Path Tracking Task Research Articles

Path Tracking Control for Underactuated Vehicles With Matched-Mismatched Uncertainties: An Uncertainty Decomposition Based Constraint-Following Approach

This paper presents a robust path tracking control method by utilizing the ideology of constraint-following approach for uncertain underactuated autonomous vehicles. The uncertainties are bounded with an unknown boundary. They do not all fall within the range space of the input matrix. Based on kinematic relations between the desired path and vehicle, the path tracking task is transformed into an equality constraint of the vehicle lateral dynamics states. The control goal is to make the underactuated vehicle follow the constraint, thus realizing the desired tracking performance. The constraint-following robust control (CFRC) is designed in two steps. First, a servo control design for the nominal system is devised without considering uncertainty and initial constraint deviation. Second, the uncertainty is meticulously decomposed into matched and mismatched portions based on the geometric structural characteristics of the constraint dynamics system. As a result, since the mismatched uncertainty is orthogonal to the constraint-following geometric space, it “disappears” in the stability analysis. The matched uncertainty is estimated by a self-adjusting leakage type adaptive law. On this basis, a robust control is designed based on the estimated matched uncertainty. Through Lyapunov minimax analysis, the proposed control method guarantees the approximate constraint-following performance. Finally, the TruckSim–Simulink co-simulations and real vehicle experiments are presented. The results show that the proposed control can robustly realize excellent tracking performance in the presence of time-vary uncertainties.

Path-Tracking Considering Yaw Stability With Passivity-Based Control for Autonomous Vehicles

In this paper, a new passivity-based control approach is designed to improve the robustness and stability of autonomous vehicles in performing path-tracking tasks. A port-Hamiltonian model is a special geometric structure and provides a systematic and insightful framework to describe many physical systems from an energy perspective. The passivity-based control establishes a new and simple structure to achieve the path-tracking task by the port-Hamiltonian structure. Firstly, the path-tracking error system is transformed into a port-Hamiltonian system with the perturbation. The energy-shaping method is utilized to ensure the asymptotic stability, and the stability proof of the closed-loop, path-tracking error system is given. The proposed real-time, passivity-based controller is directly dependent on the passive outputs, which is robust to parameter uncertainties caused by load changes. Moreover, the control performance of steering control will be degraded when the steering angle is saturated. The yaw-moment control is introduced to enhance the driving safety. In the wheel torque distribution, an optimization-based control allocation is designed to minimize the sum of tire loads and to make them more evenly distributed to each tire. Finally, simulations are implemented in MATLAB/Simulink and CarSim co-simulation to demonstrate the effectiveness of the designed strategy under different driving conditions.

대잠전용 무인수상로봇의 자율운항시스템 설계를 위한 LQR 기반 경로추종 알고리즘 연구

This paper presents the usage of LQR-based intelligent path tracking methods to control the autonomous navigation system of an Unmanned Surface Robot (USR) in sea-clutter environmental fields. Since considerable interest in the Autonomous Navigation System (ANS) of USR in sea warfare has increased, the stability of the Autonomous Navigation System (ANS) control becomes of the utmost importance. When the USR moves in sea environments, the control stability of autonomous navigation systems becomes a major concern. The Path Tracking Controller (PTC) of USRs is one of the high potential subsystems that can be further improved to achieve more accurate, robust, and comfortable tracking performance. The stability of the PTC should be taken into consideration while performing the path tracking task in autonomous navigation. To solve the automatic waypoint tracking stability of independently-developed PTCs, a waypoint tracking controller is designed based on the Linear Quadratic Regulator (LQR) theory with the kinematic model of USRs. Then, a simulation analysis of the designed waypoint tracking controller is performed, and the results are compared at two different speeds. Additionally, complex waypoint tracking tests under realistic sea conditions are performed based on the designed waypoint tracking controller. Results show good tracking performance, which indicates that the designed waypoint tracking controller can adapt to high-speed USRs.

Model-based recurrent neural network for redundancy resolution of manipulator with remote centre of motion constraints

Redundancy resolution is a critical issue to achieve accurate kinematic control for manipulators. End-effectors of manipulators can track desired paths well with suitable resolved joint variables. In some manipulation applications such as selecting insertion paths to thrill through a set of points, it requires the distal link of a manipulator to translate along such fixed point and then perform manipulation tasks. The point is known as remote centre of motion (RCM) to constrain motion planning and kinematic control of manipulators. Together with its end-effector finishing path tracking tasks, the redundancy resolution of a manipulators has to maintain RCM to produce reliable resolved joint angles. However, current existing redundancy resolution schemes on manipulators based on recurrent neural networks (RNNs) mainly are focusing on unrestricted motion without RCM constraints considered. In this paper, an RNN-based approach is proposed to solve the redundancy resolution issue with RCM constraints, developing a new general dynamic optimisation formulation containing the RCM constraints. Theoretical analysis shows the theoretical derivation and convergence of the proposed RNN for redundancy resolution of manipulators with RCM constraints. Simulation results further demonstrate the efficiency of the proposed method in end-effector path tracking control under RCM constraints based on an industrial redundant manipulator system.

