## Set-Membership
approach to autonomous navigation

Localization
and

map
building
are
crucial issues when a mobile robot must autonomously navigate in
possibly unknown environments. Both problems can be cast as a state
estimation problem for an uncertain dynamic system. Depending on the
assumptions on the uncertainty affecting the dynamic model and the
measurement equations, probabilistic or deterministic techniques can be

adopted. When the process disturbance and the measurement noise are
supposed to be

unknown-but-bounded (UBB),
localization and map-building can be tackled via set-membership state
estimation
techniques

[6].

### Localization

Given a map of the environment, the objective is to
estimate the vehicle pose. In a set-membership framework, this amounts
to

compute the

feasible
pose set, i.e. the set containing all vehicle
poses that are compatible with the robot motion mode, the collected
measurements and the bounds on the errors

[1].

Ad-hoc nonlinear estimators computing outer
approximations of the actual feasible pose set shave been developed.
The resulting estimates are sets with a fixed structure (e.g., boxes or
parallelotopes) guaranteed to contain the unknown robot pose.

### Simultaneous
localization and map building (SLAM)

When a map environment is not available (e.g., in
exploration tasks), the localization problem becomes harder. In this
case, the robot must build a map while at the same
time localizing within it. This is the so-called

Simultaneous Localization And Map building
problem (SLAM).

By include the landmark positions in the state vector to be
estimated, the problem reduces to a state estimation problem. Under the
assumption of bounded errors, set-membership estimators have been
developed to compute the feasible state set, i.e. the set containing
all vehicle
poses and landmark locations that are compatible with the available
information

[2,4]. The
resulting techniques
feature increased efficiency through state decomposition and set
approximation, provide guaranteed regions containing the unknown robot
pose and landmark
positions, and are suitable for dealing with the data association
problem. The set-membership SLAM algorithm has been successfully
extended to the multi-robot scenario

[3].

### Path planning

In the set-membership framework. a measure of the localization
uncertainty is given by the size of the estimated sets. This
information can be used in order to plan maximally informative paths,
i.e. paths minimizing the overall position uncertainty along
the path. This problem can be cast as an optimal control problem, by
defining a suitable cost function accounting for the expected
localization
uncertainty

[5,7]. The proposed
solution is
able to deal with

sensor limitations and obstacle
avoidance through
artificial potentials.

#### References

- M. Di Marco, A. Garulli, A.
Giannitrapani, A. Vicino. Set
membership pose
estimation of mobile robots based on angle measurements. In
*Proceedings
of the 40th IEEE
Conference on Decision and Control*, Orlando
(USA), December 4-7, 2001.
- M. Di Marco, A. Garulli, A.
Giannitrapani, A. Vicino. Dynamic
robot
localization and mapping using uncertainty sets. In
*Proceedings
of the 15th World
IFAC Congress*, Barcelona (Spain), July 2002.
- M.
Di Marco, A. Garulli, A. Giannitrapani, A. Vicino. Simultaneous
localization and map building for a team of cooperating robots: a set
membership approach.
*IEEE
Transactions on Robotics and Automation*, vol. 19, n. 2,
pp. 238-249, April 2003 (Regular paper).
- M. Di
Marco, A. Garulli, A. Giannitrapani, A. Vicino. A set theoretic
approach to dynamic robot localization and mapping.
*Autonomous
Robots*, vol. 16, no. 1, pp. 23-47, January 2004 (Regular paper).
- N. Ceccarelli, M. Di Marco, A.
Garulli, A. Giannitrapani. A
set theoretic
approach to path planning for mobile robots. In
*Proceedings
of the 43rd IEEE
Conference on Decision and Control*, Atlantis (Bahamas),
December 14-17, 2004.
- N.
Ceccarelli, M. Di Marco, A. Garulli, A. Giannitrapani, A.
Vicino. Set
membership localization and map building for mobile robots.
*Current
trends in nonlinear
systems and control*, L. Menini, L. Zaccarian and C.T.
Abdallah, Eds., pp. 289-308, Birkäuser, 2006.
- N.
Ceccarelli, M. Di Marco, A. Garulli, A. Giannitrapani, A.
Vicino. Path planning with uncertainty: a set membership approach.
*International Journal of Adaptive Control and Signal Processing*,
vol. 25, no. 3, pp. 273-287, March 2011 (Special issue:
Bounding methods for state and parameter estimation).

