Input Trajectories Research Articles

Input redundancy under input and state constraints

For a given unconstrained dynamical system, input redundancy has been recently redefined as the existence of distinct inputs producing identical output for the same initial state. By directly referring to signals, this definition readily applies to any input-to-output mapping. As an illustration of this potentiality, this paper tackles the case where input and state constraints are imposed on the system. This context is indeed of foremost importance since input redundancy has been historically regarded as a way to deal with input saturations. An example illustrating how constraints can challenge redundancy is offered right at the outset. A more complex phenomenology is highlighted. This motivates the enrichment of the existing framework on redundancy. Then, a sufficient condition for redundancy to be preserved when imposing constraints is offered in the most general context of arbitrary constraints. It is shown that redundancy can be destroyed only when input and state trajectories lie on the border of the set of constraints almost all the time. Finally, those results are specialized and expanded under the assumption that input and state constraints are linear.

Contrastive Learning for Graph-Based Vessel Trajectory Similarity Computation

With the increasing popularity of automatic identification system AIS devices, mining latent vessel motion patterns from AIS data has become a hot topic in water transportation research. Trajectory similarity computation is a fundamental issue to many maritime applications such as trajectory clustering, prediction, and anomaly detection. However, current non-learning-based methods face performance and efficiency issues, while learning-based methods are limited by the lack of labeled sample and explicit spatial modeling, making it difficult to achieve optimal performance. To address the above issues, we propose CLAIS, a contrastive learning framework for graph-based vessel trajectory similarity computation. A combined parameterized trajectory augmentation scheme is proposed to generate similar trajectory sample pairs and a constructed spatial graph of the study region is pretrained to help model the input trajectory graph. A graph neural network encoder is used to extract spatial dependency from the trajectory graph to learn better trajectory representations. Finally, a contrastive loss function is used to train the model in an unsupervised manner. We also propose an improved experiment and three related metrics and conduct extensive experiments to evaluate the performance of the proposed framework. The results validate the efficacy of the proposed framework in trajectory similarity calculation.

Efficient dynamic sampling of batch processes through operation recipes

The complexity of dynamic phenomena present in chemical processes often results in high evaluation costs of accurate first-principles models. This limits their real-time applicability, e.g. for advanced process control. A common solution is the derivation of simpler but faster data-driven surrogate models trained on simulated time series generated from dynamic samplings of a mechanistic model. For batch processes, known non-adaptive dynamic sampling methods lead to unrealistic or even infeasible operation cycles, raising the cost of generating simulated datasets with sufficient information content to train accurate surrogate models. An alternative sampling strategy is developed and analyzed, where sampled input trajectories are constrained to process knowledge in the form of parametrized operation recipes. The proposed methodology is tested for the case studies of full batch cycles of a crystallizer and a batch distillation column, showing that it is more efficient in terms of convergent simulations compared to an established dynamic sampling strategy.

A Cyclic Differentiable Manifold Representation of Redundant Manipulator Kinematics

Abstract An inverse kinematic mapping for redundant serial manipulators is presented at the configuration level, for which periodic manipulator operational trajectories map into periodic input trajectories, i.e., for which serial manipulators are cyclic. The inverse kinematic mapping defines a differentiable manifold on which output and self-motion coordinates comprise operational coordinates that represent manipulator redundant degrees-of-freedom. The inverse kinematic mapping and differentiable manifold are defined in analytical form and a computational method for their evaluation is presented. Numerical examples are presented to illustrate the validity of the formulation on subsets of manipulator regular configuration space, or on the entire space.

Warming up recurrent neural networks to maximise reachable multistability greatly improves learning

Training recurrent neural networks is known to be difficult when time dependencies become long. In this work, we show that most standard cells only have one stable equilibrium at initialisation, and that learning on tasks with long time dependencies generally occurs once the number of network stable equilibria increases; a property known as multistability. Multistability is often not easily attained by initially monostable networks, making learning of long time dependencies between inputs and outputs difficult. This insight leads to the design of a novel way to initialise any recurrent cell connectivity through a procedure called “warmup” to improve its capability to learn arbitrarily long time dependencies. This initialisation procedure is designed to maximise network reachable multistability, i.e., the number of equilibria within the network that can be reached through relevant input trajectories, in few gradient steps. We show on several information restitution, sequence classification, and reinforcement learning benchmarks that warming up greatly improves learning speed and performance, for multiple recurrent cells, but sometimes impedes precision. We therefore introduce a double-layer architecture initialised with a partial warmup that is shown to greatly improve learning of long time dependencies while maintaining high levels of precision. This approach provides a general framework for improving learning abilities of any recurrent cell when long time dependencies are present. We also show empirically that other initialisation and pretraining procedures from the literature implicitly foster reachable multistability of recurrent cells.

