Damian Frick

Drivetrain design optimization for electrically actuated systems via mixed integer programing

The proposed paper presents a method to optimally select components of a drivetrain for an electrically actuated machine. A simple mathematical model of the machine is established and inequality constraints which determine the choice of drivetrain components are formulated. Elements to be picked (namely, a motor, a gearbox, and a drive) are taken from a discrete set of data provided in the catalogs of industrial motors and drives manufacturers. By solving an optimization problem, a combination of components which both satisfy design requirements and minimize the total drivetrain cost is selected. The operation of the selected drivetrain is verified against the motor loadability curves. In addition, feasibility of other possible drivetrain configurations is checked and benchmarked with the optimal solution. Practical significance of the current work is demonstrated on a winch mechanism which is a popular part of many engineering applications, however, methods presented here could easily be adapted to other machines and industries. The results of the current work allow to reduce conservatism when designing actuation systems, while still satisfying the safety requirements specified by the designer. The system operating conditions are therefore effectively shifted to be closer to the constraints, which results in increasing the overall efficiency of the design and proving its cost-effectiveness.

Moving horizon estimation for induction motors

In this paper we present a systematic model based approach to state and parameter estimation for the induction machine. We use moving horizon estimation (MHE), an optimization based scheme that yields excellent performance and can be used with aggressive controllers such as model predictive controllers. The past measurements within a given horizon are combined with an a priori estimate based on the induction machine model. Under mild assumptions, this yields a maximum-likelihood estimate of the states and parameters over the horizon. The resulting optimization problem is solved using the Generalized Gauss-Newton method. A real-time iteration approach can be used to significantly reduce execution and response times. Simulation results indicate superior performance of MHE over established methods such as model reference adaptive system (MRAS) or Extended Kalman Filter (EKF). Real-time feasibility of the proposed approach up to 3.5 kHz sampling rate is demonstrated by experiments on a state-of-the-art embedded control platform.

Robust Control Policies Given Formal Specifications in Uncertain Environments

We consider robust control synthesis for linear systems with complex specifications that are affected by uncertain disturbances. This letter is motivated by autonomous systems interacting with partially known, time-varying environments. Given a specification in bounded linear temporal logic, we propose a method to synthesize control policies that fulfill the specification for all considered disturbances, where the disturbances affect the atomic propositions of the specification. Our approach relies on introducing affine disturbance feedback policies and casting the problem as a bilinear optimization problem. We introduce an inner approximation of the constraint set leading to a mixed-integer quadratic program that can be solved using general-purpose solvers. The framework is demonstrated on a numerical case study with applications to autonomous driving.

ADMM prescaling for model predictive control

The alternating direction method of multipliers (ADMM) is an iterative first order optimization algorithm for solving convex problems such as the ones arising in linear model predictive control (MPC). The ADMM convergence rate depends on a penalty (or step size) parameter that is often difficult to choose. In this paper we present an ADMM prescaling strategy for strongly convex quadratic problems with linear equality and box constraints. We apply this prescaling procedure to MPC-type problems with diagonal objective, which results in an elimination of the penalty parameter. Moreover, we illustrate our results in a numerical study that demonstrates the benefits of prescaling.

From Uncertainty Data to Robust Policies for Temporal Logic Planning

We consider the problem of synthesizing robust disturbance feedback policies for systems performing complex tasks. We formulate the tasks as linear temporal logic specifications and encode them into an optimization framework via mixed-integer constraints. Both the system dynamics and the specifications are known but affected by uncertainty. The distribution of the uncertainty is unknown, however realizations can be obtained. We introduce a data-driven approach where the constraints are fulfilled for a set of realizations and provide probabilistic generalization guarantees as a function of the number of considered realizations. We use separate chance constraints for the satisfaction of the specification and operational constraints. This allows us to quantify their violation probabilities independently. We compute disturbance feedback policies as solutions of mixed-integer linear or quadratic optimization problems. By using feedback we can exploit information of past realizations and provide feasibility for a wider range of situations compared to static input sequences. We demonstrate the proposed method on two robust motion-planning case studies for autonomous driving.

An Evolutionary Algorithm for the Block Stacking Problem

How has a stack of n blocks to be arranged in order to maximizeits overhang over a table edge while being stable? This questioncan be seen as an example application for applied statics and at the sametime leads to a challenging optimization problem that was discussed recentlyin two theoretical studies. Here, we address this problem by designing an evolutionary algorithm;the proposed method is applied to two instances of the block stackingproblem, maximizing the overhang for 20 and 50 block stacks. The studydemonstrates that the stacking problem is worthwhile to be investigatedin the context of randomized search algorithms: it represents an abstract,but still demanding instance of many real-world applications. Furthermore,the proposed algorithm may become useful in empirically testingthe tightness of theoretical upper bounds proposed for this problem.

An evolutionary algorithm for the block stacking problem

How has a stack of n blocks to be arranged in order to maximizeits overhang over a table edge while being stable? This questioncan be seen as an example application for applied statics and at the sametime leads to a challenging optimization problem that was discussed recentlyin two theoretical studies. Here, we address this problem by designing an evolutionary algorithm;the proposed method is applied to two instances of the block stackingproblem, maximizing the overhang for 20 and 50 block stacks. The studydemonstrates that the stacking problem is worthwhile to be investigatedin the context of randomized search algorithms: it represents an abstract,but still demanding instance of many real-world applications. Furthermore,the proposed algorithm may become useful in empirically testingthe tightness of theoretical upper bounds proposed for this problem.