Yusuke Tanaka

Alexander Schperberg, Yusuke Tanaka, Stefano Di Cairano et al.

This paper presents the MOBIUS platform, a bipedal robot capable of walking, crawling, climbing, and rolling. MOBIUS features four limbs, two 6-DoF arms with two-finger grippers for manipulation and climbing, and two 4-DoF legs for locomotion--enabling smooth transitions across diverse terrains without reconfiguration. A hybrid control architecture combines reinforcement learning for locomotion and force control for compliant contact interactions during manipulation. A high-level MIQCP planner autonomously selects locomotion modes to balance stability and energy efficiency. Hardware experiments demonstrate robust gait transitions, dynamic climbing, and full-body load support via pinch grasp. Overall, MOBIUS demonstrates the importance of tight integration between morphology, high-level planning, and control to enable mobile loco-manipulation and grasping, substantially expanding its interaction capabilities, workspace, and traversability.

Tomoharu Iwata, Yusuke Tanaka, Naonori Ueda

We propose a neural network-based meta-learning method to efficiently solve partial differential equation (PDE) problems. The proposed method is designed to meta-learn how to solve a wide variety of PDE problems, and uses the knowledge for solving newly given PDE problems. We encode a PDE problem into a problem representation using neural networks, where governing equations are represented by coefficients of a polynomial function of partial derivatives, and boundary conditions are represented by a set of point-condition pairs. We use the problem representation as an input of a neural network for predicting solutions, which enables us to efficiently predict problem-specific solutions by the forwarding process of the neural network without updating model parameters. To train our model, we minimize the expected error when adapted to a PDE problem based on the physics-informed neural network framework, by which we can evaluate the error even when solutions are unknown. We demonstrate that our proposed method outperforms existing methods in predicting solutions of PDE problems.

Yuki Shirai, Xuan Lin, Alexander Schperberg et al.

While motion planning of locomotion for legged robots has shown great success, motion planning for legged robots with dexterous multi-finger grasping is not mature yet. We present an efficient motion planning framework for simultaneously solving locomotion (e.g., centroidal dynamics), grasping (e.g., patch contact), and contact (e.g., gait) problems. To accelerate the planning process, we propose distributed optimization frameworks based on Alternating Direction Methods of Multipliers (ADMM) to solve the original large-scale Mixed-Integer NonLinear Programming (MINLP). The resulting frameworks use Mixed-Integer Quadratic Programming (MIQP) to solve contact and NonLinear Programming (NLP) to solve nonlinear dynamics, which are more computationally tractable and less sensitive to parameters. Also, we explicitly enforce patch contact constraints from limit surfaces with micro-spine grippers. We demonstrate our proposed framework in the hardware experiments, showing that the multi-limbed robot is able to realize various motions including free-climbing at a slope angle 45° with a much shorter planning time.

Yusuke Tanaka, Toshiyuki Tanaka, Tomoharu Iwata et al.

Aggregate data often appear in various fields such as socio-economics and public security. The aggregate data are associated not with points but with supports (e.g., spatial regions in a city). Since the supports may have various granularities depending on attributes (e.g., poverty rate and crime rate), modeling such data is not straightforward. This article offers a multi-output Gaussian process (MoGP) model that infers functions for attributes using multiple aggregate datasets of respective granularities. In the proposed model, the function for each attribute is assumed to be a dependent GP modeled as a linear mixing of independent latent GPs. We design an observation model with an aggregation process for each attribute; the process is an integral of the GP over the corresponding support. We also introduce a prior distribution of the mixing weights, which allows a knowledge transfer across domains (e.g., cities) by sharing the prior. This is advantageous in such a situation where the spatially aggregated dataset in a city is too coarse to interpolate; the proposed model can still make accurate predictions of attributes by utilizing aggregate datasets in other cities. The inference of the proposed model is based on variational Bayes, which enables one to learn the model parameters using the aggregate datasets from multiple domains. The experiments demonstrate that the proposed model outperforms in the task of refining coarse-grained aggregate data on real-world datasets: Time series of air pollutants in Beijing and various kinds of spatial datasets from New York City and Chicago.

Alexander Schperberg, Yusuke Tanaka, Feng Xu et al.

Achieving highly accurate dynamic or simulator models that are close to the real robot can facilitate model-based controls (e.g., model predictive control or linear-quadradic regulators), model-based trajectory planning (e.g., trajectory optimization), and decrease the amount of learning time necessary for reinforcement learning methods. Thus, the objective of this work is to learn the residual errors between a dynamic and/or simulator model and the real robot. This is achieved using a neural network, where the parameters of a neural network are updated through an Unscented Kalman Filter (UKF) formulation. Using this method, we model these residual errors with only small amounts of data -- a necessity as we improve the simulator/dynamic model by learning directly from real-world operation. We demonstrate our method on robotic hardware (e.g., manipulator arm, and a wheeled robot), and show that with the learned residual errors, we can further close the reality gap between dynamic models, simulations, and actual hardware.

