Observers for invariant systems on Lie groups with biased input measurements and homogeneous outputs

This paper provides a new observer design methodology for invariant systems whose state evolves on a Lie group with outputs in a collection of related homogeneous spaces and where the measurement of system input is corrupted by an unknown constant bias. The key contribution of the paper is to study the combined state and input bias estimation problem in the general setting of Lie groups, a question for which only case studies of specific Lie groups are currently available. We show that any candidate observer (with the same state space dimension as the observed system) results in non-autonomous error dynamics, except in the trivial case where the Lie-group is Abelian. This precludes the application of the standard non-linear observer design methodologies available in the literature and leads us to propose a new design methodology based on employing invariant cost functions and general gain mappings. We provide a rigorous and general stability analysis for the case where the underlying Lie group allows a faithful matrix representation. We demonstrate our theory in the example of rigid body pose estimation and show that the proposed approach unifies two competing pose observers published in prior literature.Comment: 11 page

Gradient-like observer design on the Special Euclidean group SE(3) with system outputs on the real projective space

A nonlinear observer on the Special Euclidean group $\mathrm{SE(3)}$ for full pose estimation, that takes the system outputs on the real projective space directly as inputs, is proposed. The observer derivation is based on a recent advanced theory on nonlinear observer design. A key advantage with respect to existing pose observers on $\mathrm{SE(3)}$ is that we can now incorporate in a unique observer different types of measurements such as vectorial measurements of known inertial vectors and position measurements of known feature points. The proposed observer is extended allowing for the compensation of unknown constant bias present in the velocity measurements. Rigorous stability analyses are equally provided. Excellent performance of the proposed observers are shown by means of simulations

State Estimation Using a Network of Distributed Observers With Unknown Inputs

State estimation for a class of linear time-invariant systems with distributed output measurements (distributed sensors) and unknown inputs is addressed in this paper. The objective is to design a network of observers such that the state vector of the entire system can be estimated, while each observer has access to only local output measurements that may not be sufficient on their own to reconstruct the entire system’s state. Existing results in the literature on distributed state estimation assume either that the system does not have inputs, or that all the system’s inputs are globally known to all the observers. Accordingly, we address this gap by proposing a distributed observer capable of estimating the overall system’s state in the presence of inputs, while each observer only has limited local information on inputs and outputs. We provide a design method that guarantees convergence of the estimation errors to zero under joint detectability conditions. This design suits undirected communication graphs that may have switching topologies and also applies to strongly connected directed graphs.We also give existence conditions that are consistent with existing results on unknown input observers. Finally, simulation results verify the effectiveness of the proposed estimation scheme for various scenarios

Autopoietic organization of firm: an illustration for the construction industry

Generally poor productivity, delays, low profitability and exceeded budgets are Common problems in modern construction management, however it seems that a basic obstacle lies far deeper in the understanding of a firm's fundamental mission, its existence. The main objective of this paper therefore is to examine the operational living of a construction firm and by doing that to reveal the key problem or the solution for a construction firm - its organization. A firm as a social system in which interactions between its constitutive components (employees) are surordinated to its maintenance (keeping a system alive) is an autopoietic social system. Two domains of external perturbations are uncovered to which a construction firm has to adapt (market driven and project driven perturbations). Constructed conceptual model of an autopoietic organization is based upon two necessary and sufficient operational domains that a firm has to create in order to become an autopoietic, adaptive social system. The first one is a domain of interactions between employees and other operationally external systems, which is representing an idea-generating domain of interactions. The second is employee's autonomous operational domain, which embodies employee's autonomy and individuality and represents a necessary condition for the establishment of an idea-generating domain. Finally, it is recognized that interactions within these four domains keep a construction firm alive