The isoline tracking of this work is concerned with the control design for a sensing robot to track a given isoline of an unknown 2-D scalar filed. To this end, we propose a coordinate-free controller with a simple PI-like form using only the concentration feedback for a Dubins robot, which is particularly useful in GPS-denied environments. The key idea lies in the novel design of a sliding surface based error term in the standard PI controller. Interestingly, we also prove that the tracking error can be reduced by increasing the proportion gain, and is eliminated for circular fields with a non-zero integral gain. The effectiveness of our controller is validated via simulations by using a fixed-wing UAV on the real dataset of the concentration distribution of PM 2.5 in Handan, China.
The isoline tracking of this work is concerned with the control design for a sensing vehicle to track a desired isoline of an unknown scalar field. To this end, we propose a simple PI-like controller for a Dubins vehicle in the GPS-denied environments. Our key idea lies in the design of a novel sliding surface based error in the standard PI controller. For the circular field, we show that the P-like controller can globally regulate the vehicle to the desired isoline with the steady-state error that can be arbitrarily reduced by increasing the P gain, and is eliminated by the PI-like controller…
The unknown sharp changes of vehicle acceleration rates, also called the unknown jerk dynamics, may significantly affect the driving performance of the leader vehicle in a platoon, resulting in more drastic car-following movements in platooning tracking control, which could cause safety and traffic capacity concerns. To address these issues, in this paper, we investigate cooperative platooning tracking control and intermittent optimization problems for connected automated vehicles (CAVs) with a nonlinear car-following model. We assume that the external inputs of the leader CAV contain unknown …
We investigate a linear quadratic Gaussian (LQG) tracking problem with safety and reachability constraints in the presence of an adversary who mounts an FDI attack on an unknown set of sensors. For each possible set of compromised sensors, we maintain a state estimator disregarding the sensors in that set, and calculate the optimal LQG control input at each time based on this estimate. We propose a control policy which constrains the control input to lie within a fixed distance of the optimal control input corresponding to each state estimate. The control input is obtained at each time step by…
We study the problem of optimal state-feedback tracking control for unknown discrete-time deterministic systems with input constraints. To handle input constraints, state-of-art methods utilize a certain nonquadratic stage cost function, which is sometimes limiting real systems. Furthermore, it is well known that Policy Iteration (PI) and Value Iteration (VI), two widely used algorithms in data-driven control, offer complementary strengths and weaknesses. In this work, a two-step transformation is employed, which converts the constrained-input optimal tracking problem to an unconstrained augme…
The optimal control input for linear systems can be solved from algebraic Riccati equation (ARE), from which it remains questionable to get the form of the exact solution. In engineering, the acceptable numerical solutions of ARE can be found by iteration or optimization. Recently, the gradient descent based numerical solutions has been proven effective to approximate the optimal ones. This paper introduces this method to tracking problem for heterogeneous linear systems. Differently, the parameters in the dynamics of the linear systems are all assumed to be unknown, which is intractable since…
Optimal tracking of continuous time nonlinear systems has been extensively studied in literature. However, in several applications, absence of knowledge about system dynamics poses a severe challenge to solving the optimal tracking problem. This has found growing attention among researchers recently, and integral reinforcement learning (IRL)-based method augmented with actor neural network (NN) have been deployed to this end. However, very few studies have been directed to model-free $H_{\infty}$ optimal tracking control that helps in attenuating the effect of disturbances on the system perfor…
This paper focuses on the joint multi-object tracking (MOT) and the estimate of detection probability with the \emph{Poisson multi-Bernoulli mixture} (PMBM) filter. In a majority of multi-object scenarios, the knowledge of detection probability is usually uncertain, which is often estimated offline from the training data. In such cases, online filtering is not allowed or believable, otherwise, significate parameter mismatch will result in biased estimates (state and cardinality of objects). Consequently, the ability of adaptively estimating the detection probability is essential in practice. I…
This paper studies a leader-follower formation tracking problem where the leaders are moving at the same unknown bounded velocity. A distance-based control law is proposed for follower agents to maintain the desired distances in the formation and move at the leaders' velocity. The control law consists of a component to handle the uncertainty of the leaders' velocity and a component to achieve the desired distances in finite time. Numerical simulations are also provided to support the theoretical results.