[Top]

## EKF-based SLAM
with linear features

A common representation of indoor environments is given in terms of
linear features (lines and segments). In this case the simultaneous
localization and map building problem (SLAM) consists in estimating the
robot pose and the parameters of the lines composing the map. A SLAM
algorithm is proposed which recursively updates the estimates of the
unknown quantities through a single
Extended Kalman Filter (EKF)

[1,2].
A mixed
line/segment description of the environment is adopted in order to
improve the data association algorithm. Linear features present in the
environment are extracted from
range and bearing measurements. A statistical characterization of the
observation process is derived directly from the sensor specs.

#### References

- A. Garulli, A. Giannitrapani, A.
Rossi, A. Vicino. Simultaneous
localization and map building using linear features. In
*Proceedings
of the 2nd European
Conference on Mobile Robots*, Ancona (Italy), September
7-10, 2005.
- A. Garulli,
A. Giannitrapani, A. Rossi, A. Vicino. Mobile
robot SLAM
for line-based
environment representation. In
*Proceedings of the
44th
Conference on Decision and Control*, pp.
2041-2046, Seville
(Spain), December 12-15, 2005.
- D.
Benedettelli, A. Garulli, A. Giannitrapani. Multi-Robot SLAM using M-Space
feature representation. In
*Proceedings of the
49th
IEEE Conference on Decision and Control*, pp. 3826-3831, Atlanta (USA), December 15-17, 2010.
- D. Benedettelli, A. Garulli, A. Giannitrapani. Cooperative SLAM using M-Space representation of linear features.
*Robotics and Autonomous Systems*, vol. 60, no. 10, pp. 1267-1278, October 2012 (Regular paper).

[Top]

## Collective
motion for multi-agent systems

The problem considered is that of a team of nonholonomic vehicles whose
objective is to achieve collective circular motion around a virtual
reference beacon. A decentralized control law is proposed

[1,4], which is shown to
guarantee global asymptotic stability of the counterclockwise circular
motion around a fixed beacon, in the single-vehicle case. Equilibrium
configurations of the multi-vehicle system are discussed and sufficient
conditions for local asymptotic stability are derived in terms of the
control law design parameters. Sensory limitations are explicitly taken
into account. Specifically, i) each agent can perceive only vehicles
lying in a limited visibility region; ii) a vehicle cannot measure the
orientation of another vehicle; iii) vehicles are indistinguishable.
Guidelines for the choice of the control law parameters are provided,
taking into account the trade-off between fast convergence to the
equilibrium configuration and safe collision-free trajectories.
Experimental validation of the developed control law

[2,3,5-7] has shown the
effectiveness of the proposed approach also in a real-world scenario
featuring a number of disturbance sources.

