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In this figure, base is under effects of two holonomic constraint.
Although, Gibbs-Appell method no needs for considering constraint
equations, however, these two equation are:
In these equations, and Are velocity at “A”in …and …directions. In
Figure 6 these equation has been shown. According to this Figure,
it is concluded that the constraint’s equations are completely satisfied
during simulation time.
Finally, in order to declare the efficiency of the proposed recursive
algorithm, the time required for extracting the equations of motion and
solving them for the system should be presented. Required time is 1.5s
with “Processor E7500 @ 3GHz Core TM Intel Duo 2”. This period
received by tic-toc function in MATLAB software.
3- CONCLUSION
In this paper, a recursive method based on formulation G-A to derive the
inverse dynamical equations of a mobile robot with rotational-sliding
joints are studied. Also, this method can be used for the design of the
control system and simulation of the motion equations. The main
advantage of this method is that the volume of computation is
significantly reduced, It leads to less time to study on the dynamic
behavior of model. For future works this method could be used for
movement of the robot with elastic links and prismatic joints.
4- REFERENCES
[1] Holmberg R, Khatib O (2000) Development and control of a holonomic
mobile robot for mobile manipulation tasks. International Journal of Robotics
Research 19(11): 1066–1074.
[2] Tarn TJ, Yang SP (1997) Modeling and control for underwater robotic
manipulators-An example. IEEE Int. Conf. Robotics and Automation,
Albuquerque, New Mexico: 2166–2171.
[3]Dubowsky S, Vance EE (1989) Planning mobile manipulator motions
considering vehicle dynamic stability constraints. IEEE Int. Conf. Robotics and
Automation: 1271–1276.
[4] Liu K, Lewis FL (1990) Decentralized continuous robust controller for
mobile robots. IEEE Int. Conf. Robotics and Automation: 1822–1827.
[5]Wiens GJ (1989) Effects of dynamic coupling in mobile robotic systems.
Proc. World Conf on Robot Res, Detroit, MI, SME: 43–57.
[6]Meghdari A, Durali M, Naderi D (2000) Investigating dynamic interaction
between the one D.O.F manipulator and vehicle of a mobile manipulator.
Journal of Intelligent and Robotic Systems: Theory and Applications 28(3):
[7] Yamamoto Y, Yun X (1996) Effect of the dynamic interaction on
coordinated control of mobile manipulators. IEEE Trans Robotics Automation
12(5): 816–824.
[8] Chen MW, Zalzala AMS (1997) Dynamic modeling and genetic-base
trajectory generation fornonholonomic mobile manipulators. Control
Engineering Practice 5(1): 39–48.
[9]Colbaugh R (1998) Adaptive stabilization of mobile manipulators. Journal
of Robotic Systems 15(9): 511-523.
[10] A. Reza, A.A Khayyat, K.G. Osgouie, “Neural networks control of
autonomous underwater vehicle”,in Int. Conference on Mechanical and
Electronics Engineering (ICMEE 2010), Vol. 2, pp.117-121,2010
[11] Jouybari, B.R., Osgouie, K. G., & Meghdari, A (2016). Optimization of
Kinematic redundancy and workspace analysis of a dual-arm cam-lock robot.
Robotica, 34(1), 23,42.
[8] had studied the nonholonomic constraints arising from the basic of
nature. In this research, the equations governing the system were extracted
using Newton-Euler formulation. however, all the nonholonomic constraints
governing this system in their model are not presented. Some research such
as Colbaugh [9] considered this constraint with dynamic equations; however
others, like Yamamoto et al used a kind of reduction of coordinates after
considering all the non-holonomic constraints governing the system. In their
work, the constraint equations were considered using the Lagrange
Multipliers in the motion equations of the system. Also, Amin et.al [10]
investigated the high nonlinearity of the gilder dynamics and underwater
disturbances to be one of the main reasons that make an moving robot
difficult to control. Also Jouybari et.al. [11] studied on using the Pontryagin’s
Minimum Principle by considering the Dual-Arm Cam-Lock robot, an
adaptive cooperative system capable of acting redundantly, and obtained
the best joint space trajectory based on optimal control use.
This paper deals with the extraction of n-link manipulator with rotating-
sliding joints on a movable base and its terms based on the recursive Gibbs-
Appell equations. Therefore, the structure of the full paper will be as follows;
First of all, the kinematics of the manipulator, non-holonomic base
kinematics and the kinematics of the right and left wheels will be explained.
The second part has three sections, examines the inverse system dynamic
equations in closed form. The recursive form of these equations for the
automatic and systematic extraction of inverse system dynamics equations in
the third section has been investigated. A numerical simulation has been
presented to demonstrate the capability of this method in extracting the
equations of moving robots with high degrees of freedom in the forth
section. Finally in fifth section, the conclusions and advantages of this
method have been stated.
For the presentation on poster, only numerical simulation (by MATLAB) and
conclusion has been presented to demonstrate the capability of this method
in extracting the equations about moving of robots with high degrees of
freedom.
Figure 1: Robot with two revolute-prismatic joints on a
movable base
2- NUMERICAL SIMULATION
The simulation results are presented for a manipulator with two revolute-
prismatic joints mounted on a movable base. Figure 1 illustrates a Typical
robot with this properties. Also, all the parameters required for simulation
are presented in Table No.1, in which “I”is the unit matrix. The force and
torque applied to the joints are as follows:
Also, the initial conditions are assumed to be the following:
In Figures 2 to 5, manipulator response time has been shown. Equations are
solved by using the command “ODE45”in MATLAB software.
Figure 2: Angular Position of the Arms
Figure 3: Angular Velocity of the Arms
PARAMETER
VALUE
UNIT
According to the dynamic simulation results, a constraint to the link movements
has been considered When the link reaches the beginning or the end of its
length, it moves in the opposite direction.
Figure 4: Longitudinal Position of the Links
Figure 4: Longitudinal Velocity of the Links
In figures 5,6 response of the moving base is shown:
Figure 5: Movement in XY axis
Figure 6: Robot Route in XY axis
Experimental Parameter Identification for Moving Base Nonholonomic Robot Consisting Primary Joints
Kambiz Ghaemi Osgouie, Assistant Professor – University of Tehran
Kambiz_osgouie@ut.ac.ir
Alireza Ghanbarpour, M.Sc. of Mechatronics – University of Tehran
1- INTRODUCTION
Most research on movable manipulators are limited to robots with only
rotating joints. The dynamic equations of robots with rotational and
prismatic movement is a very important subject with many applications. The
combination of this system with a movable base will bring capability of
operating in a wider area than a fixed base manipulator. The moving ability
added to the agility of the manipulator, is requirement of many application
such as; space explores, rescue operations, operation in hazardous locations,
agriculture, and so on.
Each mobile base with two independent wheels has three dynamic
constrains, two, nonholonomic and the other is holonomic. In this system,
the base should move along its axis of symmetry and not be able to move in
any directions. This un-integral kinematic constraint is known as non-
holonomic constraint. On the other hand, any mobile base with three
degrees of freedom is known as a holonomic system [1]. Given the
complexity of modeling in nonholonomic system, most of the previous
researchers worked on basic-holonomic motion [2, 3]; however, in order to
enjoy advantages of movable manipulators, a complete image of dynamic
simulation of this categories of robots is required. Considering the
interaction between the manipulator and the movable base is important in
the dynamic modeling of these systems, which had been studied by Liu and
Lewis [4], Wiens [5], Meghdari et al [6] and Yamamoto et al [7]. Chen, Zalzala