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Online Trajectory Planning for Aerial Vehicle: A Safe Approach with Guaranteed Task Completion
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
Dept. of Autonomous Systems, Swedish Defence Research Agency (FOI), Stockholm, Sweden.
Dept. of Autonomous Systems, Swedish Defence Research Agency (FOI), Stockholm, Sweden.ORCID iD: 0000-0002-7714-928X
(English)Manuscript (Other academic)
Abstract [en]

On-line trajectory optimization in three dimensional space is the main topic of the paper at hand. The high-level framework augments on-line receding horizon control with an off-line computed terminal cost that captures the global characteristics of the environment, as well as any possible mission objectives. The first part of the paper is devoted to the single vehicle case while the second part considers the problem of simultaneous arrival of multiple aerial vehicles. The main contribution of the first part is two-fold. Firstly, by augmenting a so called safety maneuver at the end of the planned trajectory, this paper extends previous results by addressing provable safety properties in a 3D setting. Secondly, assuming initial feasibility, the planning method presented is shown to have finite time task completion. Moreover, a quantitative comparison between the two competing objectives of optimality and computational tractability is made. Finally, some other key characteristics of the trajectory planner, such as ability to minimize threat exposure and robustness, are highlighted through simulations. As for the simultaneous arrival problem considered in the second part, by using a time-scale separation principle, we are able to adopt standard Laplacian control to a consensus problem which is neither unconstrained, nor first order. 

National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-6264OAI: oai:DiVA.org:kth-6264DiVA: diva2:10934
Note
QC 20100622Available from: 2006-10-15 Created: 2006-10-15 Last updated: 2011-11-21Bibliographically approved
In thesis
1. Online trajectory planning and observer based control
Open this publication in new window or tab >>Online trajectory planning and observer based control
2006 (English)Licentiate thesis, comprehensive summary (Other scientific)
Abstract [en]

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.
Series
Trita-MAT. OS, ISSN 1401-2294 ; 06:04
Keyword
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.
National Category
Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-4153 (URN)91-7178-469-1 (ISBN)
Presentation
2006-11-10, 3721, KTH, Lindstedtsvägen 25, 100 44 Stockholm, 10:00
Opponent
Supervisors
Note
QC 20101108Available from: 2006-10-15 Created: 2006-10-15 Last updated: 2010-11-08Bibliographically approved
2. On Cooperative Surveillance, Online Trajectory Planning and Observer Based Control
Open this publication in new window or tab >>On Cooperative Surveillance, Online Trajectory Planning and Observer Based Control
2009 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

The main body of this thesis consists of six appended papers. In the  first two, different  cooperative surveillance problems are considered. The second 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.In Papers A and B,  a combinatorial optimization based framework to cooperative surveillance missions using multiple Unmanned Ground Vehicles (UGVs) is proposed. In particular, Paper A  considers the the Minimum Time UGV Surveillance Problem (MTUSP) while Paper B treats the Connectivity Constrained UGV Surveillance Problem (CUSP). The minimum time formulation is the following. Given a set of surveillance UGVs and a polyhedral area, find waypoint-paths for all UGVs such that every point of the area is visible from  a point on a waypoint-path and such that the time for executing the search in parallel is minimized.  The connectivity constrained formulation  extends the MTUSP by additionally requiring the induced information graph to be  kept recurrently connected  at the time instants when the UGVs  perform the surveillance mission.  In these two papers, the NP-hardness of  both these problems are shown and decomposition techniques are proposed that allow us to find an approximative solution efficiently in an algorithmic manner.Paper C addresses the problem of designing a real time, high performance trajectory planner for an aerial vehicle that uses information about terrain and enemy threats, to fly low and avoid radar exposure on the way to a given target. The high-level framework augments Receding Horizon Control (RHC) with a graph based terminal cost that captures the global characteristics of the environment.  An important issue with RHC is to make sure that the greedy, short term optimization does not lead to long term problems, which in our case boils down to two things: not getting into situations where a collision is unavoidable, and making sure that the destination is actually reached. Hence, the main contribution of this paper is to present a trajectory planner with provable safety and task completion properties. Direct methods for trajectory optimization are traditionally based on a priori temporal discretization and collocation methods. In Paper D, 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 Paper E, the problem of active observer design for an important class of non-uniformly observable systems, namely mobile robotic 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 Paper F, a geometrically intrinsic observer for Euler-Lagrange systems is defined and analyzed. This observer is a generalization of the observer proposed by Aghannan and Rouchon. Their contractivity result is reproduced and complemented  by  a proof  that the region of contraction is infinitely thin. Moreover, 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, 2009. xii, 53 p.
Series
Trita-MAT. OS, ISSN 1401-2294 ; 2009:03
Keyword
Surveillance Missions, Minimum-Time Surveillance, Unmanned Ground Vehicles, Connectivity Constraints, Combinatorial Optimization, Computational Optimal Control, Receding Horizon Control, Mission Uncertainty, Safety, Task Completion, 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.
National Category
Computational Mathematics Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-9990 (URN)978-91-7415-246-3 (ISBN)
Public defence
2009-04-01, E2, Linstedtsvägen 3, KTH, 10:00 (English)
Opponent
Supervisors
Projects
TAIS, AURES
Note
QC 20100622Available from: 2009-03-12 Created: 2009-02-25 Last updated: 2010-07-19Bibliographically approved

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