In time-series classification, interpretable models can bring additional insights but be outperformed by deep models since human-understandable features have limited expressivity and flexibility. In this work, we present InterpGN, a framework that integrates an interpretable model and a deep neural network. Within this framework, we introduce a novel gating function design based on the confidence of the interpretable expert, preserving interpretability for samples where interpretable features are significant while also identifying samples that require additional expertise. For the interpretable expert, we incorporate shapelets to effectively model shape-level features for time-series data. We introduce a variant of Shapelet Transforms to build logical predicates using shapelets. Our proposed model achieves comparable performance with state-of-the-art deep learning models while additionally providing interpretable classifiers for various benchmark datasets. We further show that our models improve on quantitative shapelet quality and interpretability metrics over existing shapelet-learning formulations. Finally, we show that our models can integrate additional advanced architectures and be applied to real-world tasks beyond standard benchmarks such as the MIMIC-III and time series extrinsic regression datasets.

This paper presents an iterative planning framework for multi-agent systems with hybrid state spaces. The framework uses transition systems to mathematically represent planning tasks and employs multiple solvers to iteratively improve the plan until computational resources are exhausted. When integrating different solvers for iterative planning, we establish theoretical guarantees for recursive feasibility. The proposed framework enables continual improvement of solutions to reduce sub-optimality, efficiently using allocated computational resources. The proposed method is validated by applying it to an energy-aware UAV-UGV cooperative task site assignment problem. The results demonstrate continual solution improvement while preserving real-time implementation ability compared to algorithms proposed in the literature.Note to Practitioners—This paper presents an iterative planning solution for cooperative planning problems in multi-agent systems, which integrates multiple solvers to create an optimization framework. The proposed planning framework has been theoretically validated and applied in an energy-aware cooperative planning scenario for multi-vehicle task site assignments. The proposed framework can be applied to plan for any generalized task site assignment using multiple solvers iteratively.

In time-series analysis, many recent works seek to provide a unified view and representation for time-series across multiple domains, leading to the development of foundation models for time-series data. Despite diverse modeling techniques, existing models are black boxes and fail to provide insights and explanations about their representations. In this paper, we present VQShape, a pre-trained, generalizable, and interpretable model for time-series representation learning and classification. By introducing a novel representation for time-series data, we forge a connection between the latent space of VQShape and shape-level features. Using vector quantization, we show that time-series from different domains can be described using a unified set of low-dimensional codes, where each code can be represented as an abstracted shape in the time domain. On classification tasks, we show that the representations of VQShape can be utilized to build interpretable classifiers, achieving comparable performance to specialist models. Additionally, in zero-shot learning, VQShape and its codebook can generalize to previously unseen datasets and domains that are not included in the pre-training process. The code and pre-trained weights are available at https://github.com/YunshiWen/VQShape.

Industrial robots are increasingly deployed in applications requiring an end effector tool to closely track a specified path, such as in spraying and welding. Performance and productivity present possibly conflicting objectives: tracking accuracy, path speed, and motion uniformity. Industrial robots are programmed through motion primitives consisting of waypoints connected by pre-defined motion segments, with specified parameters such as path speed and blending zone. The actual executed robot motion depends on the robot joint servo controller and joint motion constraints (e.g., velocity, acceleration limits) which are largely unknown to the users. Programming a robot to achieve the desired performance today is time-consuming and mostly manual, requiring tuning a large number of coupled parameters in the motion primitives. The performance also depends on the choice of additional param-eters: possible redundant degrees of freedom, location of the target curve, and the robot configuration. This paper presents a systematic approach to optimize robot motion parameters. The approach first selects the static parameters, then chooses the motion primitives, and finally iteratively updates the waypoints to minimize the tracking error. The ultimate performance objective is to maximize the path speed subject to the tracking accuracy and speed uniformity constraints over the entire path. We have demonstrated the effectiveness of this approach both in simulation and on physical systems for ABB and FANUC robots applied to two challenging example curves. Comparing with the baseline using the current industry practice, the optimized performance shows over 100% performance improvement.