Improving path-tracking performance of an articulated tractor-trailer system using a non-linear kinematic model

This paper presents a novel non-linear mathematical model of an articulated tractor-trailer system that can be used, in combination with receding horizon techniques, to improve the performance of path tracking tasks of articulated systems. Due to its dual steering mechanisms, this type of vehicle can be very useful in precision agriculture, particularly for seeding, spraying and harvesting in small fields. The articulated tractor-trailer system model was embedded within a non-linear model predictive controller and the trailer position was monitored. When the kinematic of the trailer was considered, the deviation of trailer’s position was reduced substantially alongside not only straight paths but also in headland turns. Using the proposed mathematical model, we were able to control the trailer’s position itself rather than the tractor’s position. The Robot Operating System (ROS) framework and Gazebo simulator were used to perform realistic simulations examples.

A Noninvasive BCI System for 2D Cursor Control Using a Spectral-Temporal Long Short-Term Memory Network.

Two-dimensional cursor control is an important and challenging problem in the field of electroencephalography (EEG)-based brain computer interfaces (BCIs) applications. However, most BCIs based on categorical outputs are incapable of generating accurate and smooth control trajectories. In this article, a novel EEG decoding framework based on a spectral-temporal long short-term memory (stLSTM) network is proposed to generate control signals in the horizontal and vertical directions for accurate cursor control. Precisely, the spectral information is used to decode the subject's motor imagery intention, and the error-related P300 information is used to detect a deviation in the movement trajectory. The concatenated spectral and temporal features are fed into the stLSTM network and mapped to the velocities in vertical and horizontal directions of the 2D cursor under the velocity-constrained (VC) strategy, which enables the decoding network to fit the velocity in the imaginary direction and simultaneously suppress the velocity in the non-imaginary direction. This proposed framework was validated on a public real BCI control dataset. Results show that compared with the state-of-the-art method, the RMSE of the proposed method in the non-imaginary directions on the testing sets of 2D control tasks is reduced by an average of 63.45%. Besides, the visualization of the actual trajectories distribution of the cursor also demonstrates that the decoupling of velocity is capable of yielding accurate cursor control in complex path tracking tasks and significantly improves the control accuracy.

Human-Tailored Data-Driven Control System of Autonomous Vehicles

Path Tracking Controller (PTC) plays a key role in achieving improved dynamic behaviour of Autonomous Vehicle (AV) while it is mainly responsible for implementing the planned paths. In this work, a learning-based Model Predictive Controller (MPC) is proposed to integrate a data-driven approach to the path tracking task using human driving demonstrations. The objective is to reproduce customised vehicle motion profile that is statistically comparable to a human driver with a proper trade-off between vehicle speed-acceleration profile and tracking accuracy. A combined longitudinal and lateral MPC controller with a novel feature-based parametric cost function is designed to perform the path tracking task under different road conditions. A high precision data logging system is developed to collect human driving demonstration data. From the analysis of the collected data, relevant features are chosen based on their applicability to produce a customised motion profile while performing AV’s path tracking task. Next, a bi-level optimisation-based Inverse Optimal Controller (IOC) is designed to learn the cost function’s parameters using the human demonstration data. The outcomes of the study show that the proposed controller can effectively regenerate some characteristics of human driving, including speed, longitudinal and lateral accelerations, and yaw rate.

Motor skill learning decreases movement variability and increases planning horizon.

We investigated motor skill learning using a path tracking task, where human subjects had to track various curved paths at a constant speed while maintaining the cursor within the path width. Subjects' accuracy increased with practice, even when tracking novel untrained paths. Using a "searchlight" paradigm, where only a short segment of the path ahead of the cursor was shown, we found that subjects with a higher tracking skill differed from the novice subjects in two respects. First, they had lower movement variability, in agreement with previous findings. Second, they took a longer section of the future path into account when performing the task, i.e., had a longer planning horizon. We estimate that between one-third and one-half of the performance increase in the expert group was due to the longer planning horizon. An optimal control model with a fixed horizon (receding horizon control) that increases with tracking skill quantitatively captured the subjects' movement behavior. These findings demonstrate that human subjects not only increase their motor acuity but also their planning horizon when acquiring a motor skill.NEW & NOTEWORTHY We show that when learning a motor skill humans are using information about the environment from an increasingly longer amount of the movement path ahead to improve performance. Crucial features of the behavioral performance can be captured by modeling the behavioral data with a receding horizon optimal control model.