Application of an Encoder–Decoder Model with Attention Mechanism for Trajectory Prediction Based on AIS Data: Case Studies from the Yangtze River of China and the Eastern Coast of the U.S

With the rapid growth of shipping volumes, ship navigation and path planning have attracted increased attention. To design navigation routes and avoid ship collisions, accurate ship trajectory prediction based on automatic identification system data is required. Therefore, this study developed an encoder–decoder learning model for ship trajectory prediction, to avoid ship collisions. The proposed model includes long short-term memory units and an attention mechanism. Long short-term memory can extract relationships between the historical trajectory of a ship and the current state of encountered ships. Simultaneously, the global attention mechanism in the proposed model can identify interactions between the output and input trajectory sequences, and a multi-head self-attention mechanism in the proposed model is used to learn the feature fusion representation between the input trajectory sequences. Six case studies of trajectory prediction for ship collision avoidance from the Yangtze River of China and the eastern coast of the U.S. were investigated and compared. The results showed that the average mean absolute errors of our model were much lower than those of the classical neural networks and other state-of-the-art models that included attention mechanisms.

Advanced polynomial trajectory design for high precision control of flexible servo positioning systems

This paper develops a new approach for the design of polynomial-based reference and feedforward control trajectories for the high precision control of flexible servo actuators. First, a robust frequency-domain controller is designed for reference tracking and disturbance rejection. This controller is designed to achieve a desirable loop shape with reasonable bandwidth and stability margins. Then, the polynomial trajectories are derived based on a simplified rigid body representation of the system. To avoid the excitation of the system's resonant modes, this paper proposes the design and implementation of a set of feedforward notch filters. We further investigate the main cause of tracking error resulted from the rigid body approximation, and propose an alternative model for the derivation of the polynomial input trajectories. This model accounts for the cumulative DC gain of the resonant modes ignored in the rigid body approximation. A method for deriving the new polynomial trajectories with the appropriate initial and final time conditions is developed and evaluated for a representative flexible servo system model. Simulation results indicate that the proposed scheme provides significant improvement in the performance of system compared to the conventional methods.

PMMTss: A Parallel Multi-Way Merging-Based Trajectory Similarity Search for a Million Metro Passengers

Trajectory similarity search (TSS) is a common operation for spatiotemporal data analysis. However, the existing TSS methods are mainly focused on GPS trajectories produced by moving objects such as vehicles. Further, these corresponding optimization strategies cannot be directly applied in the metro scenario because the metro passenger trajectory is totally different from the GPS trajectory. To fill this gap, we systematically analyze the unique spatiotemporal characteristics of metro passenger trajectories and propose a similarity search solution named PMMTss for the metro system. The core idea of this solution has two key points: first, we design a multi-layer index based on the spatiotemporal feature of metro trajectories, and all points of a trajectory are stored in this index. Second, we design a parallel multi-way merging-based trajectory similar search method, in which the candidate trajectory segments are merged and filtered. We evaluate this solution on a large dataset (Shenzhen Metro data for 3 consecutive months, 6.976 million trajectories with 260 million records). When lengths of input trajectories are 16, 32, and 64, respectively, the corresponding search times are 0.004 s, 0.016 s, and 0.036 s, respectively. Compared to the baseline PPJion+, the query times are reduced by 99.7%, 98.8%, and 97.6%, respectively.

