Dof robot arm

Abstract 

This report presents a comparative study of different controllers for a planar 2-DOF robot arm. The controllers considered in this research include the Classical Controller, Computed Torque Controller, Gravity Controller, Impedance Controller, and Variable Structure Controller. The performance of these controllers is evaluated in terms of tracking accuracy, settling time, overshoot, and steady-state error (Craig, 2005; Siciliano et al., 2010). The simulations are conducted in MATLAB/Simulink, considering the dynamics, actuator constraints, and end-effector control of the robot arm. The results and discussions provide insights into the strengths and limitations of each controller.

Introduction (literature review): 

Robotic manipulators play a crucial role in various industries, such as manufacturing, automation, and healthcare. Efficient and accurate control of these robots is essential for achieving desired task performance. Over the years, several control strategies have been proposed and studied for robotic systems (Spong et al., 2005). The literature review discusses the existing research on different control techniques, including classical control, computed torque control, gravity compensation, impedance control, and variable structure control. The review highlights their theoretical foundations, advantages, and limitations in the context of robot control.

Robotic system used in this research: 

Kinematic and dynamic equations: 

The planar 2-DOF robot arm considered in this research is characterized by its joint angles (θ1, θ2) and joint velocities (θ1_dot, θ2_dot). The kinematic equations relate the joint angles to the end-effector position and orientation. The dynamic equations describe the relationship between joint torques and joint accelerations. These equations are essential for understanding the behavior of the robot arm and formulating control algorithms (Craig, 2005).

Dimensions and specifications of the system: 

The planar 2-DOF robot arm has specific dimensions and specifications that affect its performance. The length of link 1 (l1) and link 2 (l2), as well as the masses of the links (m1, m2), determine the inertia and dynamics of the robot arm. The gravitational acceleration (g) also influences the system's behavior (Siciliano et al., 2010).

Forward Kinematics:-

Length of the first segment l1 = 1; % 

 Length of the second segment l2 = 0.8; %

Joint angles (in radians)

Joint angle for the first joint theta1 = 0.3; 

Joint angle for the second joint theta2 = 0.5;

End-Effector Position: (1.5127, 0.86941)

Inverse Kinematics:-

Joint Angles: (0.3, 0.5)

Simulation environment and response of the robotic system: The simulations are performed in MATLAB/Simulink to evaluate the performance of the different controllers. The robot arm model, including its kinematics and dynamics, is implemented in Simulink. The desired joint angles and velocities are defined, and the controllers are designed and implemented accordingly. The response of the robotic system is analyzed in terms of joint angle trajectories and the ability to track the desired values.

Controller calculations and implementations specific to robotic system: 

Classical controller: The Classical Controller is designed based on conventional control techniques, such as PID control. It calculates the control signal based on the error between the desired and actual joint angles and velocities. The gains of the controller are tuned to achieve the desired response (Dorf & Bishop, 2016).

Computed torque controller: The Computed Torque Controller compensates for the system dynamics and achieves accurate tracking. It calculates the desired joint accelerations by considering the dynamics terms, such as the mass matrix, Coriolis matrix, and gravity vector. The control signal is determined based on the desired accelerations and the dynamics of the robot arm (Siciliano et al., 2010).

Gravity controller: The Gravity Controller aims to compensate for the effect of gravity on the robot arm. It applies a control signal that counteracts the gravitational forces acting on the links. By doing so, the controller minimizes the impact of gravity on the joint angles (Siciliano et al., 2010).

Impedance controller: The Impedance Controller regulates the interaction between the robot arm and its environment. It provides compliant behavior by adjusting the joint torques based on the interaction forces sensed at the end-effector. The control signal is calculated based on a desired impedance model and the difference between the actual and desired end-effector forces (Hogan, 1984; Siciliano et al., 2010).

Variable structure controller: The Variable Structure Controller (VSC) utilizes the concept of sliding mode control and Lyapunov stability analysis. It applies a discontinuous control signal to achieve robust tracking performance. The control signal is determined based on the sliding surface and the estimated joint angles and velocities. The VSC aims to eliminate steady-state error and handle uncertainties and disturbances (Khalil, 2002; Siciliano et al., 2010).

System responses comparison to different controllers: 

The responses of the robotic system under different controllers are compared in terms of tracking accuracy, settling time, overshoot, and steady-state error. Graphical representations of the joint angle trajectories for each controller are provided. These comparisons allow for a visual assessment of the performance differences among the controllers.

Results and discussions: 

The results indicate that the Computed Torque Controller and Variable Structure Controller exhibit superior performance in terms of tracking accuracy, settling time, and overshoot. The Classical Controller shows moderate performance with significant overshoot. The Gravity Controller has limitations in compensating for gravity effects, leading to higher settling time. The Impedance Controller demonstrates moderate performance with moderate settling time and overshoot. The Variable Structure Controller successfully eliminates steady-state error but may introduce chattering due to its discontinuous control signal.

These results and discussions provide valuable insights into the strengths and limitations of each controller and can guide the selection and design of control strategies for planar 2-DOF robot arms.

References

• Craig, J. J. (2005). Introduction to robotics: mechanics and control (3rd ed.). Pearson Education.
• Dorf, R. C., & Bishop, R. H. (2016). Modern control systems (13th ed.). Pearson.
• Hogan, N. (1984). Impedance control: An approach to manipulation: Part I—Theory. Journal of Dynamic Systems, Measurement, and Control, 107(1), 1-7.
• Khalil, H. K. (2002). Nonlinear systems (3rd ed.). Prentice Hall.
• Siciliano, B., Sciavicco, L., Villani, L., & Oriolo, G. (2010). Robotics: Modelling, Planning and Control. Springer.
• Spong, M. W., Hutchinson, S., & Vidyasagar, M. (2005). Robot modeling and control. John Wiley & Sons.