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Artificial-delay control is a method in which state and input measurements collected at an immediate past time instant (i.e. artificially delayed) are used to compensate the uncertain dynamics affecting the system at the current time. This work formulates an artificial-delay control method with adaptive gains in the presence of nonlinear (Euler-Lagrange) under-actuation. The appeal of studying Euler-Lagrange dynamics is to capture many robotics applications of practical interest, as demonstrated via stability and robustness analysis and via robotic ship and robotic aerial vehicle test cases., Accepted Author Manuscript, Team DeSchutter

Artificial-delay control is a method in which state and input measurements collected at an immediate past time instant (i.e. artificially delayed) are used to compensate the uncertain dynamics affecting the system at the current time. This work formulates an artificial-delay control method with adaptive gains in the presence of nonlinear (Euler-Lagrange) under-actuation. The appeal of studying Euler-Lagrange dynamics is to capture many robotics applications of practical interest, as demonstrated via stability and robustness analysis and via robotic ship and robotic aerial vehicle test cases., Accepted Author Manuscript, Team Bart De Schutter

Adaptive Sliding Mode Control (ASMC) aims to adapt the switching gain in such a way to cope with possibly unknown uncertainty. In state-of-the-art ASMC methods, a priori boundedness of the uncertainty is crucial to ensure boundedness for the switching gain and uniformly ultimately boundedness. A priori bounded uncertainty might impose a priori bounds on the system state before obtaining closed-loop stability. A design removing this assumption is still missing in literature. A positive answer to this quest is given by this note where a novel ASMC methodology is proposed which does not require a priori bounded uncertainty. An illustrative example is presented to highlight the main features of the approach, after which a general class of Euler–Lagrange systems is taken as a case study to show the applicability of the proposed design., Accepted Author Manuscript, Ship Design, Production and Operations, Team DeSchutter

Available control methods for underactuated Euler–Lagrange (EL) systems rely on structure-specific constraints that may be appropriate for some systems, but restrictive for others. A generalized (structure-independent) control framework is to a large extent missing, especially in the presence of uncertainty. This paper introduces an adaptive-robust control framework for a quite general class of uncertain underactuated EL systems. Compared to existing literature, the important attributes of the proposed solution are: (i) avoiding structure-specific restrictions, namely, symmetry condition property of the mass matrix, and a priori bounds on non-actuated states or state derivatives; (ii) considering Coriolis, centripetal, friction and gravity terms to be unknown, while only requiring the knowledge of maximum perturbation around a nominal value of the mass matrix; (iii) handling state-dependent uncertainties irrespective of their linear or nonlinear in parameters structure. These features significantly widen the range of underactuated EL systems the proposed solution can handle in comparison to the available methods. Stability is studied analytically and the performance is verified in simulation using offshore boom crane dynamics., Accepted Author Manuscript, Ship Design, Production and Operations, Team DeSchutter

In the presence of unmodelled dynamics and uncertainties with no a priori constant bounds, conventional robust adaptation strategies for switched systems cannot allow the control gains of inactive subsystems to remain constant during inactive intervals: vanishing gains are typically required in order to prove bounded stability. As a consequence, these strategies, known in literature as leakage-based adaptive methods, might introduce poor transients at each switching instant. Leakage-based adaptive control becomes even more problematic in the switched nonlinear case, where non-conservative state-dependent upper bounds for uncertainties and unmodelled dynamics are required. This work shows that, for a class of switched Euler–Lagrange systems, such difficulties can be mitigated: a novel leakage-based stable mechanism is introduced which allows the gains of inactive subsystems to remain constant. At the same time, unmodelled dynamics and uncertainties with no a priori bounds can be handled by a quadratic state-dependent upper bound structure that reduces conservativeness as compared to state-of-the-art structures. The proposed design is validated analytically and its performance is studied in simulation with a pick-and-place robotic manipulator example., Accepted Author Manuscript, Ship Design, Production and Operations, Team Bart De Schutter

Adaptive Sliding Mode Control (ASMC) aims to adapt the switching gain in such a way to cope with possibly unknown uncertainty. In state-of-the-art ASMC methods, a priori boundedness of the uncertainty is crucial to ensure boundedness for the switching gain and uniformly ultimately boundedness. A priori bounded uncertainty might impose a priori bounds on the system state before obtaining closed-loop stability. A design removing this assumption is still missing in literature. A positive answer to this quest is given by this note where a novel ASMC methodology is proposed which does not require a priori bounded uncertainty. An illustrative example is presented to highlight the main features of the approach, after which a general class of Euler–Lagrange systems is taken as a case study to show the applicability of the proposed design., Accepted Author Manuscript, Ship Design, Production and Operations, Team Bart De Schutter