RES-StS: Referring Expression Speaker via Self-Training With Scorer for Goal-Oriented Vision-Language Navigation

It is a rather practical but difficult task to find a specified target object via autonomous exploration based on natural language descriptions in an unstructured environment. Since the human-annotated data is expensive to gather for the goal-oriented vision-language navigation (GVLN) task, the size of the standard dataset is inadequate, which has significantly limited the accuracy of previous techniques. In this work, we aim to improve the robustness and generalization of the navigator by dynamically providing high-quality pseudo-instructions using a proposed RES-StS paradigm. Specifically, we establish a referring expression speaker (RES) to predict descriptive instructions for the given path to the goal object. Based on an environment-and-object fusion (EOF) module, RES derives spatial representations from the input trajectories, which are subsequently encoded by a number of transformer layers. Additionally, given that the quality of the pseudo labels is important for data augmentation while the limited dataset may also hinder RES learning, we propose to equip RES with a more effective generation ability by using the self-training approach. A trajectory-instruction matching scorer (TIMS) network based on contrastive learning is proposed to selectively use rehearsal of prior knowledge. Finally, all network modules in the system are integrated by suggesting a multi-stage training strategy, allowing them to assist one another and thus enhance performance on the GVLN task. Experimental results demonstrate the effectiveness of our approach. Compared with the SOTA methods, our method improves SR, SPL, and RGS by 4.72%, 2.55%, and 3.45% respectively, on the REVERIE dataset, and 4.58%, 3.75% and 3.14% respectively, on the SOON dataset.

Input-output data based tracking control under DoS attacks

ABSTRACT This paper investigates the secure optimal tracking control problem for cyber-physical systems, in which the controller-actuator channel is jammed by denial-of-service attacks. Without leveraging model knowledge, learning-based tracking control algorithms are proposed by utilizing the measured input-output data. The impact of malicious attacks on tracking performance is discussed. More specifically, an augmented system consisted of the system model and the reference model is derived. Then the states of the augmented system are rewritten by utilizing the input, output, and reference trajectory, following which both the Bellman equation and algebraic Riccati equation are given. The conditions of existence and uniqueness of the solution to the algebraic Riccati equation are derived. Furthermore, both policy iteration and value iteration learning-based tracking control algorithms are provided for cyber-physical systems against denial-of-service attacks, and the convergence of the algorithms is also proved. Finally, a DC motor system and a numerical example are given to illustrate the effectiveness of the proposed control algorithms.

Maximum-Entropy Multi-Agent Dynamic Games: Forward and Inverse Solutions

In this article, we study the problem of multiple stochastic agents interacting in a dynamic game scenario with continuous state and action spaces. We define a new notion of stochastic Nash equilibrium for boundedly rational agents, which we call the entropic cost equilibrium (ECE). We show that ECE is a natural extension to multiple agents of maximum entropy optimality for a single agent. We solve both the “forward” and “inverse” problems for the multi-agent ECE game. For the forward problem, we provide a Riccati algorithm to compute closed-form ECE feedback policies for the agents, which are exact in the linear-quadratic-gaussian case. We give an iterative variant to find locally ECE feedback policies for the nonlinear case. For the inverse problem, we present an algorithm to infer the cost functions of the multiple interacting agents given noisy, boundedly rational input and state trajectory examples from agents acting in an ECE. The effectiveness of our algorithms is demonstrated in a simulated multi-agent collision avoidance scenario, and with data from the INTERACTION traffic dataset. In both cases, we show that, by taking into account the agents' game theoretic interactions using our algorithm, a more accurate model of agents' costs can be learned, compared with standard inverse optimal control methods.

Optimal Pneumatic Actuator Positioning and Dynamic Stability using Prescribed Performance Control with Particle Swarm Optimization: A Simulation Study

This paper introduces an optimal control strategy for pneumatic servo systems (PSS) positioning using Finite-time Prescribed Performance Control (FT-PPC) with Particle Swarm Optimization (PSO). Pneumatic servo systems are widely used in industrial automation, as well as medical and cybernetics systems that involve robotics applications. Precision in pneumatic control is crucial not only for the sake of efficiency but also safety. The primary goal of the proposed control strategy is to optimize the convergence rate and finite time of the prescribed performance function in error transformation of the FT-PPC, as well as the Proportional, Integral and Derivative (PID) controller as the inner-loop controller for this system. The study utilizes a dynamic model of a pneumatic proportional valve with a double-acting cylinder (PPVDC) as the targeted plant and performs simulations with a multi-step input trajectory. This offline tuning method is essential for such nonlinear systems to be safely optimized, avoiding major damage to the real-time fine-tuned works on the controller. The results demonstrate that the proposed control strategy surpasses the performance of FT-PPC with a PID controller alone, significantly improving the system's performance, including suppressing overshoot and oscillation in the responses. Further validation through the actual system of PPVDC using the fine-tuned values of FT-PPC and PID with PSO is a future task and more challenging to come, as hardware constraints may vary with different environments such as temperatures.

