Graph Neural Networks (GNNs) increasingly support intelligent, data-driven management of critical urban infrastructure, including water distribution networks. Positional encodings (PEs) enhance GNN expressiveness and the integration of attention mechanisms, yet the relative benefits of geo-located versus generic PEs remain unclear. In this work, we provide the first systematic evaluation of both classes of PEs on largescale pressure estimation tasks across eight real-world water networks. Contrary to common assumptions, we find that generic PEs can match or surpass geo-located methods, achieving up to a 60 % reduction in prediction error over a state-of-the-art baseline. Through t-SNE visualizations, we show that PEs encode semantic structural cues beyond spatial position, explaining the performance of methods not relying on geographic coordinates. We further analyze their behavior in transductive, zero-shot, and transfer-learning settings, revealing differing generalization characteristics important for scalable intelligent environment deployments. Our findings demonstrate that effective PE design can substantially improve the resilience, efficiency, and autonomy of smart water infrastructure which are key components in future intelligent environments. Our code is available at https://github.com/danielSe04/PE-for-GNN-in-water-infastructure.

Embedding elastic elements into legged robots through mechanical design enables highly efficient oscillating patterns that resemble natural gaits. However, current trajectory planning techniques miss the opportunity of taking advantage of these natural motions. This work proposes a locomotion planning method that aims to unify traditional trajectory generation with modal oscillations. Our method utilizes task-space linearized modes for generating center of mass trajectories on the sagittal plane. We then use nonlinear optimization to find the gait timings that match these trajectories within the Divergent Component of Motion planning framework. This way, we can robustly translate the modes-aware centroidal motions into joint coordinates. We validate our approach with promising results and insights through experiments on a compliant quadrupedal robot.

The paper addresses the static balancing and walking of elastically actuated legged robots. The control is realized by commanding the motor positions only and exploiting the bijective relation between motor and link positions at equilibrium under static external forces. The approach is formulated in a quite general framework first. The main implementation contribution is the definition of a body coordinate system and of an appropriate set of constraints, which leads to a fully determined system of equations. In addition to the desired COM and the vertical foot positions, which are defined by the walking task and the terrain, the imposed constraints are related to distances between individual legs. The controller is experimentally validated on a compliantly actuated quadruped.

Motion planning for fast locomotion of compliantly actuated robotic legs is generally considered to be a challenging issue, posing considerable real-time problems. This is at least the case if time-continuous trajectories need to be generated online. In this paper we take advantage of a simple controller structure, which reduces the motion planning to a discrete-time planning problem, in which only a small set of input parameters need to be determined for each step. We show that for a planar leg with serial elastic actuation, hopping on a ground with stairs of irregular length and height can be planned online, based on a parameter mapping which has been learned in a data-driven manner by performing hopping trials with an adaptive exploration algorithm to evenly sample the parameter space. Experiments on a planar hopping leg prototype validate the approach.

We address the operation of robotic legs with intrinsic elasticity in hopping cycles determined by the mechanical resonant properties of the system. This ensures energy efficiency and high jumping velocity and distance. Recently, we have shown in simulation that a simple, biologically inspired bang-bang controller operating in the local coordinate of the first resonant mode leads to limit cycles which are robust with respect to leg model uncertainties and ground properties. In this paper we address the velocity control of the hopping and the planning of the bang-bang control parameters for the case that the systems should not move at steady state velocity, but should have different step lengths and heights. We exploit the discrete structure and the small number of parameters of the controller to develop a fast optimization procedure for generating an arbitrary sequence of steps. This approach can provide high motion performance, robustness and substantial computational time saving compared to continuous trajectory and controller gain planning. The stationary and the aperiodic hopping is validated by experiments on a new planar elastic leg.

The paper addresses path planning for a redundant robot arm that is maneuvering in confined spaces, where neither an explicit model nor external perception of the possibly frequently changing environment is available. Our approach is rather solely based on data from kinesthetic demonstrations of feasible configurations provided by a user. The key challenge is to create a graph-based representation of the demonstrated free space incrementally and online by means of an specifically tailored instantaneous topological map at runtime. Subsequent application of standard graph-based planning in combination with a learned generalization of the demonstrated redundancy resolution then enables the robot to safely move in the realm of the demonstrated task space areas. This model-free approach greatly enhances configurability and flexibility of the robot for assistance applications, where movement capabilities need to be realized without explicit programming.

The goal of this paper is to provide the required foundations for establishing free theorems -- statements about program equivalence, guaranteed by polymorphic types -- for the functional-logic programming language Curry. For the sake of presentation we restrict ourselves to a language fragment that we call CuMin, and that has the characteristic features of Curry (both functional and logic). We present a new denotational semantics based on partially ordered sets without limits. We then introduce an intermediate language called SaLT that is essentially a lambda-calculus extended with an abstract set type, and again give a denotational semantics. We show that the standard (logical relations) techniques can be applied to obtain a general parametricity theorem for SaLT and derive free theorems from it. Via a translation from CuMin to SaLT that fits the respective semantics, we then derive free theorems for CuMin.

Encapsulated search is a key feature of (functional) logic languages. It allows the programmer to access and process different results of a non-deterministic computation within a program. Unfortunately, due to advanced operational features (lazy evaluation, partial values, infinite structures), there is no straightforward definition of the semantics of encapsulated search in functional logic languages. As a consequence, various proposals and implementations are available but a rigorous definition covering all semantical aspects does not exist. In this paper, we analyze the requirements of encapsulated search in a functional logic language like Curry and provide a comprehensive definition that covers weak encapsulation, a modular form of encapsulation, as well as nested applications of search operators. We set up a denotational semantics that distinguishes non-termination and different levels of failures in a computation. The semantics is also the basis of a practical implementation of search operators in the functional logic language Curry.

Circular functional programs (necessarily evaluated lazily) have been used as algorithmic tools, as attribute grammar implementations, and as target for program transformation techniques. Classically, Richard Bird [1984] showed how to transform certain multitraversal programs (which could be evaluated strictly or lazily) into one-traversal ones using circular bindings. Can we go the other way, even for programs that are not in the image of his technique? That is the question we pursue in this paper. We develop an approach that on the one hand lets us deal with typical examples corresponding to attribute grammars, but on the other hand also helps to derive new algorithms for problems not previously in reach.

In this paper we show how to efficiently check whether a polymorphic function is minimally strict. A function is minimally strict if it is the minimal element of a specific less-strict ordering. We prove that we can check whether two polymorphic functions are related by the less-strict ordering by either checking it a) for an arbitrary monomorphic instance of the functions or b) for all shapes of the functions' argument type. A shape is a value of a monomorphic instance of a polymorphic data type where each polymorphic component is replaced by an element that identifies its position in the data structure. In contrast to recent publications that characterize polymorphic functions by monomorphic instances we consider non-termination and selective strictness, ie a language closer to Haskell.