Page 43 - IJEEE-2023-Vol19-ISSUE-1

Mohsin, Aldair & Al-Hussaibi | 39

features. This environment has been used effectively in other This block provides a solid element to the related frame which
applications such as Quadruped Robot [17], inverted pendulum is connected to the model using reference frame (R). All of the
system [18], Stewart Platform in [19], Rotary Inverted above layers are attached together using four rods of the solid
Pendulum [20], and 3RPS Robotic Platform Motion [21]. cylinder block with assumed dimensions of (25 cm length * 0.5
The main contribution of this work is to design a dynamical radius). However, a rigid transform block is used to connect
model for TWSBR by using the MATLAB Simscape one solid block to another because it remains fixed as one solid
Multibody package to simulate and visualize the system rigid during motion simulation. Through using this block, the
without the need for mathematical equations. This new next port (F) element is translated relative to the base port (B).
environment provides a 3D visualization motion of the Figure 1 illustrates the connections between the different
real-time behavior of constructed system model. Moreover, it mechanical parts of the robot chassis subsystem. The wheels on
allows studying the effect of road inclination on the the self-balancing platform are constructed of cylinder blocks
performance and stability regions, and recommendations for with assumed dimensions of (3.25cm radius * 1.25cm length).
identifying the stability region for TWSBR design. In A shaft is linked to the two wheels as shown in Fig.2. Each
particular, this paper includes controlling mechanical stability wheel is translated to one end of the shaft by the rigid transform
issues. The TWSBR motion controller system is designed using before being collected in the robot cart subsystem. Also, a rigid
PID and LQR methods. The auto-tuning method is used to find transform is used to connect the robot cart to the world frame
the best values for the controller parameters. Also, changing the while the rotation transform is used to connect the chassis and
object-carrying weights on robot layers under road disturbance the cart. To accurately position the shaft under the body, it
effects is utilized to demonstrate the controller's performance configured a rotation transform of 90 degrees around the !-axis
and robustness. and 180 degrees around the &-axis. Considering the rotation is
The rest of this paper is organized as follows. In Section II, the set to the ! & ' sequence. Also, the rotation joint is configured
system model is detailed. Section III explains how the control to turn the robot to face the positive '-direction.
design is carried out. Simulation results and discussion are A revolute joint is used to connect the chassis and cart which
shown in Section IV. Finally, Section V presents the paper's gives the robot rotational motion and allows the robot chassis to
conclusion. swing like a pendulum while a prismatic joint is used to connect
the whole construction to the world frame which it gives
II. SYSTEM DESIGN AND MODELING translational motion to the robot and allows it to move back and
forth. Figure 3 visualizes a 3D proposed structure of TWSBR in
A. System Design Simulink Mechanics Explorer.

The idea behind building this type of robot comes from the
inverted pendulum concept as referenced theory. The pendulum
rod is replaced with a 3-layers structure while the cart base is
replaced with two wheels. A TWSBR structure is simulated. It
consists of an assemblage of layers that are mounted on wheels
and moving along a solid body. The system goal is to keep the
layered structure (robot chassis) in upright with a zero
inclination angle. To achieve this target, an external horizontal
control force is used to drive the robot along the !-axis as the
system input. The outputs of the system are the robot position
(!) and inclination angle (%).

B. Simscape Multibody Model Fig.1: Modeling of robot chassis subsystem.
Fig.2: Modeling of robot cart subsystem.
Simscape Multibody (SimMechanics) is a modeling tool that is
used to simulate 3D robotics, vehicle suspensions, and
construction equipment. Simscape blocks can be used to
represent bodies, joints, constraints, force components, and
sensors for proposed system plant [22]. Therefore, simscape
Multibody can solve mathematical motion equations and test
the control system performance. Simulink can be used to design
a control system that is connected to the Simscape modelling
environment [23].
Simscape Multibody library configures a 3D model of TWSBR
based on the design parameters and constraints. The upper body
of the robot is built as a pendulum compared with an inverted
pendulum structure. It consists of three rectangular layers of a
solid brick block (top, middle, and bottom) with assumed
dimensions of (18cm length * 8cm width * 0.3cm thickness).