Traditionally, robots are regarded as universal motion generation machines. They are designed mainly by kinematics considerations while the desired dynamics is imposed by strong actuators and high-rate control loops. As an alternative, one can first consider the robot's intrinsic dynamics and optimize it in accordance with the desired tasks. Therefore, one needs to better understand intrinsic, uncontrolled dynamics of robotic systems. In this paper we focus on periodic orbits, as fundamental dynamic properties with many practical applications. Algebraic topology and differential geometry provide some fundamental statements about existence of periodic orbits. As an example, we present periodic orbits of the simplest multi-body system: the double-pendulum in gravity. This simple system already displays a rich variety of periodic orbits. We classify these into three classes: toroidal orbits, disk orbits and nonlinear normal modes. Some of these we found by geometrical insights and some by numerical simulation and sampling.
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Computational Intelligence (CI) techniques have shown great potential as a surrogate model of expensive physics simulation, with demonstrated ability to make fast predictions, albeit at the expense of accuracy in some cases. For many scientific and engineering problems involving geometrical design, it is desirable for the surrogate models to precisely describe the change in geometry and predict the consequences. In that context, we develop graph neural networks (GNNs) as fast surrogate models for physics simulation, which allow us to directly train the models on 2/3D geometry designs that are represented by an unstructured mesh or point cloud, without the need for any explicit or hand-crafted parameterization. We utilize an encoder-processor-decoder-type architecture which can flexibly make prediction at both node level and graph level. The performance of our proposed GNN-based surrogate model is demonstrated on 2 example applications: feature designs in the domain of additive engineering and airfoil design in the domain of aerodynamics. The models show good accuracy in their predictions on a separate set of test geometries after training, with almost instant prediction speeds, as compared to O(hour) for the high-fidelity simulations required otherwise.
Probabilistic programs are typically normal-looking programs describing posterior probability distributions. They intrinsically code up randomized algorithms and have long been at the heart of modern machine learning and approximate computing. We explore the theory of generating functions [19] and investigate its usage in the exact quantitative reasoning of probabilistic programs. Important topics include the exact representation of program semantics [13], proving exact program equivalence [5], and -- as our main focus in this extended abstract -- exact probabilistic inference. In probabilistic programming, inference aims to derive a program's posterior distribution. In contrast to approximate inference, inferring exact distributions comes with several benefits [8], e.g., no loss of precision, natural support for symbolic parameters, and efficiency on models with certain structures. Exact probabilistic inference, however, is a notoriously hard task [6,12,17,18]. The challenges mainly arise from three program constructs: (1) unbounded while-loops and/or recursion, (2) infinite-support distributions, and (3) conditioning (via posterior observations). We present our ongoing research in addressing these challenges (with a focus on conditioning) leveraging generating functions and show their potential in facilitating exact probabilistic inference for discrete probabilistic programs.
The intrinsic biomechanical characteristic of the human upper limb plays a central role in absorbing the interactive energy during physical human-robot interaction (pHRI). We have recently shown that based on the concept of ``Excess of Passivity (EoP)," from nonlinear control theory, it is possible to decode such energetic behavior for both upper and lower limbs. The extracted knowledge can be used in the design of controllers for optimizing the transparency and fidelity of force fields in human-robot interaction and in haptic systems. In this paper, for the first time, we investigate the frequency behavior of the passivity map for the upper limb when the muscle co-activation was controlled in real-time through visual electromyographic feedback. Five healthy subjects (age: 27 +/- 5) were included in this study. The energetic behavior was evaluated at two stimulation frequencies at eight interaction directions over two controlled muscle co-activation levels. Electromyography (EMG) was captured using the Delsys Wireless Trigno system. Results showed a correlation between EMG and EoP, which was further altered by increasing the frequency. The proposed energetic behavior is named the Geometric MyoPassivity (GMP) map. The findings indicate that the GMP map has the potential to be used in real-time to quantify the absorbable energy, thus passivity margin of stability for upper limb interaction during pHRI.
Autonomous robots are required to reason about the behaviour of dynamic agents in their environment. To this end, many approaches assume that causal models describing the interactions of agents are given a priori. However, in many application domains such models do not exist or cannot be engineered. Hence, the learning (or discovery) of high-level causal structures from low-level, temporal observations is a key problem in AI and robotics. However, the application of causal discovery methods to scenarios involving autonomous agents remains in the early stages of research. While a number of methods exist for performing causal discovery on time series data, these usually rely upon assumptions such as sufficiency and stationarity which cannot be guaranteed in interagent behavioural interactions in the real world. In this paper we are applying contemporary observation-based temporal causal discovery techniques to real world and synthetic driving scenarios from multiple datasets. Our evaluation demonstrates and highlights the limitations of state of the art approaches by comparing and contrasting the performance between real and synthetically generated data. Finally, based on our analysis, we discuss open issues related to causal discovery on autonomous robotics scenarios and propose future research directions for overcoming current limitations in the field.
We consider wave propagation problems over 2-dimensional domains with piecewise-linear boundaries, possibly including scatterers. Under the assumption that the initial conditions and forcing terms are radially symmetric and compactly supported (which is common in applications), we propose an approximation of the propagating wave as the sum of some special nonlinear space-time functions: each term in this sum identifies a particular ray, modeling the result of a single reflection or diffraction effect. We describe an algorithm for identifying such rays automatically, based on the domain geometry. To showcase our proposed method, we present several numerical examples, such as waves scattering off wedges and waves propagating through a room in presence of obstacles.
