Modelling, Simulation And Balance Control Of A Two-Wheeled Robotic Machine With Static Variation In Load Position

This paper focuses on the design and implementation of a control algorithm for balancing of a two-wheeled robotic machine (TWRM). The machine comprises a rod on an axle incorporating two wheels. The balancing of the rod in the upright position is achieved using a proportional-derivative (PD) controller. The NewtonEuler dynamic formulation is used to develop a mathematical model of the system. Matlab Simulink is used as a simulation environment. The intermediate body (IB) is considered to be in the upright position. An external disturbance force is applied at different locations of the IB in order to test the robustness of the developed controller. A payload is considered, and this is attached at different locations along the rod. Investigations are carried out on the effect of changing the duration and location of disturbance force, and changing the location of the payload on the system in the balancing mode. Two PD controllers are developed, one for the angular position of the rod and one for the cart linear displacement. Simulation results are presented assessing the performances of the controllers. INTRODUCTION An inverted pendulum system is an under-actuated mechanical system and inherently open loop unstable with highly non-linear dynamics. It is thus a perfect testbed for the design of a wide range of classical and contemporary control techniques. It has wide ranging applications from robotics to space rocket guidance systems. The concept of balancing a robot is based on the inverted pendulum model. This model has been widely used by researches worldwide in the design and control of wheeled legged robots, etc. (Formal and Martynenko 2005). The inverted pendulum problem is common in the field of control engineering. The uniqueness and wide application of technology derived from this unstable system has drawn interest of many researches and robotics enthusiasts around the world. In recent years, researchers have applied the idea of a mobile inverted pendulum model to various problems, such as designing walking gaits for humanoid robots, robotic wheelchairs and personal transport systems (Kim, et al. 2005). The type of intelligent robot proposed here is a mobile robot with a two wheeled inverted pendulum. This design was chosen because its mechanism has an inherently clumsy motion for stabilizing the robot’s body posture. The robot has a body with two wheels for moving in a plane and a head similar to a human head for controlling the motion. Two independent driving wheels are used for position control and for fast motion in a plane without casters. TWO-WHEELED INVERTED PENDULUM ROBOT Several kinds of wheels can be attached to the wheeled mobile robot, but they fall into one of two categories: driving wheels and auxiliary wheels. The driving wheels are rotated to permit the robot to move when torque is applied to the axles. The auxiliary wheels merely ease the movement of the robot and enable its body to be suspended when no torque is applied to the axles. In most wheeled mobile robots at least one wheel is an auxiliary wheel. For a two-wheeled mobile robot, one can ask what would happen if the auxiliary wheels were removed altogether instead of being replaced with something different or instead of improving the performance of the wheels. By removing the auxiliary wheels, the number of wheels attached on the robot would be reduced. Moreover, the mechanical characteristics of the robot would be completely altered because no elements could suspend and balance the robot’s body except for the driving wheels. That is, the robot would have to move and balance its body with only two driving wheels (Kim, et al. 2005). The mechanical structure of a robot with only two driving wheels is similar to an inverted pendulum (D’Andrea and Earl 2005). MATHEMATICAL MODELLING The dynamic characterisation of the robot is described in this section by introducing the governing main equations describing the mathematical model of the two-wheeled robotic machine (TWRM). The model is derived based on the Newton-Euler equations of motion. The dynamic model of the whole system consists of two Proceedings 22nd European Conference on Modelling and Simulation ©ECMS Loucas S. Louca, Yiorgos Chrysanthou, Zuzana Oplatkova, Khalid Al-Begain (Editors) ISBN: 978-0-9553018-5-8 / ISBN: 978-0-9553018-6-5 (CD) separate sub-models, namely: the non-linear model of the inverted pendulum, and a linear model of the permanent magnet (PM) direct current (DC) motor activating the cart. Linear model of the DC motor The robot is powered by two DC motors, Figure 1, where a V represents the applied voltage, i the armature current. The mathematical model of the DC motor is derived and then used in the dynamic model of the robot to provide a relationship between the input voltage to the DC motors and the control signal needed to stabilise the robot. Figure 1 Schematic diagram of a DC motor Using Figure 1, the following two fundamental equations of motion of the DC motor can be written as: L V L k i L R dt di a e + + = ω (1)