Available control methods for underactuated Euler–Lagrange (EL) systems rely on structure-specific constraints that may be appropriate for some systems, but restrictive for others. A generalized (structure-independent) control framework is to a large extent missing, especially in the presence of uncertainty. This paper introduces an adaptive-robust control framework for a quite general class of uncertain underactuated EL systems. Compared to existing literature, the important attributes of the proposed solution are: (i) avoiding structure-specific restrictions, namely, symmetry condition property of the mass matrix, and a priori bounds on non-actuated states or state derivatives; (ii) considering Coriolis, centripetal, friction and gravity terms to be unknown, while only requiring the knowledge of maximum perturbation around a nominal value of the mass matrix; (iii) handling state-dependent uncertainties irrespective of their linear or nonlinear in parameters structure. These features significantly widen the range of underactuated EL systems the proposed solution can handle in comparison to the available methods. Stability is studied analytically and the performance is verified in simulation using offshore boom crane dynamics., Accepted Author Manuscript, Ship Design, Production and Operations, Team Bart De Schutter

The paper deals with the simulation of dynamical models of constrained multibody systems which can be formulated as a set of Differential Algebraic Equations (DAEs). We consider the general dynamical model resulting from Euler-Lagrange formulation. We investigate the solution with the index reduction method. We illustrate our analysis by the example of the slider-crank mechanism. Among many possible representations, we derive a dynamical model based on two variables offering an easier analysis and implementation. We solve the DAE problem with a Matlab function (ode15s) which is dedicated to solve stiff Ordinary Differential Equations (ODEs). Concordant simulation results have been obtained in comparison to other methods proving an acceptable stability and accuracy of the used method for solving this problem.

Synchronization of Multi-Agent Systems (MASs) has the potential to benefit many technological areas such as formation control for unmanned vehicles, cooperative adaptive cruise control, and spacecraft attitude control. Information plays a crucial role in MASs: in centralized approaches, a central node utilizes global information to achieve synchronization, while in distributed approach agents only utilize local information, i.e. neighbors’ information. A big concern in MASs is the presence of parametric uncertainties (unknown dynamics), which might require adaptive control gains instead of fixed control gains. This work thus provides a novel adaptive distributed control for MASs of heterogeneous agents with unknown dynamics based on model reference adaptive control (MRAC). We study both the synchronization of linear systems and the synchronization of Euler- Lagrange (EL) systems. The implementation of this scheme is based on distributed matching condition assumptions. We study such matching conditions both for the statefeedback case and output-feedback case. Since all matching gains are unknown in view of the unknown dynamics, the gains are adapted online via Lyapunov-based estimation. The asymptotic convergence of the synchronization error is analytically proven by introducing an appropriately defined Lyapunov function, and numerical examples show the effectiveness of the approach. The practical advantage of the proposed distributed MRAC is the possibility of handling unknown dynamics by simply exchanging the states/output, and inputs with neighbors, without any extra auxiliary variables (distributed observer) nor sliding mode. Because of the mutual dependence of control inputs, well-posedness problems will arise in the presence of cyclic communication, if the inputs are generated without a prescribed priority. In this work, we study such well-posedness problems via par, Electrical Engineer | Embedded Systems

This paper proposes a control scheme in the operational space for bilateral teleoperation systems composed of heterogeneous robots (kinematically and dynamically different) without velocity sensors and considering variable time-delays in the interconnection. The proposed control scheme use a second order dynamical controller that back-propagates damping to the local and the remote manipulators. Under the assumptions that the human operator and the environment define passive maps from force to velocity, it is proved that velocities and pose (position and orientation) errors between the local and the remote manipulators are bounded. Moreover, in the case that the human and the environment forces are zero, the velocities and pose errors converge asymptotically to zero. The proposed approach employs, the singularity-free, unit-quaternions to represent the orientation of the end-effectors. The performance of the proposed controller is illustrated via simulations with a teleoperation system composed of robots with 3-DoF and 7-DoF., Peer Reviewed, Postprint (published version)

