Bacterial foraging-optimized PID control of a two-wheeled machine with a two-directional handling mechanism

Robotics and Biomimetics, Apr 2017

This paper presents the performance of utilizing a bacterial foraging optimization algorithm on a PID control scheme for controlling a five DOF two-wheeled robotic machine with two-directional handling mechanism. The system under investigation provides solutions for industrial robotic applications that require a limited-space working environment. The system nonlinear mathematical model, derived using Lagrangian modeling approach, is simulated in MATLAB/Simulink® environment. Bacterial foraging-optimized PID control with decoupled nature is designed and implemented. Various working scenarios with multiple initial conditions are used to test the robustness and the system performance. Simulation results revealed the effectiveness of the bacterial foraging-optimized PID control method in improving the system performance compared to the PID control scheme.

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Bacterial foraging-optimized PID control of a two-wheeled machine with a two-directional handling mechanism

Goher and Fadlallah Robot. Biomim. Bacterial foraging-optimized PID control of?a two-wheeled machine with?a two-directional handling mechanism K. M. Goher 0 S. O. Fadlallah 1 0 Department of Informatics and Enabling Technologies, Lincoln University , Lincoln , New Zealand 1 Mechanical Engineering Department, Auckland University of Technology , Auckland , New Zealand This paper presents the performance of utilizing a bacterial foraging optimization algorithm on a PID control scheme for controlling a five DOF two-wheeled robotic machine with two-directional handling mechanism. The system under investigation provides solutions for industrial robotic applications that require a limited-space working environment. The system nonlinear mathematical model, derived using Lagrangian modeling approach, is simulated in MATLAB/ Simulink? environment. Bacterial foraging-optimized PID control with decoupled nature is designed and implemented. Various working scenarios with multiple initial conditions are used to test the robustness and the system performance. Simulation results revealed the effectiveness of the bacterial foraging-optimized PID control method in improving the system performance compared to the PID control scheme. Two-wheeled machine; Inverted pendulum; Two-directional handling; Lagrangian modeling; PID; BFO - body (IB) was developed by Goher and Tokhi [3]. For providing multiple lifting levels for a carried payload, the developed machine is equipped with a linear actuator. The previously mentioned WRM was later improved by Almeshal et?al. [4]. Increasing the machine?s flexibility and workspace led to a novel five DOFs two-wheeled IP with an extended rod. its application to optimization, it helps in reducing the behavior of stagnation (i.e., being trapped in a premature solution point or local optima) often seen in such parallel search algorithms. Table? 1 represents the main parameters of BFO algorithm. Table 1 BFO algorithm parameters [12] Description Overview and?contribution This paper presents a bacterial foraging technique for determining the optimal parameters of a PID controller to control the stability of a five degrees-of-freedom (DOF) two-wheeled machine (TWM) developed by Goher [22]. The novel 5-DOF TWM provides payload handling in two mutually perpendicular directions while attached to the IB. Compared to existing TWRMs, this design increases both workspace and flexibility of two-wheeled machines and allows them to be employed in service and industrial robotic applications including objects assembly and material handling. Bacterial foraging algorithm?s potential, as illustrated in the literature, was a source of encouragement to examine the proposed optimization technique on the novel 5 DOF two-wheeled machine?s controller in order to improve the system?s stability performance. Paper organization The rest of the paper is organized as follows: ?Bacterial foraging optimization (BFO) algorithm? section presents an overview of the BFO algorithm and a rationale about the implementation on various nonlinear dynamic systems, the system description machine is presented in ?TWRM system description,? and ?System modeling? sections present the previously developed mathematical model using Lagrangian approach. ?Control system design? section describes the control system design and the implementation of bacterial foraging optimization technique including various courses of motion and testing of the robustness of the control approach. At last, the main conclusions of the paper are presented in ?Conclusions? section. Methods TWRM system description Figure? 