Underactuated Robots (UR)
Profs. Leonardo Lanari and Giuseppe Oriolo
Dipartimento di Ingegneria Informatica, Automatica e
Sapienza UniversitÓ di Roma
is the webpage of UR 2021/2022. Since 2022/2023, the
instructor for UR will be Prof. Leonardo Lanari. Check his webpage for updated information.
||17 Nov - 23 Dec 2021; Tue
16-00-18:00, room B2; Wed 16:00-18:00, room A4; Thu
16:00-19:00, room A5-A6; all rooms at DIAG, via
+ Zoom https://uniroma1.zoom.us/j/84861459266?pwd=dlBJcmtXVTRqai9EM1FjaitOUGtCdz09
14:00-16:00, room A211, DIAG, Via Ariosto 25
diag [dot] uniroma1 [dot] it; oriolo [at] diag [dot]
uniroma1 [dot] it
to the ongoing COVID-19 sanitary emergency, UR
lectures for 2021-22 will be given in class but will
also be available via streaming at the Zoom
link indicated above. Access Zoom using your Sapienza
student account, making sure that your first +
last name appear in the Zoom account profile.
that wish to attend UR should ask to join the UR Google
Group as soon as possible. Use your Sapienza
student account (@studenti.uniroma1.it) and enter your first
+ last name in "Display Name" and your master
program only (e.g., "MARR", "MCER",
"Erasmus"...) in "Reason for joining".
This 3-credits module is part of Elective in Robotics, a 4-module course offered
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 and presents a review of modeling and control methods
for underactuated robots.
Motivation. Definition of underactuated system
(generalized coordinates vs degrees of freedom). Examples of
2. Modeling and Properties
Eulero-Lagrange modeling (classic and alternate).
State-space form. Control problems of interest. Controllabiity
(STLA, STLC, natural controllability). Comparison with fully
actuated robots. Integrability conditions for passive dynamics.
Equilibrium points and linear controllability.
3. Case Studies: Acrobot and Pendubot
Modeling. Approximate linearization at equilibria. Linear
controllability. Balancing. Partial feedback linearization.
Swing-up (1) via analysis of the zero dynamics (2) via energy
4. Zero dynamics in
Normal form and zero dynamics. Importance of the zero
dynamics in control. Zero-dynamics in linear and nonlinear
underactuated systems. The homoclinic orbit.
Definition and physical interpretation. Linear and nonlinear
mechanical systems examples. Dissipativity in state space
representations. Feedback equivalence to a passive system.
Output stabilization of passive systems
6. Energy-based control of
The convey-crane and reaction-wheel cases.
7. Optimization methods for Planning and Control
Introduction to Dynamic Programming. Hamilton-Jacobi-Bellman
equation. Derivation of the Linear Quadratic Regulator.
Linear-Time-Varying LQR. Trajectory optimization with Iterative
LQR. Constrained optimization. Model Predictive Control (Linear,
LTV and Nonlinear). LQR-trees.
(with reference to the numbered topics of the syllabus)
(videos not included)
2. De Luca, Iannitti, Mattone, Oriolo: Underactuated
manipulators: Control properties and techniques,
MIROC, 2002 (pdf)
Oriolo and Nakamura: Control of
Mechanical Systems with Second-Order Nonholonomic
Constraints: Underactuated Manipulators, CDC, 1991 (pdf)
3. Spong: The swing-up problem for the Acrobot,
IEEE Control Systems, 1996 (pdf)
Oriolo: The Pendubot, notes (pdf)
4. Isidori: Nonlinear control systems,
Springer, 1995 (ch 4 up to 4.5) (pdf)
5. Byrnes, Isidori, Willems: Passivity, Feedback
Equivalence, and the Global Stabilization of Minimum Phase
Nonlinear Systems, T-AC, 1991, (up to Sect IV) (pdf)
6. Xin, Liu, Control Design and Analysis for
Underactuated Robotic Systems, Springer, 2014 (ch 2:
fundamentals of energy-based control; ch 4: Acrobot; ch 6:
Collado, Lozano, Fantoni, Control of
convey crane based on passivity, ACC, 2000 (pdf)
Spong, Corke, Lozano, Nonlinear control of the Reaction
Wheel Pendulum, Automatica, 2001 (pdf)
Part 1 and Slides:
Tedrake, Underactuated Robotics:
Algorithms for Walking, Running, Swimming, Flying, and
notes for MIT 6.832 (ch 7: dynamic programming; ch 8: LQR)
Bertsekas, Dynamic programming and
optimal control, vol 1, Athena scientific, 2017
Bemporad, Model Predictive Control,
course slides, 2020
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
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