The rising interest in autonomous systems has emphasized the significance of effective path and motion planning, particularly in coordinating multiple Unmanned Areal Vehicles (UAVs) in missions. An important research field is the problem of Multi-Agent Path Finding (MAPF), in which the objective is to find collision-free paths for multiple agents simultaneously. Various algorithms, categorized into optimal, bounded sub-optimal, and unbounded sub-optimal solvers, have been investigated in order to address MAPF problems. However, recent attention has shifted towards MAPF with kinematic constraints, particularly focusing on nonholonomic agents like cars and fixed-wing UAVs. These nonholonomic agents, distinguished by their motion constraints, require specialized methods for trajectory planning.  To investigate the potential of MAPF with nonholonomic agents, two MAPF algorithms have been implemented, incorporating the kinematic constraints of a fixed-wing UAV. The first algorithm is a UAV-like Conflict-Based Search (CBS) algorithm, belonging to the optimal MAPF solver class, and is based on a Car-like CBS algorithm. The second algorithm is a Prioritized Planner, belonging to the search-based MAPF solver class. Both algorithms utilize a common single-agent search algorithm, the Spatiotemporal Hybrid A* (SHA*), which has been enhanced to incorporate a kinematic bicycle model. This enhancement allows for a greater variety of motions, creates feasible paths for fixed-wing UAVs, and enables control over acceleration and steering rates. A comparison of the two MAPF algorithms was conducted for three different map instances. Furthermore, the use of weighted heuristics, resampling and distance-based priority have been implemented and simulated with the Prioritized Planner. Additionally, two methods of simultaneous arrival have been implemented using the UAV-like CBS, where agents have a fixed time of arrival and a variable time of arrival. The results from the simulations confirm the trade-offs between both MAPF algorithms concerning solution quality, success rate and runtime. The UAV-like CBS is capable of finding solutions of higher quality, while the Prioritized Planner is faster at finding solutions and more efficient for an increasing number of agents. However, the performance of the two algorithms varied significantly, depending on the scenario. The thesis concludes that both algorithms can be utilized for MAPF with nonholonomic fixed-wing UAVs, and that the UAV-like CBS is the best choice for a lower amount of agents, while the Prioritized Planner is preferable for a higher amount of agents. The priority of the agents has been shown to be important, and by allowing resampling, the success rate of the Prioritized Planner can be increased significantly. Additionally, simultaneous arrival at the goal position can be achieved optimally for the UAV-like CBS by solving the problem backwards.

<p>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.</p><p>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.</p><p>Direct methods for trajectory optimization are traditionally based on<i> a</i> <i>priori </i>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.</p><p>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.</p><p>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 <i>a</i> <i>priori </i>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.</p>

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. / QC 20101108