123 research outputs found
Control of a Bicycle Using Virtual Holonomic Constraints
The paper studies the problem of making Getz's bicycle model traverse a
strictly convex Jordan curve with bounded roll angle and bounded speed. The
approach to solving this problem is based on the virtual holonomic constraint
(VHC) method. Specifically, a VHC is enforced making the roll angle of the
bicycle become a function of the bicycle's position along the curve. It is
shown that the VHC can be automatically generated as a periodic solution of a
scalar periodic differential equation, which we call virtual constraint
generator. Finally, it is shown that if the curve is sufficiently long as
compared to the height of the bicycle's centre of mass and its wheel base, then
the enforcement of a suitable VHC makes the bicycle traverse the curve with a
steady-state speed profile which is periodic and independent of initial
conditions. An outcome of this work is a proof that the constrained dynamics of
a Lagrangian control system subject to a VHC are generally not Lagrangian.Comment: 18 pages, 8 figure
On the Lagrangian Structure of Reduced Dynamics Under Virtual Holonomic Constraints
This paper investigates a class of Lagrangian control systems with
degrees-of-freedom (DOF) and n-1 actuators, assuming that virtual
holonomic constraints have been enforced via feedback, and a basic regularity
condition holds. The reduced dynamics of such systems are described by a
second-order unforced differential equation. We present necessary and
sufficient conditions under which the reduced dynamics are those of a
mechanical system with one DOF and, more generally, under which they have a
Lagrangian structure. In both cases, we show that typical solutions satisfying
the virtual constraints lie in a restricted class which we completely
characterize.Comment: 23 pages, 5 figures, published online in ESAIM:COCV on April 28th,
201
Graph-based algorithms for the efficient solution of a class of optimization problems
In this paper, we address a class of specially structured problems that
include speed planning, for mobile robots and robotic manipulators, and dynamic
programming. We develop two new numerical procedures, that apply to the general
case and to the linear subcase. With numerical experiments, we show that the
proposed algorithms outperform generic commercial solvers.Comment: 27 pages, 9 figures, 1 tabl
Utilizzo dei Carbon Token nella microeconomia: Il progetto “San Marino Low Carbon Ecosystem”
Analisi di un ecosistema a basse emissioni di anidride carbonica che coinvolga i cittadini nella lotta per l'ambiente. Proposta di idee per realizzare un tale ecosistema su scala nazionale italiana
An algorithm with improved complexity for pebble motion/multi-agent path finding on trees
The pebble motion on trees (PMT) problem consists in finding a feasible
sequence of moves that repositions a set of pebbles to assigned target
vertices. This problem has been widely studied because, in many cases, the more
general Multi-Agent path finding (MAPF) problem on graphs can be reduced to
PMT.
We propose a simple and easy to implement procedure, which finds solutions of
length O(knc + n^2), where n is the number of nodes, is the number of
pebbles, and c the maximum length of corridors in the tree. This complexity
result is more detailed than the current best known result O(n^3), which is
equal to our result in the worst case, but does not capture the dependency on c
and k
Adjacency Matrix-Based Transmit Power Allocation Strategies in Wireless Sensor Networks
In this paper, we present an innovative transmit power control scheme, based on optimization theory, for wireless sensor networks (WSNs) which use carrier sense multiple access (CSMA) with collision avoidance (CA) as medium access control (MAC) protocol. In particular, we focus on schemes where several remote nodes send data directly to a common access point (AP). Under the assumption of finite overall network transmit power and low traffic load, we derive the optimal transmit power allocation strategy that minimizes the packet error rate (PER) at the AP. This approach is based on modeling the CSMA/CA MAC protocol through a finite state machine and takes into account the network adjacency matrix, depending on the transmit power distribution and determining the network connectivity. It will be then shown that the transmit power allocation problem reduces to a convex constrained minimization problem. Our results show that, under the assumption of low traffic load, the power allocation strategy, which guarantees minimal delay, requires the maximization of network connectivity, which can be equivalently interpreted as the maximization of the number of non-zero entries of the adjacency matrix. The obtained theoretical results are confirmed by simulations for unslotted Zigbee WSNs
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