Alexander Schperberg, Yusuke Tanaka, Saviz Mowlavi et al.

State estimation for legged robots is challenging due to their highly dynamic motion and limitations imposed by sensor accuracy. By integrating Kalman filtering, optimization, and learning-based modalities, we propose a hybrid solution that combines proprioception and exteroceptive information for estimating the state of the robot's trunk. Leveraging joint encoder and IMU measurements, our Kalman filter is enhanced through a single-rigid body model that incorporates ground reaction force control outputs from convex Model Predictive Control optimization. The estimation is further refined through Gated Recurrent Units, which also considers semantic insights and robot height from a Vision Transformer autoencoder applied on depth images. This framework not only furnishes accurate robot state estimates, including uncertainty evaluations, but can minimize the nonlinear errors that arise from sensor measurements and model simplifications through learning. The proposed methodology is evaluated in hardware using a quadruped robot on various terrains, yielding a 65% improvement on the Root Mean Squared Error compared to our VIO SLAM baseline. Code example: https://github.com/AlexS28/OptiState

Takeshi Koshizuka, Masahiro Fujisawa, Yusuke Tanaka et al.

In this paper, we explores the expressivity and trainability of the Fourier Neural Operator (FNO). We establish a mean-field theory for the FNO, analyzing the behavior of the random FNO from an edge of chaos perspective. Our investigation into the expressivity of a random FNO involves examining the ordered-chaos phase transition of the network based on the weight distribution. This phase transition demonstrates characteristics unique to the FNO, induced by mode truncation, while also showcasing similarities to those of densely connected networks. Furthermore, we identify a connection between expressivity and trainability: the ordered and chaotic phases correspond to regions of vanishing and exploding gradients, respectively. This finding provides a practical prerequisite for the stable training of the FNO. Our experimental results corroborate our theoretical findings.

Yeang Makara, Yusuke Tanaka, Takashi Matsubara et al.

The modeling and simulation of infinite-dimensional Hamiltonian systems are central problems in mathematical physics and engineering, however they pose significant computational and structural challenges for standard data-driven architectures. In this work, we introduce the Symplectic Neural Operator, a neural operator architecture designed to preserve the symplectic structure intrinsic to Hamiltonian PDEs. We provide a theoretical characterization of their symplecticity and establish a rigorous long-term stability result based on the combination of symplectic structure preservation and learning accuracy. Numerical experiments on canonical Hamiltonian PDEs corroborate this theoretical result and show that SNOs exhibit improved energy behavior compared with non-structure-preserving neural operators.

Yoshiaki Takimoto, Yusuke Tanaka, Tomoharu Iwata et al.

Human activities generate various event sequences such as taxi trip records, bike-sharing pick-ups, crime occurrence, and infectious disease transmission. The point process is widely used in many applications to predict such events related to human activities. However, point processes present two problems in predicting events related to human activities. First, recent high-performance point process models require the input of sufficient numbers of events collected over a long period (i.e., long sequences) for training, which are often unavailable in realistic situations. Second, the long-term predictions required in real-world applications are difficult. To tackle these problems, we propose a novel meta-learning approach for periodicity-aware prediction of future events given short sequences. The proposed method first embeds short sequences into hidden representations (i.e., task representations) via recurrent neural networks for creating predictions from short sequences. It then models the intensity of the point process by monotonic neural networks (MNNs), with the input being the task representations. We transfer the prior knowledge learned from related tasks and can improve event prediction given short sequences of target tasks. We design the MNNs to explicitly take temporal periodic patterns into account, contributing to improved long-term prediction performance. Experiments on multiple real-world datasets demonstrate that the proposed method has higher prediction performance than existing alternatives.

Baige Xu, Yusuke Tanaka, Takashi Matsubara et al.

In recent years, deep learning for modeling physical phenomena which can be described by partial differential equations (PDEs) have received significant attention. For example, for learning Hamiltonian mechanics, methods based on deep neural networks such as Hamiltonian Neural Networks (HNNs) and their variants have achieved progress. However, existing methods typically depend on the discretization of data, and the determination of required differential operators is often necessary. Instead, in this work, we propose an operator learning approach for modeling wave equations. In particular, we present a method to compute the variational derivatives that are needed to formulate the equations using the automatic differentiation algorithm. The experiments demonstrated that the proposed method is able to learn the operator that defines the Hamiltonian density of waves from data with unspecific discretization without determination of the differential operators.

