# Robot Kinematics and Dynamics

## Subject description

Homogenious transformations of diferential movements (transformation derivative, differential translation and rotation, transformation of differential movements between coordinate systems); Jacobian matrix for manipulator (calculation, geometry and analytical, inverse, singularity, redundancy, J pseudoinverse ); Statics (equvivalent joint torques, transformation of forces and moments, kinematics and statics duality, stiffness); Trajectory generation (absolute, incremental interpolator, superposition with basis functions, Dynamic Movement Primitives,

AI methods for parameter definition); Lagrange dynamics of rigid manipulator (movement equations, linearity, notation in external coordinates); Newton-Euler formulation (equilibriaum equations, calculation of kinematic quantities); Examples.

## Objectives and competences

(a) Spoznati teoretične osnove diferencialne kinematike, statike, Lagrange in Newton-Euler dinamike.

(b) Preveriti medsebojen vpliv veličin z omenjenih področij na realnih mehanizmih v laboratoriju.

(c) Dolgoročno: razumevanje podanih relacij in njihova uporaba

## Teaching and learning methods

Lectures, laboratory practice in smaller groups. In practical exercises are used larger number of modern industrial and other robots. Students have available lecture notes with condensed content of the subject. Invited are guest lectures from Slovenian industry.

## Expected study results

After successful completion of the course, students should be able to:

– describe teoretical basics of diferencial kinematics, statics, lagrange and Newton-Euler dynamics,

– develop moderately complex dynamic models of mechanism independently and more complex by using adeqaute computer tools,

– define robotic trajectories in a classical way and understand dynamic movement primitive notations,

– use relations of differential kinematics and statics in robotics, robot vision and virtual reality environments.

– perform simulations in diferencial kinematics, statics and dynamics,

– check mutual interplay of variables on real mechanisms in the laboratory,

– explain mutual dependence of diferential kinematics, statics and dynamics.

## Basic sources and literature

1. M. Munih: Diferencialna kinematika, statika in generiranje trajektorije, Založba FE in FRI, 2005.
2. L. Sciavicco, B. Siciliano: Robotics: Modelling, Planning and Control, Springer, 2009.
3. H. Choset, K. M. Lynch, S. Hutchinson, G. Kantor, W. Burgard, L. E. Kavraki, S. Thrun: Principles of robot motion, MIT Press, 2005.
4. K. M. Lynch, F.C. Park: Modern Robotics: Mechanics, Planning, and Control, Cambridge University Press, 2017.
5. A. Ijspeert, J. Nakanishi, H. Hoffmann, P. Pastor, S. Schaal, Dynamical movement primitives: Learning attractor models for motor primitives, Neural Computation 25(2), 2013.

## Stay up to date

University of Ljubljana, Faculty of Electrical Engineering Tržaška cesta 25, 1000 Ljubljana