Most existing Time series classification (TSC) models lack interpretability and are difficult to inspect. Interpretable machine learning models can aid in discovering patterns in data as well as give easy-to-understand insights to domain specialists. In this study, we present Neuro-Symbolic Time Series Classification (NSTSC), a neuro-symbolic model that leverages signal temporal logic (STL) and neural network (NN) to accomplish TSC tasks using multi-view data representation and expresses the model as a human-readable, interpretable formula. In NSTSC, each neuron is linked to a symbolic expression, i.e., an STL (sub)formula. The output of NSTSC is thus interpretable as an STL formula akin to natural language, describing temporal and logical relations hidden in the data. We propose an NSTSC-based classifier that adopts a decision-tree approach to learn formula structures and accomplish a multiclass TSC task. The proposed smooth activation functions enable the model to be learned in an end-to-end fashion. We test NSTSC on a real-world wound healing dataset from mice and benchmark datasets from the UCR time-series repository, demonstrating that NSTSC achieves comparable performance with the state-of-the-art models. Furthermore, NSTSC can generate interpretable formulas that match domain knowledge.

Control of conventional transportation networks aims at bringing the state of the network (e.g., the traffic flows in the network) to the system optimal (SO) state. This optimum is characterized by the minimality of the social cost function, i.e., the total cost of travel (e.g., travel time) of all drivers. On the other hand, drivers are assumed to be rational and selfish, and make their travel decisions (e.g., route choices) to optimize their own travel costs, bringing the state of the network to a user equilibrium (UE). A classic approach to influence users' route choice is using congestion tolls. In this paper, we study the SO and UE of future connected vehicular transportation networks, where users consider both the travel cost and the utility from data communication, when making their travel decisions. We leverage the data communication aspect of the decision making to influence the user route choices, driving the UE state to the SO state. We assume the cache-enabled vehicles can communicate with other vehicles via vehicle-to-vehicle (V2V) connections. We propose an algorithm for calculating the values of the data communication utility that drive the UE to the SO. This result provides a guideline on how the system operator can adjust the parameters of the communication network (e.g., data pricing and bandwidth) to achieve the optimal social cost. We discuss the insights that the results shed on a secondary optimization that the operator can conduct to maximize its own utility without deviating the transportation network state from the SO. We validate the proposed communication model via Veins simulation. The simulation results also show that the system cost can be lowered even if the bandwidth allocation does not exactly match the optimal allocation policy under 802.11p protocol.

This work studies the user equilibrium (UE) state and the system optimal (SO) state in vehicular communication networks that support both V2V and V2I communication. Each user in this network is assumed to make route choice that optimizes a utility function that involves the traditional travel cost and the data communication utility. The overall social cost is minimized when the network is in the SO state. However, the rational and selfish user behavior brings the network to the UE state. It is well known that, in general, the UE state does not necessarily coincide with the SO state. In this paper, we leverage the data communication aspect of the decision making to influence the users' route choices, driving the UE state to the SO state. We provide a guideline for the system operator on how to drive the network towards the SO state using the V2I bandwidth allocation scheme developed in the paper. The model and the proposed algorithm are validated using Veins simulation under IEEE 802.11p protocol. In the simulation, we also show that the system cost can be lowered compared with the UE state if the bandwidth allocation is close to the optimal solution under the proposed algorithm.

In this paper, we present a method to learn (infer) and refine a set of advices from the trajectories generated in the successful and failed attempts in a task or game, in the form of advisory signal temporal logic (STL) formulas. Each advice consists of an advisory motion STL formula that characterizes the spatial-temporal pattern of the motion as a feature of success and an advisory selection STL formula as a criterion for the environment to select the advice. For the inference of advisory STL formulas, we provide a theoretical framework of perfect classification with a labeled set of trajectories with different time lengths. We design an advisory controller that can drive the robots to satisfy an advisory motion STL formula based on the advice selected according to the advisory selection STL formula. The advisory controller can advise or guide the human operators or the robots for better performance with the shared autonomy between the human operator and the controller. We provide two case studies to test the effectiveness of the advisory controller, one with a Baxter-On-Wheels simulator and the other with two quadrotors in an experimental testbed in iteratively improving the success rates of completing the tasks with the help of the designed advisory controller.