We study a trajectory tracking problem for a multi-rotor in the presence of modeling error and external disturbances. The desired trajectory is unknown and generated from a reference system with unknown or partially known dynamics. We assume that only position and orientation measurements for the multi-rotor and position measurements for the reference system can be accessed. We adopt an extended high-gain observer (EHGO) estimation framework to estimate the feed-forward term required for trajectory tracking, the multi-rotor states, as well as modeling error and external disturbances. We design…
Multi-Step Optimal Tracking Control of Unknown Nonzero-Sum Games based on Least Squares and Linear Programming: An Application to a Fully-Automated, Dual-Hormone Artificial Pancreas
The rigid-body attitude tracking using vector and biased gyro measurements with unknown inertia matrix is studied in this note. First, a gyro-bias observer with global exponential stability is designed. Then, an attitude tracking controller based on this observer is devised, ensuring almost global asymptotic stability and almost semiglobal exponential stability. A separation property of the combined observer-controller is proved. Lastly, an adaptive attitude tracking controller relying on a modified gyro-bias observer and with no over-parametrization is developed to deal with the unknown inert…
This paper proposes a real-time neural network (NN) stochastic filter-based controller on the Lie Group of the Special Orthogonal Group $SO(3)$ as a novel approach to the attitude tracking problem. The introduced solution consists of two parts: a filter and a controller. Firstly, an adaptive NN-based stochastic filter is proposed that estimates attitude components and dynamics using measurements supplied by onboard sensors directly. The filter design accounts for measurement uncertainties inherent to the attitude dynamics, namely unknown bias and noise corrupting angular velocity measurements.…
In order to obviate the requirement of drift dynamics in adaptive dynamic programming (ADP), integral reinforcement learning (IRL) has been proposed as an alternate formulation of Bellman equation.However control coupling dynamics is still needed to obtain closed form expression of optimal control effort. In addition to this, initial stabilizing controller and two sets of neural networks (NN) (known as Actor-Critic) are required to implement IRL scheme. In this paper, a stabilizing term in the critic update law is leveraged to avoid the requirement of an initial stabilizing controller in IRL f…
We propose a tracking control law for the fully actuated rigid body system in the presence of any unknown constant disturbance by employing quaternions with the stable embedding technique and Lyapunov stability theory. The stable embedding technique extends the attitude dynamics from the set of unit quaternions to the set of quaternions, which is a Euclidean space, such that the set of unit quaternions is an invariant set of the extended dynamics. Such a stable extension of the system dynamics to a Euclidean space allows us to employ well studied Lyapunov techniques in Euclidean spaces such as…
In this paper, we will consider a class of continuous-time stochastic control systems with both unknown nonlinear structure and unknown disturbances, and investigate the capability of the classical proportional-integral-derivative(PID) controller in tracking time-varying reference signals. First, under some suitable conditions on system nonlinear functions, reference signals, and unknown disturbances, we will show that PID controllers can be designed to globally stabilize such systems and ensure the boundedness of the tracking error. Analytic design formulae for PID gain matrices are also prov…
We present a distributed optimization algorithm for solving online personalized optimization problems over a network of computing and communicating nodes, each of which linked to a specific user. The local objective functions are assumed to have a composite structure and to consist of a known time-varying (engineering) part and an unknown (user-specific) part. Regarding the unknown part, it is assumed to have a known parametric (e.g., quadratic) structure a priori, whose parameters are to be learned along with the evolution of the algorithm. The algorithm is composed of two intertwined compone…
We address the problem of maintaining resource availability in a networked multi-robot team performing distributed tracking of unknown number of targets in an environment of interest. Based on our model, robots are equipped with sensing and computational resources enabling them to cooperatively track a set of targets in an environment using a distributed Probability Hypothesis Density (PHD) filter. We use the trace of a robot's sensor measurement noise covariance matrix to quantify its sensing quality. While executing the tracking task, if a robot experiences sensor quality degradation, then r…
In this paper, a new yet indirect performance guaranteed framework is established to address the distributed tracking control problem for networked uncertain nonlinear strict-feedback systems with unknown time-varying gains under a directed interaction topology. The proposed framework involves two steps: In the first one, a fully distributed robust filter is constructed to estimate the desired trajectory for each agent with guaranteed observation performance that allows the directions among the agents to be non-identical. In the second one, by establishing a novel lemma regarding Nussbaum func…