1 illustrates the schematics diagram of the twowheeled robotic machine (TWRM). The proposed system consists of a chassis with center of gravity at point P1 and the mass of the linear actuators with center of gravity at point P2. The coordinates of P1 and P2 will change as long as the robot maneuvers away from its initial position along the X axis. The two motors attached to each wheel are in charge of providing the necessary torque, ?R and ?L, for controlling the TWRM. For enabling the control strategy to maintain the two-wheeled machine?s position at the upright position continuously, the system is equipped with both accelerometer and gyroscope sensors that provide multiple state variables information at any given time. The system design provides compactness with offering proper rooms for system electronics and accessories. Other targeted features include a lightweight structure without affecting the robot stiffness and Fig. 1 System schematic diagrams Fig. 2 TWRM courses of motion Associated DOFs Linear actuator I, F1 Linear actuator II, F2 Moving and picking IB extension Extension: end effector Reverse: end effector IB contraction Placing the object counts on the selected subtask (i.e., picking, placing, both tasks). As a main part of the control algorithms, switching mechanisms are designed to define the period of engagement of each individual actuator in service. System modeling Among the diverse methods of deriving the equations of motion, and due to the fact that it is a powerful approach, Lagrangian modeling approach is employed to model the TWRM. Based on the system schematic diagrams illustrated earlier, the vehicle?s mathematical model is derived by relating the system?s kinematics to the torques/forces applied (details of the model derivation can be found in the work of Goher [22]). The system?s mathematical model is presented as five nonlinear-coupled differential equations as follows: For the vertical linear link displacement (h1): 1 2 m2 2g cos ? ? 2h1??2 ? 4h? 2?? ? 2h2?? + 2h? 1 For the horizontal link displacement (h2): 1 2 m2 2g sin ? + 2h2??2 ? 4h? 1?? ? 2h1?? ? 2h? 2 1 1 2 ??R + 2 ??L ? l??2 sin ? + l?? cos ? ? + 2mw??R + 2Jw ?R2 = ?R ? ?w R + ?? J1 + J2 + m1l2 + m2h22 + m2h1 2 Table 3 System simulation parameters Parameter Description Mass of the chassis Mass of the linear actuators Mass of wheel Gravitational acceleration Distance of chassis?s center of mass for wheel axle Wheel radius Rotation inertia of chassis Rotation inertia of moving mass Rotation inertia of a wheel Coefficient of friction between chassis and wheel Coefficient of friction between wheel 0 and ground Coefficient of friction of vertical linear 0.3 actuator Coefficient of friction of horizontal linear 0.3 actuator BFO?optimized PID control design In this part, bacterial foraging optimization technique is applied on the system in order to optimize the PID controller gains employed in a previous research study [22] by maintaining the system in the upright position and to counteract the disturbances occurring in different motion scenarios. where e(t) is the error signal in time domain. Results and?Discussions Implementation of?BFO?PID algorithm The behavior of the robotic machine was observed for the tilt angle of the entire vehicle, angular displacements MSE = ITAE = (e(t))2dt, t|e(t)|dt, IAE = |e(t)|dt, ISE = e(t)2dt, ITSE = te(t)2dt, Fig. 3 TWRM?s BFO-optimized PID control scheme of the two wheels, and linear displacements of the linear actuators using different motion scenarios. Payload free motion (h1?=?h2?=?0) Figure? 5a, b demonstrates the simulation results of the system performance and inputs control signals. The Fig. 4 Simulink? model of the BFO-optimized PID controller 0.9650 0.7800 1.8720 0.8080 1.0140 0.2150 0.2300 0.1970 0.2480 0.2230 0.3950 0.4400 0.3540 0.4610 0.4110 ITAE ITSE Performance index Percent overshoot Settling time (s) Rise time (s) Peak time (s) Payload vertical movement only In addition, the system stability was examined for each BFO optimization criterion against the vertical linear motion of its center of mass. Considering the following initial conditions: ? = ? 