Joris Gillis

Optimal periodic control of power harvesting tethered airplanes: How to fly fast without wind and without propellor?

This paper proposes reversed pumping as a strategy to keep tethered kites airborne in a wind-free condition without any on-board propulsion. In the context of kite power, it is shown to be a necessary addition to a rotational startup scheme. The enhanced scheme ultimately allows for injection into power harvesting orbits at high altitude, in case no wind is present near ground level. The need for reversed pumping is advocated with scaling laws, and is demonstrated in simulation by solving a proposed open-loop periodic optimal control problem. The obtained periodic orbits can be used as reference for feedback control.

A Computational Framework for Environment-Aware Robotic Manipulation Planning

In this paper, we present a computational framework for direct trajectory optimization of general manipulation systems with unspecified contact sequences, exploiting environmental constraints as a key tool to accomplish a task. Two approaches are presented to describe the dynamics of systems with contacts, which are based on a penalty formulation and on a velocity-based time-stepping scheme, respectively. In both cases, object and environment contact forces are included among the free optimization variables, and they are rendered consistent via suitably devised sets of complementarity conditions. To maximize computational efficiency, we exploit sparsity patterns in the linear algebra expressions generated during the solution of the optimization problem and leverage Algorithmic Differentiation to calculate derivatives. The benefits of the proposed methods are evaluated in three simulated planar manipulation tasks, where essential interactions with environmental constraints are automatically synthesized and opportunistically exploited.

A positive definiteness preserving discretization method for Lyapunov differential equations

Periodic Lyapunov differential equations can be used to formulate robust optimal periodic control problems for nonlinear systems. Typically, the added Lyapunov states are discretized in the same manner as the original states. This straightforward technique fails to guarantee conservation of positive-semidefiniteness of the Lyapunov matrix under discretization. This paper describes a discretization method, coined PDPLD, that does come with such a guarantee. The applicability is demonstrated at hand of a tutorial example, and is specifically suited for direct collocation methods.

Joint design of stochastically safe setpoints and controllers for nonlinear constrained systems by means of optimization

Abstract Implementing complex control schemes for a mechanically fragile and expensive system can be a risky undertaking. We can reduce the operational risks by a) identifying regions of state-space where the system is far from critical system bounds and exhibits natural stability, and b) designing a backup controller that keeps the system from crashing if we venture beyond those regions. We propose to maximize the safety-margin of the systems operational bounds, using a stochastic interpretation of the algebraic Lyapunov equation. This technique allows us to find optimally safe open-loop stable setpoints of the system. Next, we propose to add the parameters of a linear output feedback controller as optimization variables, such that setpoint and controller are jointly designed to yield the safest operational regimes. We demonstrate these methods on the application of rotational launch of tethered airplanes for power-generation.

Experimental validation of a combined global and local LPV system identification approach with ℓ 2,1 -norm regularization

This paper explores a combined global and local identification approach for linear parameter-varying systems. Ideally, the combined approach retains advantages of its two extremes - global and local - with the possibility to emphasize one or the other. Practically, it is prone to overfitting. This paper proposes a remedy based on the ℓ2,1-norm regularization, describes its implementation within the nonlinear least squares framework, and gives an experimental validation. The results show a substantial decrease in the Euclidean norm of the model parameters, which resulted in a significantly smoother frequency response function surface and in overall, less-deviating model behavior.