Yusuke Tanaka, Takaharu Yaguchi, Tomoharu Iwata et al.

The operator learning has received significant attention in recent years, with the aim of learning a mapping between function spaces. Prior works have proposed deep neural networks (DNNs) for learning such a mapping, enabling the learning of solution operators of partial differential equations (PDEs). However, these works still struggle to learn dynamics that obeys the laws of physics. This paper proposes Energy-consistent Neural Operators (ENOs), a general framework for learning solution operators of PDEs that follows the energy conservation or dissipation law from observed solution trajectories. We introduce a novel penalty function inspired by the energy-based theory of physics for training, in which the energy functional is modeled by another DNN, allowing one to bias the outputs of the DNN-based solution operators to ensure energetic consistency without explicit PDEs. Experiments on multiple physical systems show that ENO outperforms existing DNN models in predicting solutions from data, especially in super-resolution settings.

Yusuke Tanaka, Yuki Shirai, Zachary Lacey et al.

Current rigid linkage grippers are limited in flexibility, and gripper design optimality relies on expertise, experiments, or arbitrary parameters. Our proposed rigid gripper can accommodate irregular and off-center objects through a whippletree mechanism, improving adaptability. We present a whippletree-based rigid under-actuated gripper and its parametric design multi-objective optimization for a one-wall climbing task. Our proposed objective function considers kinematics and grasping forces simultaneously with a mathematical metric based on a model of an object environment. Our multi-objective problem is formulated as a single kinematic objective function with auto-tuning force-based weight. Our results indicate that our proposed objective function determines optimal parameters and kinematic ranges for our under-actuated gripper in the task environment with sufficient grasping forces.

Maya Okawa, Tomoharu Iwata, Yusuke Tanaka et al.

Sequences of events including infectious disease outbreaks, social network activities, and crimes are ubiquitous and the data on such events carry essential information about the underlying diffusion processes between communities (e.g., regions, online user groups). Modeling diffusion processes and predicting future events are crucial in many applications including epidemic control, viral marketing, and predictive policing. Hawkes processes offer a central tool for modeling the diffusion processes, in which the influence from the past events is described by the triggering kernel. However, the triggering kernel parameters, which govern how each community is influenced by the past events, are assumed to be static over time. In the real world, the diffusion processes depend not only on the influences from the past, but also the current (time-evolving) states of the communities, e.g., people's awareness of the disease and people's current interests. In this paper, we propose a novel Hawkes process model that is able to capture the underlying dynamics of community states behind the diffusion processes and predict the occurrences of events based on the dynamics. Specifically, we model the latent dynamic function that encodes these hidden dynamics by a mixture of neural networks. Then we design the triggering kernel using the latent dynamic function and its integral. The proposed method, termed DHP (Dynamic Hawkes Processes), offers a flexible way to learn complex representations of the time-evolving communities' states, while at the same time it allows to computing the exact likelihood, which makes parameter learning tractable. Extensive experiments on four real-world event datasets show that DHP outperforms five widely adopted methods for event prediction.

Tomoharu Iwata, Yusuke Tanaka

We propose a few-shot learning method for spatial regression. Although Gaussian processes (GPs) have been successfully used for spatial regression, they require many observations in the target task to achieve a high predictive performance. Our model is trained using spatial datasets on various attributes in various regions, and predicts values on unseen attributes in unseen regions given a few observed data. With our model, a task representation is inferred from given small data using a neural network. Then, spatial values are predicted by neural networks with a GP framework, in which task-specific properties are controlled by the task representations. The GP framework allows us to analytically obtain predictions that are adapted to small data. By using the adapted predictions in the objective function, we can train our model efficiently and effectively so that the test predictive performance improves when adapted to newly given small data. In our experiments, we demonstrate that the proposed method achieves better predictive performance than existing meta-learning methods using spatial datasets.

Yasunori Akagi, Yusuke Tanaka, Tomoharu Iwata et al.

Optimal Transport (OT) is being widely used in various fields such as machine learning and computer vision, as it is a powerful tool for measuring the similarity between probability distributions and histograms. In previous studies, OT has been defined as the minimum cost to transport probability mass from one probability distribution to another. In this study, we propose a new framework in which OT is considered as a maximum a posteriori (MAP) solution of a probabilistic generative model. With the proposed framework, we show that OT with entropic regularization is equivalent to maximizing a posterior probability of a probabilistic model called Collective Graphical Model (CGM), which describes aggregated statistics of multiple samples generated from a graphical model. Interpreting OT as a MAP solution of a CGM has the following two advantages: (i) We can calculate the discrepancy between noisy histograms by modeling noise distributions. Since various distributions can be used for noise modeling, it is possible to select the noise distribution flexibly to suit the situation. (ii) We can construct a new method for interpolation between histograms, which is an important application of OT. The proposed method allows for intuitive modeling based on the probabilistic interpretations, and a simple and efficient estimation algorithm is available. Experiments using synthetic and real-world spatio-temporal population datasets show the effectiveness of the proposed interpolation method.

