E. de Weerdt

Optimization of Human Perception Modeling Using Interval Analysis

Estimating multi-modal pilot model parameters from experiment or simulation data requires solving a global nonlinear optimization problem with many local minimums. Using the traditional parameter estimation techniques, finding the global optimum is dependent on the initial parameter estimate. In this paper the parameter optimization is performed by using the theory of interval analysis, which deals with intervals of numbers instead of crisp numbers. Interval analysis has been shown to be an excellent tool for global nonlinear optimization and it can guarantee that the global minimum of the cost function is found. The interval optimization method is applied to data from an experiment investigating the role of optic flow and the influence of physical motion cues during control of self-motion. A comparison between gradient based and interval optimization shows that the interval method can find the global minimum of the cost function, resulting in the optimal set of model parameters, while the gradient-based method often converges to a local minimum.

Neural Network Output Optimization Using Interval Analysis

The problem of output optimization within a specified input space of neural networks (NNs) with fixed weights is discussed in this paper. The problem is (highly) nonlinear when nonlinear activation functions are used. This global optimization problem is encountered in the reinforcement learning (RL) community. Interval analysis is applied to guarantee that all solutions are found to any degree of accuracy with guaranteed bounds. The major drawbacks of interval analysis, i.e., dependency effect and high-computational load, are both present for the problem of NN output optimization. Taylor models (TMs) are introduced to reduce these drawbacks. They have excellent convergence properties for small intervals. However, the dependency effect still remains and is even made worse when evaluating large input domains. As an alternative to TMs, a different form of polynomial inclusion functions, called the polynomial set (PS) method, is introduced. This new method has the property that the bounds on the network output are tighter or at least equal to those obtained through standard interval arithmetic (IA). Experiments show that the PS method outperforms the other methods for the NN output optimization problem.

The appearance variation cue for obstacle avoidance

The appearance variation cue captures the variation in texture in a single image. Its use for obstacle avoidance is based on the assumption that there is less such variation when the camera is close to an obstacle. For videos of approaching frontal obstacles, it is demonstrated that combining the cue with optic flow leads to better performance than using either cue alone. In addition, the cue is successfully used to control the 16-g flapping-wing micro air vehicle DelFly II.

Adaptive Nonlinear Dynamic Inversion for Spacecraft Attitude Control with Fuel Sloshing

Through the years researchers have developed many different forms of spacecraft attitude controllers ranging from simple linear controllers to highly nonlinear ones. For Nonlinear Dynamic Inversion controllers, the tracking performance depends on the model on the plant dynamics. In this paper we explore the response of a controlled satellite with liquid sloshing and apply neural networks to create an adaptive NDI controller. Feedforward neural networks are used to model any unknown system dynamics. The fuel motion is modeled using a mechanical model often used in the field of liquid sloshing. The equations of motion of the combined satellite/fuel system are derived and a simulation is constructed. Results in the form of tracking performance for both the standard and the adaptive NDI controller will be shown using a model of SloshSat, an experimental liquid sloshing satellite of ESA and the Netherlands Agency for Aerospace Programs. The results will demonstrate that an adaptive controller is indeed needed and that the proposed NDI controller with neural network is capable of excellent reference tracking in case of fuel sloshing.

Terminal Area Energy Management Trajectory Optimization using Interval Analysis

*† ‡ § ¶ A new trajectory optimization algorithm for the Terminal Area Energy Management phase is presented based on interval analysis. Through a branch and bound strategy, interval analysis is able to yield guaranteed and rigorous bounds on the global minimum, i.e., on the best possible trajectory. It does so by using intervals instead of crisp numbers and interval arithmetic instead of crisp arithmetic. Even the numerical roundoff errors introduced by computers are considered and do not affect the rigor of the solution. The steering commands of the vehicle are optimized in order to regulate the kinematic and potential energies of the vehicle while aligning it with the runway. Normalized total energy is used as independent variable. Additionally, an interval algorithm for determining the initial gate of the Terminal Area Energy Management phase is presented, which is mathematically guaranteed to enclose the true solution and that facilitates the execution of sensitivity analyses. Nomenclature α = angle-of-attack subsonic α = constant angle-of-attack during the subsonic regime β = sideslip angle CD = aerodynamic drag coefficient CL = aerodynamic lift coefficient χr = vehicle’s heading angle relative to the runway’s centerline J e = stopping criterion (user-defined) E = normalized total energy of the vehicle γ = flight-path angle g = gravity’s acceleration h = altitude

Level Set Method Based on Interval Analysis

Level set methods are used to determine the reachable set for a given time domain. In the aerospace industry level set methods are used to determine for example flight envelopes. A new level set method is presented which uses interval analysis to give guaranteed bounds on the solution. Unlike the current grid-based methods the new method does not use a grid and has a lower computation complexity. The guaranteed bounds are a product of using interval analysis. Both an inner and outer bound can be derived. The time step and accuracy are easily controlled by the user and can be automatically adapted during processing. Initial tests show that the new method provides accurate solutions and does so using lower computational loads. The new method is tested on a one-dimensional and a two-dimensional test bed, showing that correct outer bounds of the reachable sets can be computed.

Optimization of Human Perception Modeling using Interval Analysis

Estimating multimodal pilot model parameters from experimental data requires solving a global nonlinear optimization problem with many local minimums. With traditional parameter estimation techniques, the solution depends on the initial parameter estimate and a local optimum can be found instead of the global optimum. In this paper, the parameter optimization is performed by using the theory of interval analysis, which describes the properties of intervals of numbers instead of crisp numbers. Interval analysis has been shown to be an excellent tool for global nonlinear optimization and it can guarantee that the global minimum of the cost function is found. The interval optimization method is applied to data from an experiment investigating the role of optic flow and the influence of physical motion cues during control of self-motion. A comparison between gradient-based and interval optimization shows that the interval method can find the global minimum of the cost function, resulting in the optimal set of model parameters, whereas gradient-based methods often converge to a local minimum.

Trajectory Optimization Based on Interval Analysis

Trajectory optimization has been a large field of research for many years. The drawback is that for non-convex, constrained problems practically all available solvers cannot guarantee that the globally optimal trajectory is found. Interval analysis based solvers however can provide this guarantee. Interval analysis has been applied to trajectory optimization before, but the previously presented methods suffered from major drawbacks which limited their application to small scale problems. In this paper a new interval based method is introduced which incorporates state parameterization to prevent explicit integration. The performance of the proposed method is demonstrated by applying it to a spacecraft formation flying optimization problem. The results are compared with a gradient based solver and it is shown that the interval method is guaranteed to find the global optimal solution. Finally the first steps for another new trajectory optimization method based on interval analysis and direct collocation are presented.