Robotics and Autonomous Systems 87 (2017) 226–236 Contents lists available at ScienceDirect Robotics and Autonomous Systems journal homepage: www.elsevier.com/locate/robot Flat control of industrial robotic manipulators Elisha D. Markus a, *, John T. Agee b , Adisa A. Jimoh c a Department of Electrical, Electronic and Computer Systems, Central University of Technology, Free State, South Africa b Department of Electrical Engineering, University of Kwazulunatal, Durban, South Africa c Department of Electrical Engineering, Tshwane University of Technology, Pretoria, South Africa highlights • Computational burden of high order robotic control significantly reduced. • Computation of flat output for 6-DOF robotic manipulator presented. • Comparison between PID and Flatness based control of ABB IRB140 robot provided. • Tracking control of 6-DOF ABB IRB140 robot in Joint space and Task space presented. article info Article history: Received 11 April 2015 Received in revised form 13 September 2016 Accepted 6 October 2016 Available online 24 October 2016 Keywords: Industrial robots Six degrees of freedom robot Differential flatness Trajectory planning Tracking control abstract A new approach to tracking control of industrial robot manipulators is presented in this paper. The highly coupled nonlinear dynamics of a six degrees of freedom (6-DOF) serial robot is decoupled by expressing its variables as a function of a flat output and a finite number of its derivatives. Hence the derivation of the flat output for the 6-DOF robot is presented. With the flat output, trajectories for each of the generalized coordinates are easily designed and open loop control is made possible. Using MATLAB/Simulink S- functions combined with the differential flatness property of the robot, trajectory tracking is carried out in closed loop by using a linear flat controller. The merit of this approach reduces the computational complexity of the robot dynamics by allowing online computation of a high order system at a lower computational cost. Using the same processor, the run time for tracking arbitrary trajectories is reduced significantly to about 10 s as compared to 30 min in the original study (Hoifodt, 2011). The design is taken further by including a Jacobian transformation for tracking of trajectories in cartesian space. Simulations using the ABB IRB140 industrial robot with full dynamics are used to validate the study. © 2016 Elsevier B.V. All rights reserved. 1. Introduction The development of industrial robots has been advanced in the last decade. This is mainly due to increase in the complex- ity of tasks that they execute. The controller which is a major component of robots has received a lot of attention from robotic researchers. This is because it has a direct impact on their per- formance and could inhibit their deployability and applicability in certain areas [1–3]. Many control techniques have been proposed for modern industrial robot manipulators including the classical PID, Computed torque, feedback linearization, inverse dynamics, neurofuzzy, model predictive control etc. More recently, robot control methods have been model based which simply relies on the mathematical model of the robot. Model based control has been applied in trajectory tracking tasks [4–6]. However, the computational requirements of these * Corresponding author. E-mail address: emarkus@cut.ac.za (E.D. Markus). model based systems are quite high as it is required to solve very large equations in their controls. Despite fast computer processor speeds, effective control algorithms become very computationally expensive with high run times and in some cases impossible to achieve. Most researchers in dealing with trajectory robot tracking applications have had to work with lower order robotic dynamics such as in wheeled robots [7–9], parallel robots [10] and un- deractuated robots [1,8,11] in proposing their control algorithms. Underactuating robotic manipulators reduces the order from a high degree of freedom (DOF) to a lower one. As the number of degree of freedom increases, the computational complexity of computing the control also increases. We refer to chapter 6 of [12] where the computational complexity of the 6-dof robot dynamics is discussed. In this study, a 6-dof robot is modeled using the Newton–Euler approach. The computations done with the MAPLE software re- sulted in very long dynamic equations, literally running into sev- eral pages. The mere size of the equations can be a challenge to the control engineer in terms of the computing time. The equations http://dx.doi.org/10.1016/j.robot.2016.10.009 0921-8890/© 2016 Elsevier B.V. All rights reserved. brought to you by CORE View metadata, citation and similar papers at core.ac.uk provided by Central University Of Technology Free State - LibraryCUT, South Africa