Underactuated Robots

Prof. Leonardo Lanari and Prof. Giuseppe Oriolo

Dipartimento di Ingegneria Informatica, Automatica e Gestionale
Sapienza UniversitÓ di Roma

NOTICE: The 2017/18 UR course will start one week later. The first class will be on March 6 at 14:00.


schedule26 Feb - 31 May 2018; Tue 14-00-16:00, Thu 14:00-18:00, room A4
office hoursThu 14:00-16:00, room A211, DIAG, Via Ariosto 25
e-maillanari [at] diag [dot] uniroma1 [dot] it; oriolo [at] diag [dot] uniroma1 [dot] it


This 3-credits module is part of Elective in Robotics, a 4-module course offered to students of the Master in Artificial Intelligence and Robotics at Sapienza University of Rome. It can also be taken by students of the Master in Control Engineering as one of the two modules of Control Problems in Robotics.


The course focuses on underactuation as a pervasive principle in advanced robotic systems (flexible robots, gymnast robots, humanoids, flying robots), and presents a review of modeling and control methods for underactuated robots.

Syllabus (preliminary)

In this class, we will consider the problems of motion planning and control of underactuated robots, i.e., robots for which the number of actuators is strictly less than the number of degrees of freedom. Classical examples with a small number of degrees of freedom include robot arms that contain unactuated joints (e.g., the Acrobot or Pendubot), robot arms with flexible joints, the cart-pole system, and the Furuta pendulum. In addition to these basic systems, most all robots that are capable of locomotion are underactuated. This includes legged robots, flying robots, swimming robots, snake-like robots. For such robots, there is no actuator that can directly control the position and velocity of the center of mass. In the case of bipedal locomotion, the state of a humanoid's center of mass can only be controlled indirectly, using impact forces that occur at footfalls. For aerial vehicles such as quadrotors or fixed wing aircraft, the position of the center of mass is again indirectly controlled, in this case through the use of aerodynamic forces. This latter class of systems is typically far more complex than the classical examples.

The first part of the course will consider methods that decompose the system dynamics into actuated and unactuated components, and then apply methods from nonlinear and geometric control. Such methods include partial feedback linearization, energy-based methods (which often exploit passivity properties), backstepping, and geometric control techniques that exploit differential flatness.

The second part of the course will consider optimization-based methods. At their core, these algorithms rely on numerical optimization algorithms, and they are viable for systems with many degrees of freedom. These methods often exploit classical results from optimal control, including the Hamilton-Jacobi-Bellman equation and Pontryagin's maximum principle, along with methods from linear quadratic regulator theory for cases in which local linearization is feasible.

It is assumed that students taking this course are familiar with classical algorithms for path planning (e.g., notions of configuration space, and sampling-based planning algorithms such as PRM and RRT), concepts of stability for nonlinear systems (mainly Lyapunov theory), and robot dynamics and control (including state-space control, feedback linearization).

Material (will be added during the course)

Introduction: companion slides (videos not included).


Any student who has attended at least 2/3 of the lectures can pass this module by either giving a presentation on a certain topic (based on technical papers) or developing a small project (typically involving simulations). For more details, see the main pages of Elective in Robotics or Control Problems in Robotics.

Master Theses at the Robotics Laboratory

Master Theses on the topics studied in this course are available at the DIAG Robotics Lab. More information can be found here.
Questions/comments: oriolo [at] diag [dot] uniroma1 [dot] it