We consider the solution of nonlinear optimal control problems subject to stochastic perturbations with incomplete observations. In particular, we generalize results obtained by Ito and Kunisch in [8] where they consider a receding horizon control (RHC) technique based on linearizing the problem on small intervals. The linear-quadratic optimal control problem for the resulting time-invariant (LTI) problem is then solved using the linear quadratic Gaussian (LQG) design. Here, we allow linearization about an instationary reference trajectory and thus obtain a linear time-varying (LTV) problem on each time horizon. Additionally, we apply a model predictive control (MPC) scheme which can be seen as a generalization of RHC and we allow covariance matrices of the noise processes not equal to the identity. We illustrate the MPC/LQG approach for a three dimensional reaction-diffusion system. In particular, we discuss the benefits of time-varying linearizations over time-invariant ones.

This thesis consists of four independent papers concerningthe control of mobile robots in the context of obstacleavoidance and formation keeping. The first paper describes a new theoreticallyv erifiableapproach to obstacle avoidance. It merges the ideas of twoprevious methods, with complementaryprop erties, byusing acombined control Lyapunov function (CLF) and model predictivecontrol (MPC) framework. The second paper investigates the problem of moving a fixedformation of vehicles through a partiallykno wn environmentwith obstacles. Using an input to state (ISS) formulation theconcept of configuration space obstacles is generalized toleader follower formations. This generalization then makes itpossible to convert the problem into a standard single vehicleobstacle avoidance problem, such as the one considered in thefirst paper. The properties of goal convergence and safetyth uscarries over to the formation obstacle avoidance case. In the third paper, coordination along trajectories of anonhomogenuos set of vehicles is considered. Byusing a controlLyapunov function approach, properties such as boundedformation error and finite completion time is shown. Finally, the fourth paper applies a generalized version ofthe control in the third paper to translate,rotate and expanda formation. It is furthermore shown how a partial decouplingof formation keeping and formation mission can be achieved. Theapproach is then applied to a scenario of underwater vehiclesclimbing gradients in search for specific thermal/biologicalregions of interest. The sensor data fusion problem fordifferent formation configurations is investigated and anoptimal formation geometryis proposed. Keywords:Mobile Robots, Robot Control, ObstacleAvoidance, Multirobot System, Formation Control, NavigationFunction, Lyapunov Function, Model Predictive Control, RecedingHorizon Control, Gradient Climbing, Gradient Estimation. / QC 20111121

We consider the solution of nonlinear optimal control problems subject to stochastic perturbations with incomplete observations. In particular, we generalize results obtained by Ito and Kunisch in [8] where they consider a receding horizon control (RHC) technique based on linearizing the problem on small intervals. The linear-quadratic optimal control problem for the resulting time-invariant (LTI) problem is then solved using the linear quadratic Gaussian (LQG) design. Here, we allow linearization about an instationary reference trajectory and thus obtain a linear time-varying (LTV) problem on each time horizon. Additionally, we apply a model predictive control (MPC) scheme which can be seen as a generalization of RHC and we allow covariance matrices of the noise processes not equal to the identity. We illustrate the MPC/LQG approach for a three dimensional reaction-diffusion system. In particular, we discuss the benefits of time-varying linearizations over time-invariant ones.

This thesis presents a predictive energy management controller for long-haul hybrid trucks. In a receding horizon control framework, the vehicle speed reference, battery energy reference, and engine on/off decision are optimized over a prediction horizon. A mixed-integer quadratic program (MIQP) is formulated by performing modelling approximations and by including the binary engine on/off decision in the optimal control problem. The branch-and-bound algorithm is applied to solve this problem. Simulation results show fuel consumption reductions between 10-15%, depending on driving cycle, compared to a conventional truck. The hybrid truck without the predictive control saves significantly less. Fuel consumption is reduced by 3-8% in this case. A sensitivity analysis studies the effects on branch-and-bound iterations and fuel consumption when varying parameters related to the binary engine on/off decision. In addition, it is shown that the control strategy can maintain a safe time gap to a leading vehicle. Also, the introduction of the battery temperature state makes it possible to approximately model the dynamic battery power limitations over the prediction horizon. The main contributions of the thesis are the MIQP control problem formulation, the strategy to solve this with the branch-and-bound method, and the sensitivity analysis.

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. / QC 20100622 / TAIS, AURES

<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