Yuki Shirai, Xuan Lin, Yusuke Tanaka et al.

We present a motion planning algorithm with probabilistic guarantees for limbed robots with stochastic gripping forces. Planners based on deterministic models with a worst-case uncertainty can be conservative and inflexible to consider the stochastic behavior of the contact, especially when a gripper is installed. Our proposed planner enables the robot to simultaneously plan its pose and contact force trajectories while considering the risk associated with the gripping forces. Our planner is formulated as a nonlinear programming problem with chance constraints, which allows the robot to generate a variety of motions based on different risk bounds. To model the gripping forces as random variables, we employ Gaussian Process regression. We validate our proposed motion planning algorithm on an 11.5 kg six-limbed robot for two-wall climbing. Our results show that our proposed planner generates various trajectories (e.g., avoiding low friction terrain under the low risk bound, choosing an unstable but faster gait under the high risk bound) by changing the probability of risk based on various specifications.

Yusuke Tanaka, Toshiyuki Tanaka, Tomoharu Iwata et al.

We propose a probabilistic model for inferring the multivariate function from multiple areal data sets with various granularities. Here, the areal data are observed not at location points but at regions. Existing regression-based models can only utilize the sufficiently fine-grained auxiliary data sets on the same domain (e.g., a city). With the proposed model, the functions for respective areal data sets are assumed to be a multivariate dependent Gaussian process (GP) that is modeled as a linear mixing of independent latent GPs. Sharing of latent GPs across multiple areal data sets allows us to effectively estimate the spatial correlation for each areal data set; moreover it can easily be extended to transfer learning across multiple domains. To handle the multivariate areal data, we design an observation model with a spatial aggregation process for each areal data set, which is an integral of the mixed GP over the corresponding region. By deriving the posterior GP, we can predict the data value at any location point by considering the spatial correlations and the dependences between areal data sets, simultaneously. Our experiments on real-world data sets demonstrate that our model can 1) accurately refine coarse-grained areal data, and 2) offer performance improvements by using the areal data sets from multiple domains.

Maya Okawa, Tomoharu Iwata, Takeshi Kurashima et al.

Predicting when and where events will occur in cities, like taxi pick-ups, crimes, and vehicle collisions, is a challenging and important problem with many applications in fields such as urban planning, transportation optimization and location-based marketing. Though many point processes have been proposed to model events in a continuous spatio-temporal space, none of them allow for the consideration of the rich contextual factors that affect event occurrence, such as weather, social activities, geographical characteristics, and traffic. In this paper, we propose \textsf{DMPP} (Deep Mixture Point Processes), a point process model for predicting spatio-temporal events with the use of rich contextual information; a key advance is its incorporation of the heterogeneous and high-dimensional context available in image and text data. Specifically, we design the intensity of our point process model as a mixture of kernels, where the mixture weights are modeled by a deep neural network. This formulation allows us to automatically learn the complex nonlinear effects of the contextual factors on event occurrence. At the same time, this formulation makes analytical integration over the intensity, which is required for point process estimation, tractable. We use real-world data sets from different domains to demonstrate that DMPP has better predictive performance than existing methods.

Yusuke Tanaka, Tomoharu Iwata, Toshiyuki Tanaka et al.

We propose a probabilistic model for refining coarse-grained spatial data by utilizing auxiliary spatial data sets. Existing methods require that the spatial granularities of the auxiliary data sets are the same as the desired granularity of target data. The proposed model can effectively make use of auxiliary data sets with various granularities by hierarchically incorporating Gaussian processes. With the proposed model, a distribution for each auxiliary data set on the continuous space is modeled using a Gaussian process, where the representation of uncertainty considers the levels of granularity. The fine-grained target data are modeled by another Gaussian process that considers both the spatial correlation and the auxiliary data sets with their uncertainty. We integrate the Gaussian process with a spatial aggregation process that transforms the fine-grained target data into the coarse-grained target data, by which we can infer the fine-grained target Gaussian process from the coarse-grained data. Our model is designed such that the inference of model parameters based on the exact marginal likelihood is possible, in which the variables of fine-grained target and auxiliary data are analytically integrated out. Our experiments on real-world spatial data sets demonstrate the effectiveness of the proposed model.