In statistics, independent, identically distributed random samples do not carry a natural ordering, and their statistics are typically invariant with respect to permutations of their order. Thus, an $n$-sample in a space $M$ can be considered as an element of the quotient space of $M^n$ modulo the permutation group. The present paper takes this definition of sample space and the related concept of orbit types as a starting point for developing a geometric perspective on statistics. We aim at deriving a general mathematical setting for studying the behavior of empirical and population means in spaces ranging from smooth Riemannian manifolds to general stratified spaces. We fully describe the orbifold and path-metric structure of the sample space when $M$ is a manifold or path-metric space, respectively. These results are non-trivial even when $M$ is Euclidean. We show that the infinite sample space exists in a Gromov-Hausdorff type sense and coincides with the Wasserstein space of probability distributions on $M$. We exhibit Fr\'echet means and $k$-means as metric projections onto 1-skeleta or $k$-skeleta in Wasserstein space, and we define a new and more general notion of polymeans. This geometric characterization via metric projections applies equally to sample and population means, and we use it to establish asymptotic properties of polymeans such as consistency and asymptotic normality.
Motivated by the success of Bayesian optimisation algorithms in the Euclidean space, we propose a novel approach to construct Intrinsic Bayesian optimisation (In-BO) on manifolds with a primary focus on complex constrained domains or irregular-shaped spaces arising as submanifolds of R2, R3 and beyond. Data may be collected in a spatial domain but restricted to a complex or intricately structured region corresponding to a geographic feature, such as lakes. Traditional Bayesian Optimisation (Tra-BO) defined with a Radial basis function (RBF) kernel cannot accommodate these complex constrained conditions. The In-BO uses the Sparse Intrinsic Gaussian Processes (SIn-GP) surrogate model to take into account the geometric structure of the manifold. SInGPs are constructed using the heat kernel of the manifold which is estimated as the transition density of the Brownian Motion on manifolds. The efficiency of In-BO is demonstrated through simulation studies on a U-shaped domain, a Bitten torus, and a real dataset from the Aral sea. Its performance is compared to that of traditional BO, which is defined in Euclidean space.
Large Language Models (LLMs) handle physical commonsense information inadequately. As a result of being trained in a disembodied setting, LLMs often fail to predict an action's outcome in a given environment. However, predicting the effects of an action before it is executed is crucial in planning, where coherent sequences of actions are often needed to achieve a goal. Therefore, we introduce the multi-modal task of predicting the outcomes of actions solely from realistic sensory inputs (images and text). Next, we extend an LLM to model latent representations of objects to better predict action outcomes in an environment. We show that multi-modal models can capture physical commonsense when augmented with visual information. Finally, we evaluate our model's performance on novel actions and objects and find that combining modalities help models to generalize and learn physical commonsense reasoning better.
As knowledge graph has the potential to bridge the gap between commonsense knowledge and reasoning over actionable capabilities of mobile robotic platforms, incorporating knowledge graph into robotic system attracted increasing attention in recent years. Previously, graph visualization has been used wildly by developers to make sense of knowledge representations. However, due to lacking the link between abstract knowledge of the real-world environment and the robot's actions, transitional visualization tools are incompatible for expert-user to understand, test, supervise and modify the graph-based reasoning system with the embodiment of the robots. Therefore, we developed an interface which enables robotic experts to send commands to the robot in natural language, then interface visualizes the procedures of the robot mapping the command to the functions for querying in the commonsense knowledge database, links the result to the real world instances in a 3D map and demonstrate the execution of the robot from the first-person perspective of the robot. After 3 weeks of usage of the system by robotic experts in their daily development, some feedback was collected, which provides insight for designing such systems.
Advances in artificial intelligence often stem from the development of new environments that abstract real-world situations into a form where research can be done conveniently. This paper contributes such an environment based on ideas inspired by elementary Microeconomics. Agents learn to produce resources in a spatially complex world, trade them with one another, and consume those that they prefer. We show that the emergent production, consumption, and pricing behaviors respond to environmental conditions in the directions predicted by supply and demand shifts in Microeconomics. We also demonstrate settings where the agents' emergent prices for goods vary over space, reflecting the local abundance of goods. After the price disparities emerge, some agents then discover a niche of transporting goods between regions with different prevailing prices -- a profitable strategy because they can buy goods where they are cheap and sell them where they are expensive. Finally, in a series of ablation experiments, we investigate how choices in the environmental rewards, bartering actions, agent architecture, and ability to consume tradable goods can either aid or inhibit the emergence of this economic behavior. This work is part of the environment development branch of a research program that aims to build human-like artificial general intelligence through multi-agent interactions in simulated societies. By exploring which environment features are needed for the basic phenomena of elementary microeconomics to emerge automatically from learning, we arrive at an environment that differs from those studied in prior multi-agent reinforcement learning work along several dimensions. For example, the model incorporates heterogeneous tastes and physical abilities, and agents negotiate with one another as a grounded form of communication.
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