In this paper, we define a novel census signal temporal logic (CensusSTL) that focuses on the number of agents in different subsets of a group that complete a certain task specified by the STL. CensusSTL consists of an “inner logic” STL formula and an “outer logic” STL formula. We present a new inference algorithm to infer CensusSTL formulas from the trajectory data of a group of agents. We first identify the “inner logic” STL formula and then infer the subgroups based on whether the agents' behaviors satisfy the “inner logic” formula at each time point. We use two different approaches to infer the subgroups based on similarity and complementarity, respectively. The “outer logic” CensusSTL formula is inferred from the census trajectories of different subgroups. We apply the algorithm in analyzing data from a soccer match by inferring the CensusSTL formula for different subgroups of a soccer team.

The model-based fault diagnosability analysis is concerned with the timely detection and isolation of faults by using the system model and observations of the system output. In this paper, we propose the (δd, δm, α)-diagnosability notion for hybrid systems with probabilistic reset, where the faults are diagnosed by observing the timed event sequences. We also present an approach for the analysis of such diagnosability.

This paper investigates the use of single control signal (magnetic field direction) and PSO-MPC algorithm to control multiple magnetized Tetrahymena pyriformis (T. pyriformis) cells to move from their initial positions to their target positions simultaneously while avoiding the obstacle. The magnetized T. pyriformis cells are generated by adding iron-oxide spherical particles into the cells. We control the cells' moving direction by changing the magnetic field direction. Based on Model Predictive Control (MPC) algorithm, we define a cost function which is composed of the target cost function and the obstacle potential function. The target cost function is to measure the sum of differences between cells' predicted positions and their target positions. The obstacle potential function is used to measure the repulsive force of the obstacle. The input variables of the cost function are the sequence of control signals. We use Particle Swarm Optimization (PSO) method to find a cost value which is close to the global minimum of the cost function. In the experimental result section, we show the control of three m3pi robots to move from their initial positions to their target positions with avoiding the obstacle. Since the similar control strategy has successfully controlled one T. pyriformis cell in our previous work, we believe our PSO-MPC algorithm is applicable on the multiple T. pyriformis cells' control task.

As microscale robots are becoming increasingly popular due to their potential for medical and industrial applications, various designs of microscale robotic system have been developed. However, there has not been much work on autonomous control algorithms for microscale robots in microfluidic environments. In this paper, we introduce an autonomous navigation algorithm for the bacteria-powered microrobots (BPMs) in a workspace with moving obstacles. A BPM consists of a rigid inorganic body with bacteria attached on the surface. The attached bacteria provide propulsive force and are controllable using electric fields, which had been demonstrated in previous work. We take the controllability of BPMs and the unpredictable motion of dynamic obstacles into account to develop a dynamic obstacle avoidance approach. Moreover, we use finite element simulation to observe an electric field around a moving obstacle to model the field's deformation. Demonstration of dynamic obstacle avoidance approach through simulation results and experimental data are presented in the paper.

Biological robots can be produced in large numbers, but are often controlled by uniform inputs. This makes position control of multiple robots inherently challenging. This paper uses magnetically-steered ciliate eukaryon {Tetrahymena pyriformis) as a case study. These cells swim at a constant speed, and can be turned by changing the orientation of an external magnetic field. We show that it is possible to steer multiple T. pyriformis to independent goals if their turning - modeled as a first-order system - has unique time constants. We provide system identification tools to parameterize multiple cells in parallel. We construct feedback control-Lyapunov methods that exploit differing phase-lags under a rotating magnetic field to steer multiple cells to independent target positions. We prove that these techniques scale to any number of cells with unique first-order responses to the global magnetic field. We provide simulations steering hundreds of cells and validate our procedure in hardware experiments with multiple cells.

