Online Trajectory Planning and Observer
Based Control
David A. Anisi
Optimization and Systems Theory, Royal Institute of
Technology (KTH), Stockholm, Sweden
ABSTRACT:
The main body of this thesis consists of four appended papers. The
first two consider different aspects of the trajectory planning problem,
while the last two deal with observer design for mobile robotic and
Euler-Lagrange systems respectively.
The first paper addresses the problem of designing a real time, high
performance trajectory planner for aerial vehicles. %The high-level
framework augments Receding Horizon Control (RHC) with a graph based
terminal cost that captures the global characteristics of the
environment, as well as any possible mission objectives. The main
contribution is two-fold. Firstly, by augmenting a novel safety maneuver
at the end of the planned trajectory, this paper extends previous
results by having provable safety properties in a 3D setting. Secondly,
assuming initial feasibility, the planning method is shown to have
finite time task completion. Moreover, in the second part of the paper,
the problem of simultaneous arrival of multiple aerial vehicles is
considered. By using a time-scale separation principle, one is able to
adopt standard Laplacian control to this consensus problem, which is
neither unconstrained, nor first order.
Direct methods for trajectory optimization are traditionally based on a priori temporal discretization and
collocation methods. In the second paper, the problem of adaptive node
distribution is formulated as a constrained optimization problem, which
is to be included in the underlying nonlinear mathematical programming
problem. The benefits of utilizing the suggested method for
online trajectory optimization are illustrated by a missile
guidance example.
In the third paper, the problem of active observer design for an
important class of non-uniformly observable systems, namely mobile
robotics systems, is considered. The set of feasible configurations and
the set of output flow equivalent states are defined. It is shown that
the inter-relation between these two sets may serve as the basis for
design of active observers. The proposed observer design methodology is
illustrated by considering a unicycle robot model, equipped with a
set of range-measuring sensors.
Finally, in the fourth paper, a geometrically intrinsic observer for
Euler-Lagrange systems is defined and analyzed. This observer is a
generalization of the observer recently proposed by Aghannan and
Rouchon. Their contractivity result is reproduced and complemented
by a proof that the region of contraction is infinitely
thin. However, assuming a priori
bounds on the velocities, convergence of the observer is shown by means
of Lyapunov's direct method in the case of configuration manifolds with
constant curvature.