We propose a combinatorial method for computing explicit solutions to multi-parametric quadratic programs, which can be used to compute explicit control laws for linear model predictive control. In contrast to classical methods, which are based on geometrical adjacency, the proposed method is based on combinatorial adjacency. After introducing the notion of combinatorial adjacency, we show that the explicit solution forms a connected graph in terms of it. We then leverage this connectedness to propose an algorithm that computes the explicit solution. The purely combinatorial nature of the algorithm leads to computational advantages since it enables demanding geometrical operations (such as computing facets of polytopes) to be avoided. Compared with classical combinatorial methods, the proposed method requires fewer combinations to be considered by exploiting combinatorial connectedness. We show that an implementation of the proposed method can yield a speedup of about two orders of magnitude compared with state-of-the-art software packages such as MPT and POP.

This paper introduces a disturbance-parametrized (DP) robust lattice-based motion-planning framework for nonlinear systems affected by bounded disturbances. A key idea in this work is to rigorously exploit the available knowledge about the disturbance, starting already offline at the time when a library of DP motion primitives is computed and ending not before the motion has been executed online. Given an up-to-date-estimate of the disturbance, the lattice-based motion planner performs a graph search online, to non-conservatively compute a disturbance aware optimal motion plan with formally motivated margins to obstacles. This is done utilizing the DP motion primitives, around which tubes are generated utilizing a suitably designed robust controller. The sizes of the tubes are dependent on the upper bounds of the disturbance appearing in the error between the actual system trajectory and the DP nominal trajectory, which in turn along with the overall optimality of the plan is dependant on the user-selected resolution of the available disturbance estimates. Increasing the resolution of the disturbance parameter results in smaller sizes of tubes around the motion primitives and can significantly reduce the conservativeness compared to traditional approaches, thus increasing the performance of the computed motion plans. The proposed strategy is implemented on an Euler-Lagrange-based ship model which is affected by a significant wind disturbance and the efficiency of the strategy is validated through a suitable simulation example.

This letter considers the problem of detecting and tracking objects in a sequence of images. The problem is formulated in a filtering framework, using the output of object-detection algorithms as measurements. An extension to the filtering formulation is proposed that incorporates class information from the previous frame to robustify the classification. Further, the properties of the object-detection algorithm are exploited to quantify the uncertainty of the bounding box detection in each frame. The complete filtering method is evaluated on camera trap images of the four large Swedish carnivores, bear, lynx, wolf, and wolverine. The experiments show that the class tracking formulation leads to a more robust classification.

Optimal task and motion planning (TAMP) has seen an increase in interest in recent years. In this paper we propose methods for using numerical optimal control to improve upon a feasible solution to a TAMP rearrangement problem. The methods are extensions of existing improvement methods for pure motion planning. The first method poses an optimal control problem (OCP) to simultaneously improve all motions in the plan. The second method, which we denote multiple finite horizons (MFH), takes inspiration from finite horizon control and poses a sequence of finite horizon OCPs involving variables for the positions of temporary placements of movable objects as well as motions in the plan, such that after solving each problem a feasible plan is maintained and the plan cost is non-increasing after each step. The methods are evaluated on a TAMP problem for tractor-trailers in numerical experiments, and the results show that both methods improve the plan for the evaluated problems. The results also show that MFH can reduce the computation time compared to the first method, and that on one example problem it achieves plans of similar or better quality as when all the motions are optimized at the same time provided that the horizon length is sufficiently long.

Optimal task and motion planning (TAMP) has seen an increase in interest in recent years. An important performance bottleneck when solving such problems is that solving motion-planning problems for nonholonomic systems to (resolution) optimality is relatively costly, and when this has to be done a potentially large number of times, in the form of a subroutine, time quickly adds up. In this work, we significantly increase the efficiency of our previously presented optimal TAMP algorithm for rearrangement problems. The core idea that we introduce in this work is to use intermediary results from the motion planner to infer solutions to other related motion-planning problems that might be of interest to the overall TAMP problem. We also introduce the concept of equivalent states to recognize state-action pairs that require the solution of the same motion-planning problem in order to compute their associated cost. Evaluations on numerical examples considering rearrangement TAMP problems involving tractor-trailers show that the proposed strategies can significantly reduce the total computation time of the TAMP planner, as well as the number of motion-planning problems that are solved, and the number of candidate task plans that are computed.

