Robotics Course

This course aims to introduce the fundamentals of mechanics and control of robotic manipulators. In this course, a conceptual and analytic approach is preferred rather than the usual iterative methods being followed in some textbooks. In order to accomplish that, motion description in space with the emphasis on screw-axis representation is given. Forward and Inverse kinematics of robotic manipulator is elaborated base on geometrical methods, Differential kinematics is followed through the definition of twist and wrench, and general Jacobian derivation methods including screw-based jacobians. Inverse problems, redundancy resolution, and stiffness analysis are explained in this context. For dynamic analysis, the Lagrange approach is followed, while the properties of dynamic matrices are explained in detail. For the sake of position control of the robots, linear models for the robots with gearbox is formulated, and identification methods are explained. then linear and nonlinear control schemes joint-space and task-pace will be introduced.

Tentative Course Timetable

Time: Teaching Contents
Week 1 Introduction: Robotics: A human dream comes true, robotics definition and evolution, serial and parallel robots, cylindrical, spherical, cartesian, SCARA, and different parallel robots, robotics application, ARAS developed robots.
Week 2 Motion Description: Robot components, coordinate systems, position and orientation representation, rotation matrix, rotation matrix properties, screw axis, unit quaternion, Euler angles. Chasles’s theorem, rotation plus orientation, screw axis representation, homogeneous transformation, and arithmetics.
Week 3 Forward Kinematics Analysis: Definitions, kinematic loop closure, forward and inverse kinematics, joint, and task space variables, forward kinematics, motivating example, geometric and algorithmic approach, frame assignment, DH parameters,DH homogeneous transformations, case studies, successive screw method, screw-based transformations, Case studies.
Week 4 Inverse Kinematics Analysis: Inverse problem, solvability, existence of solutions, reachable and dexterous workspace, methods of solution,  algebraic, trigonometric, geometric solutions, reduction to polynomials, Pieper’s solution, method of successive screws, Case studies.
Week 5 Differential Kinematics: Definition of angular and linear velocities, rotation matrix rate related to the angular velocity and Euler angle rates, twist and wrench. Definition of Jacobian map, motivating example, direct method, general and iterative methods, case studies.
Week 6 Differential Kinematics: Screw-based Jacobian, general and iterative methods, case studies. Static wrench and Jacobian transpose, the principle of virtual work, singularity, singularity decoupling, dexterity, dexterity ellipsoid, isotropy, manipulability, condition number.
Week 7 Differential Kinematics: Inverse Jacobian solutions,  fully-, under-, and redundantly-actuated robots, redundancy resolution, optimization problem, inverse acceleration, obstacle avoidance, singularity circumvention, stiffness analysis, sources of compliance, Compliance and stiffness matrix, force ellipsoid, case studies.
Week 8
Midterm Exam
Week 9 Dynamics: Linear and angular acceleration, Lagrange method, general derivation method, case studies.
Week 10 Dynamics:  properties of manipulator dynamics, iterative Lagrange method, case studies.
Week 11 Path Planning: Joint space and Cartesian space methods, cubic interpolation, Parabolic Blend interpolation, multiple points with via points.
Week 12 Linear Position Control: Robots with gearbox, dynamic remodeling, linear identification, linear controller design.
Week 13 Nonlinear and Robust Control: General controller topology, Feedforward control, Feedback linearization, computed torque method. Cartesian space control schemes, Inverse Jacobian method, Jacobian Transpose method, Modified JT method.
Week 14 Force and Impedance Control: The general topology, virtual damper-spring concept, force measurements, Stiffness control, force control schemes, force-position control, matrix inclusion method, hybrid force-motion control topology,
Week 15 Force and Impedance Control: Impedance definition, Impedance control topology, Impedance control methods, relation to Stiffness control.

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Course Materials

Lecture Notes


HW 03 | Sol 03

HW 04 | Sol 04


Research Task 01:

Explore methods to remedy the degeneracy and singularity of the inverse problems in different orientation representations.

Research Task 02:

Find the workspace for the SCARA manipulator via the interval analysis method in MATLAB. Document the necessary steps in the corresponding toolbox.


More Contents

2001 2003 | 2006

2008 | 2009 | 2010