Synchronization of Multi-Agent Systems (MASs) has the potential to benefit many technological areas such as formation control for unmanned vehicles, cooperative adaptive cruise control, and spacecraft attitude control. Information plays a crucial role in MASs: in centralized approaches, a central node utilizes global information to achieve synchronization, while in distributed approach agents only utilize local information, i.e. neighbors’ information. A big concern in MASs is the presence of parametric uncertainties (unknown dynamics), which might require adaptive control gains instead of fixed control gains. This work thus provides a novel adaptive distributed control for MASs of heterogeneous agents with unknown dynamics based on model reference adaptive control (MRAC). We study both the synchronization of linear systems and the synchronization of Euler- Lagrange (EL) systems. The implementation of this scheme is based on distributed matching condition assumptions. We study such matching conditions both for the statefeedback case and output-feedback case. Since all matching gains are unknown in view of the unknown dynamics, the gains are adapted online via Lyapunov-based estimation. The asymptotic convergence of the synchronization error is analytically proven by introducing an appropriately defined Lyapunov function, and numerical examples show the effectiveness of the approach. The practical advantage of the proposed distributed MRAC is the possibility of handling unknown dynamics by simply exchanging the states/output, and inputs with neighbors, without any extra auxiliary variables (distributed observer) nor sliding mode. Because of the mutual dependence of control inputs, well-posedness problems will arise in the presence of cyclic communication, if the inputs are generated without a prescribed priority. In this work, we study such well-posedness problems via par, Electrical Engineering | Embedded Systems

This paper deals with the problem of achieving consensus of multiple interconnected Euler-Lagrange (EL) systems using the energy shaping plus damping injection principles of passivity-based control. It proposes a novel decentralized controller that is capable of solving the leaderless consensus problem in networks of fully-actuated EL-systems with interconnecting time-varying delays and without employing velocity measurements. The paper also presents experimental results that provide evidence of the performance of the novel controller, Peer Reviewed, Postprint (published version)

This paper proposes a control algorithm for networks of multiple heterogeneous robot manipulators, which solves the leader follower and the leaderless consensus problems in the operational space. In the leader-follower scenario, the controller ensures that all the robots in the network asymptotically reach a given leader pose (position and orientation), provided that, at least, one follower robot has access to the leader pose. Without a leader pose, in the leaderless problem, the robots asymptotically reach a pose of consensus. The controller is a simple distributed proportional plus clamping injection (P+d) scheme which does not require velocity measurements. A singularity-free representation, unit quaternions, is used to describe the orientation of each manipulator. The paper presents some simulations, with a network of six 6-Degrees-of-Freedom (DoF) manipulators, and experiments, with a network of three 6-DoF manipulators, to show the effectiveness of the proposed controller. (C) 2013 The Franklin Institute. Published by Elsevier Ltd. All rights reserved., Postprint (published version)

In this paper, the robust coordination of multi-agent systems via energy-shaping is studied. The agents are nonidentical, Euler–Lagrange systems with uncertain parameters which are regulated (with and without exchange of information between the agents) by the classical energy-based controller where the potential energy function is shaped such that, if the parameters are known, all agents converge globally to the same desired constant equilibrium. Under parameter uncertainty, the globally asymptotically stable (GAS) equilibrium point is shifted away from its desired value and this paper shows that adding information exchange between the agents to the decentralized control policy improves the steady-state performance. More precisely, it proves that if the undirected communication graph is connected, the equilibrium of the networked controller isalways closer (in a suitable metric) to the desired one than that of the decentralized controller. The result holds for all interconnection gains if the potential energy functions are quadratic, else, it is true for sufficiently large gains. An additional advantage of networking is that the asymptotic stabilization objective can be achieved by using lower gains into the loop. Some experimental results (using two nonlinear manipulators) given support to the main results of the paper, Postprint (published version)

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, QC 20100622, TAIS, AURES

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, QC 20100622, TAIS, AURES

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, QC 20100622, TAIS, AURES

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, QC 20100622, TAIS, AURES

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 intrinsi, QC 20101108

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 intrinsi, QC 20101108

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 intrinsi, QC 20101108

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 intrinsi, QC 20101108

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 intrinsi, QC 20101108

In this paper, a geometrically intrinsic observer for Euler-Lagrange systems is defined and analysed. This observer is an generalization of the observer recently proposed by Aghannan and Rouchon. Their contractivity result is reproduced and complemented by a proof that the region of contractivity 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. The convergence properties of the observer are illustrated by an example where the configuration manifold is the three-dimensional sphere, S3., QC 20100622. Updated from manuscript to conference paper.