lassifiers based on neural networks (nn) often lack a measure of uncertainty in the predicted class. We propose a method to estimate the probability mass function (pmf) of the different classes, as well as the covariance of the estimated pmf. First, a local linear approach is used during the training phase to recursively compute the covariance of the parameters in the nn. Secondly, in the classification phase, another local linear approach is used to propagate the covariance of the learned nn parameters to the uncertainty in the output of the last layer of the nn. This allows for an efficient Monte Carlo (mc) approach for; (i) estimating the pmf; (ii) calculating the covariance of the estimated pmf; and (iii) proper risk assessment and fusion of multiple classifiers. Two classical image classification tasks, i.e., mnist, and cfar10, are used to demonstrate the efficiency of the proposed method.

The uncertainty in the prediction calculated using the delta method for an over-parameterized (parametric) black-box model is shown to be larger or equal to the uncertainty in the prediction of a canonical (minimal) model. Equality holds if the additional parameters of the overparameterized model do not add flexibility to the model. As a conclusion, for an overparameterized black-box model, the calculated uncertainty in the prediction by the delta method is not underestimated. The results are shown analytically and are validated in a simulation experiment where the relationship between the normalized traction force and the wheel slip of a car is modelled using e.g., a neural network.

A case study of the use of reflections within the Applied physics and electrical engineering program at Linköping University is presented. Reflections have been used for several years and they are done at four stages in the program, in terms of reflections at the end of the Introductory course in year one, design-implement experiences in year three and five, and a reflection document that is the last component of the Master’s thesis. In the first three stages a project model is used to support the planning and execution of the project, and in the project model the project work ends with a reflection. In the reflection document connected to the Master’s thesis the student reflects upon both the thesis work itself and the entire education program, according to the sections and subsections of the CDIO Syllabus. The paper describes how the reflections are integrated in the program. Experiences from student perspective are collected in a small-scale study via interviews with students from year one and year five. 

Neural Networks (NNS) can solve very hard classification and estimation tasks but are less well suited to solve complex sensor fusion challenges, such as end-to-end control of autonomous vehicles. Nevertheless, NN can still be a powerful tool for particular sub-problems in sensor fusion. This would require a reliable and quantifiable measure of the stochastic uncertainty in the predictions that can be compared to classical sensor measurements. However, current NN'S output some figure of merit, that is only a relative model fit and not a stochastic uncertainty. We propose to embed the NN'S in a proper stochastic system identification framework. In the training phase, the stochastic uncertainty of the parameters in the (last layers of the) NN is quantified. We show that this can be done recursively with very few extra computations. In the classification phase, Monte-Carlo (MC) samples are used to generate a set of classifier outputs. From this set, a distribution of the classifier output is obtained, which represents a proper description of the stochastic uncertainty of the predictions. We also show how to use the calculated uncertainty for outlier detection by including an artificial outlier class. In this way, the NN fits a sensor fusion framework much better. We evaluate the approach on images of handwritten digits. The proposed method is shown to be on par with MC dropout, while having lower computational complexity, and the outlier detection almost completely eliminates false classifications.

Model predictive control (MPC) with linear cost function for hybrid systems requires the solution of a mixed-integer linear program (MILP) at each sampling time. The branch and bound (B&B) method is a commonly used tool for solving mixed-integer problems. In this work, we present an algorithm to exactly certify the computational complexity of a standard B&B-based MILP solver. By the proposed method, guarantees on worst-case complexity bounds, e.g., the worst-case iterations or size of the B&B tree, are provided. This knowledge is a fundamental requirement for the implementation of MPC in a real-time system. Different node selection strategies, including best-first, are considered when certifying the complexity of the B&B method. Furthermore, the proposed certification algorithm is extended to consider warm-starting of the inner solver in the B&B. We illustrate the usefulness of the proposed algorithm by comparing against the corresponding online MILP solver in numerical experiments using both cold-started and warm-started LP solvers.