Erwan Salaün

The true role of accelerometer feedback in quadrotor control

A revisited quadrotor model is proposed, including in particular the so-called rotor drag. It differs from the model usually considered, even at first order, and much better explains the role of accelerometer feedback in control algorithms. The theoretical derivation is supported by experimental data.

Invariant Extended Kalman Filter: theory and application to a velocity-aided attitude estimation problem

A new version of the extended Kalman filter (EKF) is proposed for nonlinear systems possessing symmetries. Instead of using a linear correction term based on a linear output error, it uses a geometrically adapted correction term based on an invariant output error; in the same way the gain matrix is not updated from of a linear state error, but from an invariant state error. The benefit is that the gain and covariance equations converge to constant values on a much bigger set of trajectories than equilibrium points as is the case for the EKF, which should result in a better convergence of the estimation. This filter is applied to the practically relevant problem of estimating the velocity and attitude of a moving rigid body, e.g. an aircraft, from GPS velocity, inertial and magnetic measurements. In this context it can be seen as an extension of the ¿multiplicative EKF¿ often used for quaternion estimation.

Generalized Multiplicative Extended Kalman Filter for Aided Attitude and Heading Reference System

In this paper, we propose a “Generalized Multiplicative Extended Kalman Filter” (GMEKF) to estimate the position and velocity vectors and the orientation of a flying rigid body, using measurements from lowcost Earth-fixed position and velocity, inertial and magnetic sensors. Thanks to well-chosen state and output errors, the gains and covariance equations converge to constant values on a much bigger set of trajectories than equilibrium points as it is the case for the standard Multiplicative Extended Kalman Filter (MEKF). We recover thus the fundamental properties of the Kalman filter in the linear case, especially the convergence and optimality properties, for a large set of trajectories, and it should result in a better convergence of the estimation. We illustrate the good performance and the nice properties of the GMEKF on simulation and on experimental comparisons with a commercial system.

Determining bounds on controller workload rates at an intersection

This paper considers the problem of determining the maximum controller workload associated with two intersecting flows of aircraft according to aircraft arrival rates. Based on the structure of the aircraft arrivals, an optimal control strategy is presented for minimizing the maximum rate of resolutions required to deconflict traffic at the intersection. Bounds on the rate of resolution take into account magnitude constraints in the conflict resolution commands issued to aircraft. The goal of this research is to establish worst-case measures of workload such that air traffic flow managers can route traffic along network structures without exceeding human-controller performance capabilities.

Airspace Complexity Estimations Based on Data-Driven Flow Modeling

This paper presents a new methodology that aims to rapidly generate airspace complexity estimations, which are principally based on the probability of presence of at least one or two aircraft at any given point in a considered sector. Three-dimensional complexity maps are generated using an aircraft flow model driven from historical data. Time-varying flow characteristics such as routes, speed, probability density function of the inter-arrival time between two consecutive aircraft, are determined using Enhanced Traffic Management System (ETMS) data. In addition to the flow characteristics, the complexity maps take into account the sector geometrical configuration and the probability of severe weather. From the complexity maps, a scalar estimation of the airspace complexity is proposed. The complexity estimations presented in this paper are intended to be a predictive tool to support traffic flow management, in order to anticipate for a given time period how different flows may interact together. Especially, the 3-D complexity maps allow to predict which “critical” regions may be subject to possible conflict between aircraft or to the presence of aircraft in severe weather area.

A simplified approach to determine airspace complexity maps under automated conflict resolution

This paper presents a new methodology for rapidly generating complexity maps for various configurations taking into account the influence of some conflict avoidance algorithm at a pair-wise intersection level. The complexity maps are based on analytical expressions, validated through simulations, of the probability of conflict and the spatial distribution of aircraft. This ¿closed-loop¿ analysis explicitly considers the role of the conflict resolution algorithm, here the offset method. It gives therefore a more realistic image of the current and future health of the considered airspace as a function of the encounter and aircraft flows characteristics. Some results of the usual ¿open-loop¿ approach are also validated, while highlighting their limitations.

Fully Autonomous Indoor Flight Relying on Only Five Very Low-Cost Range Sensors

Answering what is the bare minimum combination of avionics and vehicle platform design that enables useful autonomous indoor flight without a Global Positioning System (GPS) is required to understand the lower-cost bounds for indoor unmanned aerial system (UAS) technology. The GTLama indoor UAS, capable of autonomously exploring indoor areas in the GPS-denied environment discussed here, was designed in an attempt to answer this question. TheGTLamaweighs around 600 g (1.3 lb), has a diameter of approximately 70 cm (27.6 in.), and costs less than 900 U.S. dollars. Cost and weight savings are realized through development of an innovative indoor guidance, navigation, and control algorithm that uses only five small off-the-shelf low-cost range sensors rather than expensive and sophisticated sensors such as inertial measurement units, scanning laser range sensors, andGPS. The onboard software leverages the inherent stability of the coaxial rotorcraft platform and fuses information from the low-fidelity range sensors to detect and follow walls and other stationary obstacles. The algorithms are designed to encourage maximum exploration of the perimeter of an indoor environment in a reasonable amount of time. The avionics design and the guidance, navigation, and control algorithms used are discussed in detail and validated through flight tests.

A simple nonlinear filter for low-cost ground vehicle localization system

This paper introduces a simple and intuitive nonlinear observer for low-cost ground vehicle localization system, using measurements from an inertial measurement unit, two wheel speed sensors, and a GPS. Taking advantage of the nonholonomic constraints, the design of the observer takes into account imperfections of the embedded sensors measurements, such as slowly time-varying gyroscope biases or some uncertainty on the angle between the vehicles frame and the road, to estimate the attitude, velocity and position of a ground vehicle. Thanks to a simple nonlinear structure based on the theory of symmetry-preserving observers, the estimator is easy to tune, easy to implement, and well-behaved even at very low speed. Moreover, the proposed filter presents some guaranteed convergence properties when GPS is available. Simulations and experiments in urban area illustrate the good performances of this simple algorithm.

A Separation Principle on Lie Groups

Abstract For linear time-invariant systems, a separation principle holds: stable observer and stable state feedback can be designed for the time-invariant system, and the combined observer and feedback will be stable. For non-linear systems, a local separation principle holds around steady-states, as the linearized system is time-invariant. This paper addresses the issue of a nonlinear separation principle on Lie groups. For invariant systems on Lie groups, we prove there exists a large set of (time-varying) trajectories around which the linearized observer-controler system is time-invariant, as soon as a symmetry-preserving observer is used. Thus a separation principle holds around those trajectories. The theory is illustrated by a mobile robot example, and the developed ideas are then extended to a class of Lagrangian mechanical systems on Lie groups described by Euler-Poincare equations.

A Conflict Resolution Algorithm For Reduced Controller Taskload

This paper considers the con ict resolution problem arising from a large number of aircraft traversing a shared airspace. Aircraft are issued lateral and longitudinal shifts commands over their trajectory to resolve potential con icts. Lateral and longitudinal shifts given to each aircraft can be abstracted to represent the heading and speed changes over the trajectories. Through this formulation, the resulting con ict resolution algorithm can be formulated as a mixed-integer linear program solvable in real-time. In this model, the procedure aims to assign to each aircraft a sequence of maneuvers instead of a single one. This new method is based on a centralized algorithm with the goal of minimizing the total number of maneuvers issued by the controller while regularizing the trajectories.