An L₁-Norm Based Optimization Method for Sparse Redundancy Resolution of Robotic Manipulators

For targeted motion control tasks of manipulators, it is frequently necessary to make use of full levels of joint actuation to guarantee successful motion planning and path tracking. Such way of motion planning and control may keep the joint actuation in a non-sparse manner during motion control process. In order to improve sparsity of joint actuation for manipulator systems, a novel motion planning scheme which can optimally and sparsely adopt joint actuation is proposed in this brief. The proposed motion planning strategy is formulated as a constrained <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$L_{1}$ </tex-math></inline-formula> norm optimization problem, and an equivalent enhanced optimization solution dealing with bounded joint velocity is proposed as well. A new primal dual neural network with a new solution set division is further proposed and applied to solve such bounded optimization which can sparsely adopt joint actuation for motion control. Simulation and experiment results demonstrate the efficiency, accuracy and superiority of the proposed method for optimally and sparsely adopting joint actuation. The average sparsity (i.e., - <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\|\dot \theta \|_{p}$ </tex-math></inline-formula> where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\theta $ </tex-math></inline-formula> denotes the joint angle) of the joint motion of the manipulator can be increased by 39.22% and 51.30% for path tracking tasks in <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$X - Y$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$X - Z$ </tex-math></inline-formula> planes respectively, indicating that the sparsity of joint actuation can be enhanced.

Performance analysis of real-time and general-purpose operating systems for path planning of the multi-robot systems

In general, modern operating systems can be divided into two essential parts, real-time operating systems (RTOS) and general-purpose operating systems (GPOS). The main difference between GPOS and RTOS is the system istime-critical or not. It means that; in GPOS, a high-priority thread cannot preempt a kernel call. But, in RTOS, a low-priority task is preempted by a high-priority task if necessary, even if it’s executing a kernel call. Most Linux distributions can be used as both GPOS and RTOS with kernel modifications. In this study, two Linux distributions, Ubuntu and Pardus, were analyzed and their performances were compared both as GPOS and RTOS for path planning of the multi-robot systems. Robot groups with different numbers of members were used to perform the path tracking tasks using both Ubuntu and Pardus as GPOS and RTOS. In this way, both the performance of two different Linux distributions in robotic applications were observed and compared in two forms, GPOS, and RTOS.

Path Tracking and Position Control of Nonholonomic Differential Drive Wheeled Mobile Robot

Differential drive wheeled mobile robot (DDWMR) is one example of a robot with a constrained movement, Multiple Input Multiple Output (MIMO), and nonlinear system. Designing a low resource position and heading controller using linear MIMO methods such as LQR became a problem because of the linearization of robot dynamics at zero value. One of the solutions is to design a MIMO controller using a Single Input Single Output (SISO) controller. This work design a controller using PID for DDWMR Jetbot and selects the best feedback gain using different scenarios. The designed controller manipulates both motors by using calculated control signal to achieve a complex task such as path tracking with robot position in x-Axis, y-Axis, and heading angle as the feedback. The priority between position and heading angle can be adjusted by changing three feedback gains. The controller was tested, and the best gain was selected using Integral Absolute Error (IAE) metrics in a path tracking task with four different path shapes. The proposed methods can track square, circle, and two types of infinity shape paths, with the less well-formed shape being the four edges square path.

Adaptive dynamic programming for nonaffine nonlinear optimal control problem with state constraints

This paper presents a constrained adaptive dynamic programming (CADP) algorithm to solve general nonlinear nonaffine optimal control problems with known dynamics. Unlike previous ADP algorithms, it can directly deal with problems with state constraints. Firstly, a constrained generalized policy iteration (CGPI) framework is developed to handle state constraints by transforming the traditional policy improvement process into a constrained policy optimization problem. Next, we propose an actor-critic variant of CGPI, called CADP, in which both policy and value functions are approximated by multi-layer neural networks to directly map the system states to control inputs and value function, respectively. CADP linearizes the constrained optimization problem locally into a quadratically constrained linear programming problem, and then obtains the optimal update of the policy network by solving its dual problem. A trust region constraint is added to prevent excessive policy update, thus ensuring linearization accuracy. We determine the feasibility of the policy optimization problem by calculating the minimum trust region boundary and update the policy using two recovery rules when infeasible. The vehicle control problem in the path-tracking task is used to demonstrate the effectiveness of this proposed method.