This work provides a framework for nonlinear model-free control of systems with unknown input-output dynamics, but outputs that can be controlled by the inputs. This framework leads to real-time control of the system such that a feasible output trajectory can be tracked by the inputs. Unlike existing model-free or data-driven control approaches, this framework guarantees nonlinear stability. The controller and observer designs in the proposed framework are nonlinearly stable and robust to the unknown dynamics as well as unknown measurement noise. For ease of computer implementation, the framew…
Feedforward control is essential to achieving good tracking performance in positioning systems. The aim of this paper is to develop an identification strategy for inverse models of systems with nonlinear dynamics of unknown structure using input-output data, which directly delivers feedforward signals for a-priori unknown tasks. To this end, inverse systems are regarded as noncausal nonlinear finite impulse response (NFIR) systems and modeled as a Gaussian Process with a stationary kernel function that imposes properties such as smoothness and periodicity. The approach is validated experimenta…
University of Pennsylvania（宾夕法尼亚大学）；Instituto de Ciencias Matematicas (CSIC-UAM-UCM-UC3M)（数学科学研究所（西班牙国家研究委员会-马德里自治大学-马德里康普顿斯大学-卡洛斯三世大学））；Technical University of Munich（慕尼黑工业大学）
Underactuated vehicles have gained much attention in the recent years due to the increasing amount of aerial and underwater vehicles as well as nanosatellites. Trajectory tracking control of these vehicles is a substantial aspect for an increasing range of application domains. However, external disturbances and parts of the internal dynamics are often unknown or very time-consuming to model. To overcome this issue, we present a tracking control law for underactuated rigid-body dynamics using an online learning-based oracle for the prediction of the unknown dynamics. We show that Gaussian proce…
Accuracy and stability are common requirements for Quadrotor trajectory tracking systems. Designing an accurate and stable tracking controller remains challenging, particularly in unknown and dynamic environments with complex aerodynamic disturbances. We propose a Quantile-approximation-based Distributional-reinforced Uncertainty Estimator (QuaDUE) to accurately identify the effects of aerodynamic disturbances, i.e., the uncertainties between the true and estimated Control Contraction Metrics (CCMs). Taking inspiration from contraction theory and integrating the QuaDUE for uncertainties, our n…
Geometric Fault-Tolerant Neural Network Tracking Control of Unknown Systems on Matrix Lie Groups
Department of Mechanical, Industrial, and Mechatronics Engineering, Toronto Metropolitan University（机械、工业与机电工程系，多伦多 metropolitan 大学）；Department of Electrical Engineering, Amirkabir University of Technology（电气工程系，阿米卡比尔技术大学）
In this paper, we present a Nonlinear-Proportional Integrator (N-PI) disturbance observer (DOB) to enhance the motion tracking of the performance of a surface-mounted Permanent Magnet Synchronous Motor (SPMSM) in rapidly speed varying regions. By presenting an N-PI-DOB for load torque estimation with torque modulation technique, we show that the tracking error dynamics of angular position/velocity are coupled with tracking errors of currents loop and estimation errors. After analyzing disturbances of currents tracking error dynamics, we design the N-PI-DOB and Lyapunov-based nonlinear currents…
Indian Institute of Science（印度科学学院）；WIRIN Lab（WIRIN实验室）
This paper presents a coupled, neural network-aided longitudinal cruise and lateral path-tracking controller for an autonomous vehicle with model uncertainties and experiencing unknown external disturbances. Using a feedback error learning mechanism, an inverse vehicle dynamics learning scheme utilizing an adaptive Radial Basis Function (RBF) neural network, referred to as the Extended Minimal Resource Allocating Network (EMRAN) is employed. EMRAN uses an extended Kalman filter for online learning and weight updates, and also incorporates a growing/pruning strategy for maintaining a compact ne…
AI-MOLE: Autonomous Iterative Motion Learning for Unknown Nonlinear Dynamics with Extensive Experimental Validation
Institute of Mechatronic Systems, Leibniz Universität Hannover（汉诺威莱布尼茨大学机电系统研究所）；Department Artificial Intelligence in Biomedical Engineering, FAU Erlangen-Nürnberg（埃尔朗根-纽伦堡大学生物医学工程人工智能系）
We present a method for contraction-based feedback motion planning of locally incrementally exponentially stabilizable systems with unknown dynamics that provides probabilistic safety and reachability guarantees. Given a dynamics dataset, our method learns a deep control-affine approximation of the dynamics. To find a trusted domain where this model can be used for planning, we obtain an estimate of the Lipschitz constant of the model error, which is valid with a given probability, in a region around the training data, providing a local, spatially-varying model error bound. We derive a traject…
Stable Gaussian Process based Tracking Control of Euler-Lagrange Systems
Chair of Information-oriented Control (ITR), Department of Electrical and Computer Engineering, Technical University of Munich（信息导向控制研究所（ITR），电气与计算机工程系，慕尼黑技术大学）；Adaptive Systems Laboratory, Department of Electrical and Computer Engineering, University of Waterloo（自适应系统实验室，电气与计算机工程系，滑铁卢大学）
Geometry-Aware Safety-Critical Local Reactive Controller for Robot Navigation in Unknown and Cluttered Environments
The Hong Kong University of Science and Technology（香港科技大学）；Hong Kong Baptist University（香港浸会大学）；The Hong Kong University of Science and Technology (Guangzhou)（香港科技大学（广州））