We demonstrate three-dimensional control with the eukaryotic cell Tetrahymena pyriformis (T. pyriformis) using two sets of Helmholtz coils for xy-plane motion and a single electromagnet for vertical motion. T. pyriformis is modified to have artificial magnetotaxis with internalized magnetite. Since the magnetic fields exerted by electromagnets are relatively uniform in the working space, the magnetite exerts only torque, without translational force, which enabled us to guide the cell's swimming direction while the swimming force is exerted only by the cell's motile organelles. A stronger magnetic force was necessary to steer cells to the z-axis, and, as a result, a single electromagnet placed just below our sample area is utilized for vertical motion. To track the cell's positions in the z-axis, intensity profiles of non-motile cells at varying distances from the focal plane are used. During vertical motion along the z-axis, the intensity difference from the background decreases while the cell size increases. Since the cell is pear-shaped, the eccentricity is high during planar motion, but lowers during vertical motion due to the change in orientation. The three-dimensional control of the live organism T. pyriformis as a cellular robot shows great potential to be utilized for practical applications in microscale tasks, such as target transport and cell therapy.

The use of live microbial cells as microscale robots is an attractive premise, primarily because they are easy to produce and to fuel. In this paper, we study the motion control of magnetotactic Tetrahymena pyriformis cells. Magnetotactic T. pyriformis is produced by introducing artificial magnetic dipole into the cells. Subsequently, they can be steered by using an external magnetic field. We observe that the external magnetic field can only be used to affect the swimming direction of the cells, while the swimming velocity depends largely on the cells' own propulsion. Feedback information for control is obtained from a computer vision system that tracks the cell. The contribution of this paper is twofold. First, we construct a discrete-time model for the cell dynamics that is based on first principle. Subsequently, we identify the model parameters using the Least Squares approach. Second, we formulate a model predictive approach for feedback control of magnetotactic T. pyriformis. Both the model fitness and the performance of the feedback controller are verified using experimental data.

In this paper, we present a control strategy using real-time feedback combined with feasible path planning to manipulate a type of microorganism, Tetrahymena pyriformis (T. pyriformis), as a micro-bio-robot using artificial magnetotaxis. Artificially magnetotactic T. pyriformis cells were created by the internalization of iron oxide nano particles. Following the magnetization of the internalized particles, the cells become controllable using an external time-varying magnetic field. The behavior of artificially magnetotactic T. pyriformis under a magnetic field has been investigated in a manual control experiment. A feasible path planner called rapidly-exploring random tree (RRT) and a feedback control scheme are implemented to guide the cell to a desired position and orientation. Since the motion of T. pyriformis is nonlinear like that of a car, combining the RRT and feedback control allows the cell to be controlled in 3-dimensional (x, y, ¸) space. In the results, real-time feedback control of T. pyriformis in 3-dimensional space demonstrated the potential of utilizing T. pyriformis as a micro-bio-robot for microscale tasks.

In this paper, we describe how signaling networks and actuation in bacterial cells and biomolecular networks of bacteria can be used to develop an integrated micro-bio-robotic system. SU8 microstructures blotted with swarmer cells of Serratia Marcescens in a monolayer are propelled by the bacteria in the absence of any environmental stimulus. We call such microstructures with bacteria Micro Bio Robots (MBRs) and the uncontrolled motion in the absence of stimuli self actuation. Our paper has two primary contributions. First, we demonstrate the control of MBRs using self-actuation, DC electric fields and ultra-violet radiation, and develop experimentally validated mathematical model for the MBRs. This model allows us to use self-actuation and electrokinetic actuation to steer the MBR to any position and orientation in a planar micro channel. Second, we describe the development of biosensors for the MBRs. This is done by attaching genetically engineered Escherichia coli cells that are capable of sensing nonmetabolizable lactose analog methyl-β-D-thiogalactoside (TMG). We describe the fabrication process for MBRs and show experimental results demonstrating sensing, actuation and control.

This paper presents a systematic analysis of the motion of microscale structures actuated by flagellated bacteria. We perform the study both experimentally and theoretically. We use a blotting procedure to attach flagellated bacteria to a buoyancy-neutral plate called a microbarge. The motion of the plate depends on the distribution of the cells on the plate and the stimuli from the environment. We construct a stochastic mathematical model for the system, based on the assumption that the behavior of each bacterium is random and independent of that of its neighbors. The main finding of the paper is that the motion of the barge plus bacteria system is a function of a very small set of parameters. This reduced-dimensional model can be easily estimated using experimental data. We show that the simulation results obtained from the model show an excellent match with the experimentally-observed motion of the barge.