Prof. Leonardo Lanari and Prof. Giuseppe Oriolo
Dipartimento di Ingegneria Informatica, Automatica e Gestionale
Sapienza UniversitÓ di Roma
NOTICE: In 2018/19, the UR course will be in class during Semester 1. Classes will start on Nov 13.
|schedule||13 Nov (new start date!) - 20 Dec 2018; Tue 16-00-18:00, Thu 16:00-19:00, room A4|
|office hours||Thu 14:00-16:00, room A211, DIAG, Via Ariosto 25|
|e-mail||lanari [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.
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
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
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
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