Tracking periodic parametric references using model predictive control

AbstractThis paper presents a model predictive controller for tracking periodic parametric reference curves. The controller is formulated in a single layer so that the time‐parameterization of the reference curve, the trajectory planning, and the trajectory tracking tasks are solved in a single optimization problem which is computed at each sampling time. The auxiliary state and input trajectories are introduced into the optimization problem as decision variables, which become the planned trajectory to be effectively followed. By design, the closed‐loop system guarantees of recursive feasibility of the optimization problem while being able to handle arbitrary changes of reference during execution time. Such properties are discussed in detail, and new results on the asymptotic average performance are presented. Simulation results show the benefits of the proposed strategy.

Trajectory-Regulation-Based Segmented Control for Dead Center Positions Tracking of Free-Piston Linear Generator

Free-piston linear generator (FPLG), as a novel energy converter, has attracted wide attention due to its unique operating characteristics. However, the high-precision and robust tracking of the dead center positions in the presence of frequent combustion variation is still a tricky problem. In this respect, in this article, we present a trajectory-regulation-based segmented control (TRBSC) to actively control the linear electric machine (LEM) of FP LG. The target stroke is divided into the high-speed zone and low-speed zone, where active tracking of the input reference trajectory of LEM and free damped motion are performed separately. Especially, the input trajectory is selected as a variable sinusoidal reference velocity profile, which is adjusted by the combinations of the dead center errors. The segmented control decouples the specific interaction between the dead center positions and velocity curve, reducing the heavy dependence of the algorithm on speed tracking accuracy. A full theoretical analysis is provided with emphasis on the regulation rules of the reference speed profile based on the modeling of the displacement profiles. The performance of the TRBSC is experimentally verified on an 18 kW permanent-magnet linear synchronous motor setup in motoring mode.

Memory and Management: Competing Controls on Long‐Term Nitrate Trajectories in U.S. Rivers

AbstractExcess nitrogen from intensive agricultural production, atmospheric N deposition, and urban point sources elevates stream nitrate concentrations, leading to problems of eutrophication and ecosystem degradation in coastal waters. A major emphasis of current US‐scale analysis of water quality is to better our understanding of the relationship between changes in anthropogenic N inputs within watersheds and subsequent changes in riverine N loads. While most water quality modeling assumes a positive linear correlation between watershed N inputs and riverine N, many efforts to reduce riverine N through improved nutrient management practices result in little or no short‐term improvements in water quality. Here, we use nitrate concentration and load data from 478 US watersheds, along with developed N input trajectories for these watersheds, to quantify time‐varying relationships between N inputs and riverine N export. Our results show substantial variations in watershed N import‐export relationships over time, with quantifiable hysteresis effects. Our results show that more population‐dense urban watersheds in the northeastern U.S. more frequently show clockwise hysteresis relationships between N imports and riverine N export, with accelerated improvements in water quality being achieved through the implementation of point‐source controls. In contrast, counterclockwise hysteresis dynamics are more common in agricultural watersheds, where time lags occur between the implementation of nutrient management practices and water‐quality improvements. Finally, we find higher tile‐drainage densities to be associated with more linear relationships between N inputs and riverine N. The empirical analysis in this study is bolstered by modeled simulations to reproduce and further explain drivers behind the hysteretic relationships commonly observed in the monitored watersheds.

Fast model-based scenario optimization in NSTX-U enabled by analytic gradient computation

Model-based optimization offers a systematic approach to advanced scenario planning. In this case, the feedforward-control inputs (actuator trajectories) that are needed to attain and sustain a desired scenario are obtained by solving a nonlinear constrained optimization problem. This class of problems generally minimize a cost function that measures the difference between desired and actual plasma states. Several numerical optimization algorithms, such as sequential quadratic programming, require repeated calculation of the cost function gradients with respect to the input trajectories. Calculating these gradients numerically can be computationally intensive, increasing the time needed to solve the feedforward-control optimization problem. This work introduces a method to analytically calculate these cost function gradients from the current profile evolution model. This can significantly reduce the computational time and allow for fast feedforward-control optimization, which would eventually enable optimal scenario planning between discharges. The performance of the feedforward optimizer with analytical gradients is compared to a traditional optimization algorithm based on numerical gradients for different NSTX-U scenarios. The plasma dynamics in the optimization algorithm are simulated using the Control Oriented Transport SIMulator (COTSIM). Results of the work show that analytical gradients consistently reduce the computation time while achieving trajectories that are comparable to those obtained by traditional optimization algorithms based on numerical gradients.

