PUMA 560: Control of a 6-DOF Robot Arm

This is a project for controlling a fully-actuated robot arm with six degrees of freedom (DOF). The manipulator is a PUMA 560 with six rotoidal joints. The manipulator's description and Denavit-Hartenberg table are based on [1], and the regression matrix was computed using [2].

Prerequisites • Use • Presentation • Sample Images

Overview

The project includes several control aspects, including inverse kinematic control, dynamic control, and adaptive control. The following is a list of the simulations and techniques included in the project:

Inverse Kinematic Control

• Gradient descent method for posture control
• Levenberg-Marquardt method for posture control and circular trajectory tracking
• Newton-Raphson method is not used due to its instability in singular configurations of the Jacobian

Dynamic Control

• Proportional-Derivative (PD) controller synthesis and simulation for pick and place task
• Computed torque controller synthesis and simulation for pick and place task and circular trajectory tracking
• Backstepping controller synthesis and simulation for pick and place task and circular trajectory tracking

Adaptive Control

• Computed torque adaptive controller synthesis and simulation for trajectory tracking using Finite Fourier Series (FFS) and parameter estimation
• Backstepping adaptive controller synthesis and simulation for trajectory tracking using FFS and parameter estimation

Prerequisites

1. Robotics Toolbox for MATLAB - a package that provides functions for the study and simulation of classical arm-type and mobile robotics
2. SymPyBotics - a Python-based symbolic framework used for modeling and identifying the dynamics of robots

How to Use

Non-Adaptive Control Methods

To use inverse kinematic (using gradient descent and Levenberg-Marquardt), proportional-derivative, computed torque control, or backstepping controllers, follow these steps:

1. Edit src/main_puma560.m:
   1. Choose a controller by modifying the controller variable:
      • Kinematic_grad: inverse kinematic using gradient descent method
      • Kinematic_LevMar: inverse kinematic using Levenberg-Marquardt method
      • PD: proportional-derivative
      • CT: computed torque
      • BS: backstepping
   2. Choose a task by modifying the task variable:
      • position_control: position control (compatible with Kinematic_grad and Kinematic_LevMar)
      • pick_and_place: pick and place (compatible with PD, CT, and BS)
      • circular_trajectory_tracking: circular trajectory tracking (compatible with CT, BS, and Kinematic_LevMar)
2. Edit src/plot_Simulation.m:
   1. Set saving_flag to 1 if you want to save plot images
   2. Set title_flag to 1 if you want to add titles to the plots
   3. Set threeDplot_flag to 1 if you want to plot the robot's trajectory in 3D space
   4. Set image_extension to the file format you want to use when saving the plots (if title_flag is 1), e.g., 'pdf', 'png', 'jpg'.
   5. Set images_path to the directory where you want to save the plot images (if title_flag is 1), e.g., '/Users/username/Documents/MATLAB/puma560-control/img/'
   6. Set main_path to the directory where the source code is located (if title_flag is 1), e.g., '/Users/username/Documents/MATLAB/puma560-control/src/'
3. Run src/main_puma560.m

Adaptive Control Methods

To use adaptive computed torque and adaptive backstepping controllers:

1. Edit src_adaptive/main_puma560_adaptive.m:
   1. Choose a controller by modifying the controller variable:
      • adaptiveCT: adaptive computed torque
      • adaptiveBS: adaptive backstepping
   2. Choose a task by modifying the task variable: * position_control: position control
      • sinusoidal_trajectory_tracking: sinusoidal trajectory tracking in joint space
      • finite_fourier_series_trajectory_tracking: Finite Fourier Series (FFS) trajectory tracking in joint space
2. Edit src_adaptive/plot_adaptive.m:
   1. Set saving_flag to 1 if you want to save plot images
   2. Set title_flag to 1 if you want to add titles to the plots
   3. Set threeDplot_flag to 1 if you want to plot the robot's trajectory in 3D space
   4. Set image_extension to the file format you want to use when saving the plots (if title_flag is 1), e.g., 'pdf', 'png', 'jpg'.
   5. Set images_path to the directory where you want to save the plot images (if title_flag is 1), e.g., '/Users/username/Documents/MATLAB/puma560-control/img/'
   6. Set main_path to the directory where the source code is located (if title_flag is 1), e.g., '/Users/username/Documents/MATLAB/puma560-control/src/'
3. Run src_adaptive/main_puma560_adaptive.m

References

1. P. I. Corke and B. Armstrong-Helouvry "A search for consensus among model parameters reported for the PUMA 560 robot" in Proceedings of the 1994 IEEE International Conference on Robotics and Automation, 1994, pp. 1608-1613 vol.2, doi:10.1109/ROBOT.1994.351360.
2. C. D. Sousa and R. Cortesao, "SageRobotics: Open Source Framework for Symbolic Computation of Robot Models" in Proceedings of the 27th Annual ACM Symposium on Applied Computing, Trento, Italy, 2012, pp. 262-267, doi:10.1145/2245276.2245329.

Sample Images

Some images of the PUMA 560 robot during different simulations:

• End-effector trajectory (Lissajous, inverse kinematic controller)

Backstepping

Pick and Place

• End-effector trajectory

• EE translation - orientation - XY view - 3D view

• Joint trajectories

• Joint errors

Pick and Place

• End-effector trajectory

• EE translation - orientation - XY view - 3D view

• Joint trajectories

• Joint errors