Topics in Modelling, Motion Planning and Control for Underactuated Mechanical Systems

Recorded Introductory Lecture

Keywords: dynamic constraints, mechanical systems with one or several passive degrees of freedom, trajectory planning based on nested representation of a forced motion, moving Poincare sections, transverse coordinates, transverse linearization, Lyapunov, Poincare and Zhukovski stability, walking robots, hybrid transverse linearization, sensitivity analysis, non-prehensile manipulation, AI-tools for robotics

Short Course Summary

The course helps students systematically explore topics of modern robotics and nonlinear control theory focused on developing scalable methods for performing and analyzing agile movements of dynamically constrained robotic systems. Modeling, motion planning and control algorithms for such systems become important and unavoidable, for instance, in describing problem settings for automating various labor-intensive tasks such as grasping, manipulating or handling of external objects performed nowadays in industry and service applications primarily by humans. Most of dynamic constraints in applications are case specific or linked to scenarios of work of mechanisms. Meanwhile, some constraints are generic and can be simultaneously present in describing behaviors of quite distant nonlinear systems. Constraints due to under-actuation provide examples of such generic structural features of nonlinear mechanical systems.

The main part of lectures emphasize challenges of model based and first principles approaches to handle and overcome such and similar constraints. The other part of the course includes lectures devoted to illustrating theoretical arguments, and to practicing on available software and hardware realization of the methods developed for solving trajectory planning and control assignments for performing non-prehensile manipulation of a passive disc on a hand of a Butterfly robot. The idea of the robot and the problem to be solved can be devised from the movies:

Organization of the course

The course is developed for graduate students interested in modelling, motion planning and control for under-actuated mechanical systems. The material is organized around four complimentary themes that help gradually enter and explore the subject:
  1. Introduction to Underactuated Systems: Examples, concepts, math and models for planning, control and analysis

  2. Motion and Trajectory Planning for Underactuated Systems: Nested representation and motion generator of a robot behavior; analytic and computational steps in parametrizing agile behaviors; AI-tools in searching feasible behaviors; examples

  3. Motion Control for Underactuated Systems: Transverse dynamics; Andronov-Vitt theorem; (hybrid) transverse linearization for a motion of a controlled mechanical system; numerical methods, challenges and examples

  4. Case study: Planning and performing non-prehensile manipulation of a passive disc on a hand of the "Butterfly robot"

The syllabus of the lectures can be found here.
The literature, the lectures are based on, can be found here.

Scheduled Activities and Past Records

In 2022 the course will be run at
The graduate course was previously read at


The course is run by Dr. Anton Shiriaev (Department of Engineering Cybernetics, NTNU, Norway) with the help of Dr. Maksim Surov, Dr. Leonid Freidovich, Dr. Sergey Gusev and Robotikum AB