#### References

- N.
Ceccarelli, M. Di Marco, A. Garulli, A. Giannitrapani. Collective
circular motion of multi-vehicle systems with sensory limitations.
In
*Proceedings of the
44th
Conference on Decision and Control*, pp. 740-745, Seville
(Spain), December 12-15, 2005.
- N.
Ceccarelli, M. Di Marco, A. Garulli, A. Giannitrapani. Experimental
analysis of
collective circular motion for multi-vehicle systems. In
*Proceedings
of the 8th
International IFAC Symposium on Robot Control*. Bologna
(Italy), September
6-8, 2006.
- D.
Benedettelli, N. Ceccarelli, A. Garulli, A. Giannitrapani. Experimental
validation of a
decentralized control law for multi-vehicle collective motion.
In
*Proceedings of the
2007 IEEE/RSJ International Conference on Intelligent Robots and
Systems, pp. 4170-4175* San Diego (USA), October 29 -
November 2, 2007.
- N. Ceccarelli, M. Di Marco, A.
Garulli, A. Giannitrapani. Collective
circular motion of
multi-vehicle systems.
*Automatica,* vol. 44, no. 12,
pp. 3025-3035, December
2008 (Regular paper).
- D.
Benedettelli, M. Casini, A. Garulli, A. Giannitrapani, A. Vicino. A LEGO Mindstorms experimental setup for
multi-agent systems.
In
*Proceedings of the
3rd IEEE Multi-Conference on Systems and Control*, pp. 1230-1235,
St. Petersburg (Russia), July 8-10, 2009.
- M. Casini, A. Garulli, A. Giannitrapani, A. Vicino. A Matlab-based remote lab for multi-robot
experiments.
In
*Proceedings of the
8th IFAC Symposium on Advances in Control Eduction*, Kumamoto
(Japan), October 21-23, 2009.
- D.
Benedettelli, N. Ceccarelli, A. Garulli, A. Giannitrapani. Experimental
validation of collective circular motion for nonholonomic multi-vehicle
systems.
*Robotics and Autonomous Systems,* vol. 58,
no. 8, pp. 1028-1036, August 2010 (Regular paper).
- F. Morbidi, A. Giannitrapani, D.
Prattichizzo. Maintaining connectivity among multiple agents in cyclic
pursuit: a geometric approach. In
*Proceedings of the
49th
IEEE Conference on Decision and Control*, pp. 7461-7466, Atlanta (USA), December 15-17, 2010.
- M. Casini, A. Garulli, A. Giannitrapani, A. Vicino. A LEGO Mindstorms multi-robot setup in the Automatic Control Telelab. In Proceedings of the 18th IFAC World Congress, pp. 9812-9817, Milan (Italy), August 28 - September 2, 2011.
- M. Casini, A. Garulli, A. Giannitrapani, A. Vicino. A remote lab for multi-robot experiments with virtual obstacles. In Proceedings of the 9th IFAC Symposium on Advances in Control Education, pp. 354-359, Nizhny Novgorod (Russia), June 19-21, 2012.

[Top]

## Mobile haptic
interfaces

The increasing demand of realism for virtual reality applications calls
for the design of advanced force-feedback devices allowing not only
kinesthetic interaction with virtual objects but also locomotion and
navigation inside virtual worlds. A possible solution is to resort to
mobile haptic interfaces (MHI), built by combining standard
force-feedback devices with mobile platforms. In

[1-4] we investigated both theoretically and
experimentally which factors may affect the transparency of this kind
of devices, identifying in mobile robot dynamics a possible cause of
loss of transparency. A method to analyze dynamic performance of an MHI
and some basic guidelines to design controller in order to meet desired
specifications are also provided.

#### References

- A. Formaglio, A. Giannitrapani, M.
Franzini, D.
Prattichizzo, F. Barbagli. Current issues in haptic rendering using
mobile haptic interfaces. In
*Proceedings
of the 1st joint EuroHaptics Conference and Symposium on Haptic
Interfaces*, Pisa (Italy), March 18-20, 2005.
- A. Formaglio, A. Giannitrapani, M.
Franzini, D.
Prattichizzo, F. Barbagli. Performance
of Mobile Haptic Interfaces. In
*Proceedings of the
44th
Conference on Decision and Control*, pp.
8343-8348, Seville (Spain), December 12-15, 2005.
- F.
Barbagli, A. Formaglio, M. Franzini, A. Giannitrapani, D. Prattichizzo.
An
experimental
study of the limitations of Mobile Haptic Interfaces.
*Springer
Tracts in Advanced
Robotics - Experimental Robotics IX*, Springer Verlag -
Berlin, 2006.
- A.
Formaglio, D. Prattichizzo, F. Barbagli, A. Giannitrapani. Dynamic performance of Mobile
Haptic Interfaces.
*IEEE Transactions on
Robotics, *vol. 24, no. 3, pp. 559-575, June 2008 (Regular paper).

