walkers have two distinct gaits at arbitrarily small ground-slopes, of which the longer-step gait is stable at small slopes. Energy dissipation can be dominated by a term proportional to (speed) 2 from tangential foot velocity at heelstrike and from kneestrike, or a term proportional to (speed) 4 from normal foot collisions at heelstrike, depending on the gait, ground-slope, and walker design. For all zeroslope capable straight-legged walkers, the long-step gaits have negligible tangential foot velocity at heelstrike and are hence especially fast at low power. Some apparently chaotic walking motions are numerically demonstrated for a kneed walker.
Full-text available
We demonstrate that an irreducibly simple, uncontrolled, two-dimensional, two-link model, vaguely resembling human legs, can walk down a shallow slope, powered only by gravity. This model is the simplest special case of the passive-dynamic models pioneered by McGeer (1990a). It has two rigid massless legs hinged at the hip, a point-mass at the hip, and infinitesimal point-masses at the feet. The feet have plastic (no-slip, no-bounce) collisions with the slope surface, except during forward swinging, when geometric interference (foot scuffing) is ignored. After nondimensionalizing the governing equations, the model has only one free parameter, the ramp slope gamma. This model shows stable walking modes similar to more elaborate models, but allows some use of analytic methods to study its dynamics. The analytic calculations find initial conditions and stability estimates for period-one gait limit cycles. The model exhibits two period-one gait cycles, one of which is stable when 0 < gamma < 0.015 rad. With increasing gamma, stable cycles of higher periods appear, and the walking-like motions apparently become chaotic through a sequence of period doublings. Scaling laws for the model predict that walking speed is proportional to stance angle, stance angle is proportional to gamma 1/3, and that the gravitational power used is proportional to v4 where v is the velocity along the slope.
A mathematical model of the swing phase of walking is presented. The lower extremities are represented by links, and the rest of the body by a point mass at the hip joint. It is assumed that no muscular moments are provided to any of the joints of the extremities during the swing phase. The body then moves under the action of gravity alone. The model analyzed here is an improvement of a previous model by the same authors. The range of possible times of swing for each step length is computed for the model, and the results are compared with published experimental data. Typical histograms of forces applied to the ground and angles of the limbs against time are also given. The computed forces and angles have the same general time course as those found experimentally in normal walking, with the exception of the vertical force. The reasons responsible for this are discussed. The comparison of the results of the model with normal walking also suggests the possible effects that the absent determinants have on gait.
There exists a class of two-legged machines for which walking is a natural dynamic mode. Once started on a shallow slope, a machine of this class will settle into a steady gait quite comparable to human walking, without active control or en ergy input. Interpretation and analysis of the physics are straightforward; the walking cycle, its stability, and its sensi tivity to parameter variations are easily calculated. Experi ments with a test machine verify that the passive walking effect can be readily exploited in practice. The dynamics are most clearly demonstrated by a machine powered only by gravity, but they can be combined easily with active energy input to produce efficient and dextrous walking over a broad range of terrain.
Simple mathematical models capable of walking or running are used to compare the merits of bipedal gaits. Stride length, duty factor (the fraction of the stride, for which the foot is on the ground) and the pattern of force on the ground are varied, and the optimum gait is deemed to be the one that minimizes the positive work that the muscles must perform, per unit distance travelled. Even the simplest model, whose legs have neither mass nor elastic compliance, predicts the changes of duty factor and force pattern that people make as they increase their speed of walking. It predicts a sudden change to running at a critical speed, but this is much faster than the speed at which people make the change. When elastic compliance is incorporated in the model, unnaturally fast walking becomes uncompetitive. However, a slow run with very brief foot contact becomes the optimum gait at low speeds, at which people would walk, unless severe energy dissipation occurs in the compliance. A model whose legs have mass as well as elastic compliance predicts well the relationship between speed and stride length in human walking.
A simple model predicts the energy cost of bipedal locomotion for given speed, stride length, duty factor and shape factor. (The duty factor is the fraction of stride duration, for which a foot is on the ground, and the shape factor describes the pattern of force exerted on the ground). The parameters are varied to find the gait that minimizes metabolic energy cost, for each speed. A previous model by Alexander calculated the work that muscles have to do, but the metabolic cost (calculated in this paper) is more likely to be the principal criterion for gait selection. This model gives good predictions of human stride lengths, and of the speed at which we break into a run. It predicts lower duty factors and higher shape factors than are normally used, but the relationships between these gait parameters and speed parallel the empirical relationships.
Simple models of human motion
Alexander. Simple models of human motion. Appl Mech Rev. 1995; 48:461-9.
Mechanics of bipedal locomotion
Alexander. Mechanics of bipedal locomotion. Perspectives in Experimental Biology 1. In: Davies PS, editor. Oxford: Pergamon; 1976. p. 493-504.