Online trajectory planning and observer based control
2006 (English)Licentiate thesis, comprehensive summary (Other scientific)
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 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.
Place, publisher, year, edition, pages
Stockholm: KTH , 2006. , x, 37 p.
Trita-MAT. OS, ISSN 1401-2294 ; 06:04
Computational Optimal Control, Receding Horizon Control, Mission Uncertainty, Safety, Task Completion, Consensus Problem, Simultaneous Arrival, Adaptive Grid Methods, Missile Guidance, Nonlinear Observer Design, Active Observers, Non--uniformly Observable Systems, Mobile Robotic Systems, Intrinsic Observers, Differential Geometric Methods, Euler-Lagrange Systems, Contraction Analysis.
IdentifiersURN: urn:nbn:se:kth:diva-4153ISBN: 91-7178-469-1OAI: oai:DiVA.org:kth-4153DiVA: diva2:10938
2006-11-10, 3721, KTH, Lindstedtsvägen 25, 100 44 Stockholm, 10:00
Cheng, Daizhan, Professor
QC 201011082006-10-152006-10-152010-11-08Bibliographically approved
List of papers