Bio-inspired vision-based leader-follower formation flying in the presence of delays

Flocking starlings at dusk are known for the mesmerizing and intricate shapes they generate, as well as how fluid these shapes change. They seem to do this effortlessly. Real-life vision-based flocking has not been achieved in micro-UAVs (micro Unmanned Aerial Vehicles) to date. Towards this goal, we make three contributions in this paper: (i) we used a computational approach to develop a bio-inspired architecture for vision-based Leader-Follower formation flying on two micro-UAVs. We believe that the minimal computational cost of the resulting algorithm makes it suitable for object detection and tracking during high-speed flocking; (ii) we show that provided delays in the control loop of a micro-UAV are below a critical value, Kalman filter-based estimation algorithms are not required to achieve Leader-Follower formation flying; (iii) unlike previous approaches, we do not use external observers, such as GPS signals or synchronized communication with flock members. These three contributions could be useful in achieving vision-based flocking in GPS-denied environments on computationally-limited agents

Near-optimal deterministic filtering on the rotation group

Abstract—This paper considers the problem of obtaining minimum-energy state estimates for a system defined on the rotation group, SO(3). The signals of the system are modeled as purely deterministic signals. We derive a non-linear observer (“filter”) posed directly on SO(3) that respects the geometry of the group and achieves a performance that is close to optimal in the sense of minimizing an integral cost that is measuring the state energy. The performance of the proposed filter is demonstrated in simulations involving large initialization, process and measurement errors where the results are compared against a quaternion implementation of an Extended Kalman Filter (EKF). Our results indicate that the proposed filter achieves better robustness against a range of noise levels and initialization errors

Rigid Body Motion Estimation based on the Lagrange-d'Alembert Principle

Stable estimation of rigid body pose and velocities from noisy measurements, without any knowledge of the dynamics model, is treated using the Lagrange-d'Alembert principle from variational mechanics. With body-fixed optical and inertial sensor measurements, a Lagrangian is obtained as the difference between a kinetic energy-like term that is quadratic in velocity estimation error and the sum of two artificial potential functions; one obtained from a generalization of Wahba's function for attitude estimation and another which is quadratic in the position estimate error. An additional dissipation term that is linear in the velocity estimation error is introduced, and the Lagrange-d'Alembert principle is applied to the Lagrangian with this dissipation. This estimation scheme is discretized using discrete variational mechanics. The presented pose estimator requires optical measurements of at least three inertially fixed landmarks or beacons in order to estimate instantaneous pose. The discrete estimation scheme can also estimate velocities from such optical measurements. In the presence of bounded measurement noise in the vector measurements, numerical simulations show that the estimated states converge to a bounded neighborhood of the actual states.Comment: My earlier submitted manuscript (arXiv:1508.07671), is an extended version of this work, containing detailed proofs and more elaborated numerical simulations, currently under review in Automatica. This paper will be cited in the extended journal version (arXiv:1508.07671) upon publicatio

Robust mixed H-2/H∞ control for a class of nonlinear stochastic systems

The problem of mixed H2/H∞ control is considered for a class of uncertain discrete-time nonlinear stochastic systems. The nonlinearities are described by statistical means of the stochastic variables and the uncertainties are represented by deterministic norm-bounded parameter perturbations. The mixed H2/H∞ control problem is formulated in terms of the notion of exponentially mean-square quadratic stability and the characterisations of both the H2 control performance and the H∞ robustness performance. A new technique is developed to deal with the matrix trace terms arising from the stochastic nonlinearities and the well-known S-procedure is adopted to handle the deterministic uncertainities. A unified framework is established to solve the addressed mixed H2/H∞ control problem using a linear matrix inequality approach. Within such a framework, two additional optimisation problems are discussed, one is to optimise the H∞ robustness performance, and the other is to optimise the H2 control performance. An illustrative example is provided to demonstrate the effectiveness of the proposed method.This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant GR/S27658/01, the Nuffield Foundation of the UK under Grant NAL/00630/G and the Alexander von Humboldt Foundation of Germany, the National Natural Science Foundation of China under Grant 60474049 and the Fujian provincial Natural Science Foundation of China under Grant A0410012

A second order minimum-energy filter on the special orthogonal group

Abstract— This work documents a case study in the application of Mortensen’s nonlinear filtering approach to invariant systems on general Lie groups. In this paper, we consider the special orthogonal group SO(3) of all rotation matrices. We identify the exact form of the kinematics of the minimumenergy (optimal) observer on SO(3) and note that it depends on the Hessian of the value function of the associated optimal control problem. We derive a second order approximation of the dynamics of the Hessian by neglecting third order terms in the expansion of the dynamics. This yields a Riccati equation that together with the optimal observer equation form a second order minimum-energy filter on SO(3). The proposed filter is compared to the multiplicative extended Kalman filter (MEKF), arguably the industry standard for attitude estimation, by means of simulations. Our studies indicate superior transient and asymptotic tracking performance of the proposed filter as compared to the MEKF