[Top]

## Satellite
localization for deep space missions

When GPS signals
are not available (e.g., high-Earth orbits, Earth-to-Moon transfers)
estimation of satellite position is a fundamental requirement for
autonomous navigation. This is especially true when dealing with
spacecraft propelled by electric propulsion systems featuring a
continuous thrusting strategy which requires an accurate knowledge of
the spacecraft position and attitude. In

[1,2] the problem of
spacecraft self-localization is addressed using angular measurements. A
dynamic model of the spacecraft is derived, which takes into account
several perturbing effects such as Earth and Moon gravitational field
asymmetry and errors associated with the Moon ephemerides . It is
assumed that the spacecraft is equipped with line of sight sensors
providing measurements of elevation and azimuth of Moon and Earth with
respect to the spacecraft reference system Range measurements, which
are often difficult to obtain or not sufficiently reliable, are not
required. Position and velocity of the spacecraft are estimated by
employing both the classical Extended Kalman Filter (EKF) and the
recently developed Unscented Kalman Filter (UKF). The performance of
the filters has been tested on simulated data concerning two different
missions (Earth-to-Moon transfer and GEO orbit raising), showing that
the proposed algorithms provide reliable estimates, whose accuracy is
sufficient for autonomous navigation in the considered class of
missions.

#### References

- N.
Ceccarelli, A. Garulli, A. Giannitrapani, M. Leomanni, F.
Scortecci. Spacecraft
localization via angle measurements for autonomous navigation in deep
space. In
*Proceedings
of the 17th IFAC Symposium on Automatic Control in Aerospace. *Toulouse (France),
June 25-29, 2007.
- A. Giannitrapani, N. Ceccarelli, F. Scortecci, A. Garulli. Comparison of EKF and UKF for spacecraft localization via angle measurements.
*IEEE Transactions on Aerospace and Electronic Systems*, vol. 47, no. 1, pp. 75-84, January 2011
- A. Garulli, A. Giannitrapani, M. Leomanni,
F. Scortecci. Autonomous low Earth orbit station-keeping
with electric propulsion.
*Journal of Guidance, Control, and Dynamics*, vol. 34, no. 6, pp. 1683-1693, November 2011 (Regular paper).
- A. Garulli, A. Giannitrapani, M. Leomanni, F. Scortecci.
Autonomous station keeping for LEO missions with a hybrid
continuous/impulsive electric propulsion system. In Proceedings of the 32nd International Electric Propulsion Conference, Kurhaus (Germany), September 11-15, 2011.

[Top]

## Consensus
protocols in presence of bounded errors

In

[1,2] we analyze two classes of
consensus algorithms in a set-theoretic framework. Under the assumption
of unknown but bounded measurement errors, the feasible state set
(i.e., the set of all states compatible with the bounds on the noise)
is explicitly derived. The evolution of the feasible state set is used
to evaluate the agreement of the team. Linear consensus protocols
adopting both constant weights and vanishing weights are considered, in
the case of undirected and stationary communication graph. It is shown
that for both types of protocols, asymptotic consensus cannot be
guaranteed with respect to all possible noise realizations, and bounds
on the asymptotic difference of the agents' states are explicitly
derived, as a function of the bounds on the measurement errors and the
weight matrix.

#### References

- A. Garulli, A. Giannitrapani. A
set-membership approach to consensus problems with bounded measurement
errors.
*Proceedings of the
47th
IEEE Conference on Decision and Control, pp. 2276-2281,* Cancun
(Mexico), December 9-11, 2008.
- A. Garulli, A. Giannitrapani. Analysis of consensus protocols with bounded measurement errors.
*Systems and Control Letters*, vol. 60, no. 1, pp. 44-52, January 2011.

[Top]