Trajectory Forecasting Using Graph Convolutional Neural Networks Based on Prior Awareness and Information Fusion

Predicting the future trajectories of multiple agents is essential for various applications in real life, such as surveillance systems, autonomous driving, and social robots. The trajectory prediction task is influenced by many factors, including individual historical trajectory, interactions between agents, and the fuzzy nature of an agent’s motion. While existing methods have made great progress on the topic of trajectory prediction, a lot of trajectory prediction methods take into account all pedestrians in the scene when simply modeling the influence of nearby pedestrians, and this inevitably brings redundant information. We propose a pedestrian trajectory prediction model based on prior awareness and information fusion. To make the input information more effective, for the different levels of importance of input trajectory information, we design a time information weighting module to weigh the observed trajectory information differently at different moments based on the original observed trajectory information. To reduce the impact of redundant information on trajectory prediction and to improve interaction between pedestrians, we present a spatial interaction module of multi-pedestrians and a topological graph fusion module. In addition, we use a temporal convolutional network module to obtain the temporal interactions between pedestrians. Compared to Social-STGCNN, the experimental results show that the model we propose reduces the average displacement error (ADE) and final displacement error (FDE) by 32% and 38% in the datasets of ETH and UCY, respectively. Moreover, based on this model, we design an autonomous driving obstacle avoidance system that can effectively ensure the safety of road pedestrians.

Model-free Computation Method in First-order Linear Quadratic Mean Field Games

This paper considers first-order continuous-time systems of mean field games in which agents are coupled via their dynamics and individual cost functions. For such games, a mean field equilibrium is developed by using the state space augmentation technique and the Nash certainty equivalence (NCE) principle. This decentralized strategy consists of two constant gains and a mean field state corresponding to the optimal strategy, where the coefficients are obtained by solving two algebraic Riccati equations and the time-varying mean field is solved from the ordinary differential equation. Note that solving these equations requires agents’ models. In order to eliminate the use of system information, two-agents model-free method is proposed. First, model-based iterative equations are proposed to approximate the feedback constant gain. By the integral reinforcement learning (IRL) technique, the system dynamics in the iterative equations are replaced by real-time data. Moreover, based on the learned solution, the coefficient of input can be calculated. Then, a model-free computational equation is developed by embedding the same collected data. Finally, the mean field state is computed depending on the obtained gains and the observed state and input trajectories from agents.

Long Duration Stochastic MPC With Mission-Wide Probabilistic Constraints Using Waysets

A stochastic Model Predictive Control (MPC) formulation is presented for systems operating for a finite time subject to constraints on the Mission-Wide Probability of Safety (MWPS). For linear discrete-time systems subject to unknown disturbances, the goal is to formulate an MPC controller to achieve a desired probability of mission success, where the entire closed-loop state and input trajectories stay within the state and input constraint sets and the final state reaches the desired terminal set. To enable longer missions under greater uncertainty, a wayset-based approach is proposed that allows for the prediction horizon of the MPC to be significantly shorter than the length of the mission. Using a scenario-based approach to stochastic MPC, the use of constrained zonotopes makes the computation of these waysets efficient and practical. Numerical results demonstrate the utility of the waysets for increasing the feasibility of MWPS constraints to longer missions and that the percentage of successful missions asymptotically converges above the desired probability.

Formal Verification of Robotic Contact Tasks via Reachability Analysis

Verifying the correct behavior of robots in contact tasks is challenging due to model uncertainties associated with contacts. Standard methods for testing often fall short since all (uncountable many) solutions cannot be obtained. Instead, we propose to formally and Efficiently verify robot behaviors in contact tasks using reachability analysis, which enables checking all the reachable states against user-provided specifications. To this end, we extend the state of the art in reachability analysis for hybrid (mixed discrete and continuous) dynamics subject to discrete-time input trajectories. In particular, we present a novel and scalable guard intersection approach to reliably compute the complex behavior caused by contacts. We model robots subject to contacts as hybrid automata in which crucial time delays are included. The usefulness of our approach is demonstrated by verifying safe human-robot interaction in the presence of constrained collisions, which was out of reach for existing methods.