5?, h1 = 0.28 m and neglecting the effect of the horizontal linear actuators h2, Fig.?6 demonstrates outputs and inputs simulation of the system in the case where the payload is kept fixed for a period of 12? s from the start of the simulation and then activated to move in a vertical direction along the IB for a distance of 10?cm before settling again at a height of around 38?cm from the chassis of the vehicle. It is clear, since no disturbance occurred in the stabilization condition of the IB, that the control scheme was robust and maintained the system?s stability against the motion of h1. Out of the five methods, the BFO optimized by IAE performed better than the other methods. criterion, the system stability was affected by the activation of the horizontal actuator and the TWRM keeps moving instead of maintaining its position. On the other hand, the remaining methods produce better performance and good robust against the movement of the horizontal actuator. Trajectory of?a 1?m straight?line motion The system stability was examined during moving the TWRM in a straight line for 1? m after balancing the robot in the upside position, and the simulation results are shown in Fig.? 9. Referring to Fig.? 9a, the control scheme, including the five tested criterions, was capable to counter the occurred disturbances caused by the wheels? motors? activation at the beginning (8?s) and the end (18?s) of the straight-line motion. As can be observed in Fig.?9b, the maximum control effort spent for maneuvering the system in a 1-m straight-line trajectory, compared to the other criterions, was noted for the ITSE method, around 1.8?N. Control system robustness Moreover, the system stability was examined against the effect of disturbance forces illustrated in Fig.? 10a and the simulation results are shown in Fig.? 10b, c. As it is shown that disturbance force affects the system, but the controller reacts against this force to stabilize the system. However, the controller resulted from MSE shows that the displacement of the system is effected with slight change, while the other optimized controllers show better performance. Comparison between?implementation of?PID and?BFO?optimized PID The boundary limits of the controller gain parameters for each loop that were applied in MATLAB/Simulink environment were obtained by trial and error. In this section, the authors carry out a comparison of the system response based on the implementation of two approaches. The control gain parameters employed in each control loop for the control schemes in order to achieve a satisfactory system performance are listed in Table?5. For the following cases, payload free movement, payload vertical movement only, payload horizontal movement only, simultaneous horizontal and vertical motion, and 1-m straight-line vehicle motion, Figs.?11, 12, 13, 14, and 15 demonstrate the output results of the simulated TWRM model and the applied control effort. It is clear, from the previous figures, that the optimized controller by BFO provides better performance for the system and minimizes the applied force demanded for the TWRM stabilization process. Observing the payload free movement (h1? =? h2? =? 0) scenario, as an example of how the BFO-optimized PID controller performance is better way than the PID, Table? 6 illustrates a system performance comparison between the previously mentioned controllers in terms of overshoots, settling time, peak time, and rise time. Starting with system overshoot, the BFO-optimized PID control scheme provides better overshoot value (27.9%), which is much less than the PID-recorded overshoot value by almost 42%. Moving to settling time, it is observable that by implementing the PID control strategy the system takes around 2.3? s to settle, which is greater than the BFO-optimized PID control method?s settling time (0.78? s). Therefore, the Table 5 Gain values for?different control schemes Output parameter Gain parameters PID?+?switching BFO?+?switching Lower boundary Calculated gain Upper boundary )m0.3 ( 1 h Table 6 Comparison between? the system?s performance using PID and?BFO 2.2870 0.7800 0.5710 0.4400 0.2790 0.2300 where the optimum controller values are resultant from the IAE criterion. in terms of performance, robustness, and instability minimization. The upper and lower boundaries, shown in Table?5, are associated with the BFO-optimized control scheme with switching mechanism. 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K. M. Goher, S. O. Fadlallah. Bacterial foraging-optimized PID control of a two-wheeled machine with a two-directional handling mechanism, Robotics and Biomimetics, 2017, 1, DOI: 10.1186/s40638-017-0057-3