Implementation of six degree-of-freedom high-precision robotic phantom on commercial industrial robotic manipulator

This technical note discloses our implementation of a six degree-of-freedom (DOF) high-precision robotic phantom on a commercially available industrial robot manipulator. These manipulators are designed to optimize their set point tracking accuracy as it is the most important performance metric for industrial manipulators. Their in-house controllers are tuned to suppress its error less than a few tens of micrometers. However, the use of industrial robot manipulators in six DOF robotic phantom can be a difficult problem since their in-house controller are not optimized for continuous path tracking in general. Although instantaneous tracking error in a continuous path tracking task will not exceed five millimeters during motion with the in-house controller, it seriously matters for a robotic phantom, as the tracking error should remain within one millimeter in three dimensional space for all time during motion. The difficulty of the task is further increased since the reference trajectory of a robotic phantom, which is a six DOF tumor motion of a patient, cannot be as smooth as the ones used in factories. The present study presents a feedforward controller for a feedback-controlled industrial six DOF robotic manipulator to be used as a six DOF robotic phantom to drive the water equivalent phantom (WEP). We first trained a set of six recurrent neural networks (RNNs) to capture the six DOF input/output behavior of the robotic manipulator controlled by its in-house controller, and we proceed to formulate an iterative learning control (ILC) using the trained model to generate an augmented reference trajectory for a specific patient that enables very high tracking accuracy to that trajectory. Experimental evaluation results demonstrate clear improvements in the accuracy of the proposed robotic phantom compared to our previous robotic phantom, which uses the same manipulator but is driven by a different corrected reference trajectory.

Dynamic Modeling and Control of a Parallel Mechanism Used in the Propulsion System of a Biomimetic Underwater Vehicle

Incorporation of parallel mechanisms inside propulsion systems in biomimetic autonomous underwater vehicles (BAUVs) is a novel approach for motion generation. The vehicle to which the studied propulsion system is implemented presents thunniform locomotion, and its thrust depends mainly on the oscillation from its caudal fin. This paper describes the kinematic and dynamic modeling of a 3-DOF spherical 3UCU-1S parallel robotic system to which the caudal fin of a BAUV is attached. Lagrange formalism was employed for inverse dynamic modeling, and its derivation is detailed throughout this paper. Additionally, the implementation of control strategies to compute forces required to actuate limbs to change platform’s flapping frequencies was developed. Four controllers: classic PD, a feedforward plus feedback PD, an adaptive Fuzzy-PD, and a feedforward plus Fuzzy-PD were compared in different simulations. Results showed that augmenting oscillating frequencies (from 0.5 to 5 Hz) increased the complexity of the path tracking task, where the classic control strategy (i.e., PD) was not sufficient, reaching percentage errors above 9%. Control strategies using feedforward terms combined with adaptive feedback techniques reduced tracking error below 2% even during the presence of external disturbances.

Path-tracking control for autonomous vehicles using double-hidden-layer output feedback neural network fast nonsingular terminal sliding mode

In this paper, a double-hidden-layer output feedback neural network fast nonsingular terminal sliding mode control strategy is developed for path-tracking tasks of autonomous vehicles. First, a vehicle kinematic-and-dynamic model is established to describe the vehicle’s fundamental lateral dynamics in path-tracking behavior. Afterwards, detailed design procedure of the proposed controller is shown, where the control system’s stability is verified in the Lyapunov sense. Finally, MATLAB-Carsim co-simulations are executed for the aim of testing the control performance. Simulation results illustrate that the designed control algorithm possesses remarkable superiority reflected in higher tracking precision, faster convergence rate and firmer robustness in comparison with a conventional sliding mode controller and a nonsingular terminal sliding mode controller.

Design and Optimization of Robust Path Tracking Control for Autonomous Vehicles With Fuzzy Uncertainty

Uncertainty is a major concern in vehicle path tracking control design. The coefficients of the uncertainty bound are unknown. They are assumed to lie within prescribed fuzzy sets. First, based on the path tracking kinematic model, this paper innovatively formulates the vehicle path tracking task as a constraint-following problem. Second, we put forward a deterministic adaptive robust control law with a tunable parameter to ensure the uniform boundedness and ultimate uniform boundedness of the closed-loop system. Third, an optimal scheme for the tunable parameter is proposed based on the fuzzy uncertainty. The resulting optimal robust control (ORC) minimizes a comprehensive fuzzy performance index that involves the fuzzy system performance and the control cost. The results of the CarSim-Simulink co-simulation and the Hardware-in-loop (HIL) experiment together show that the proposed optimal robust control exhibits a superior path tracking performance.

Inverse kinematics for cooperative mobile manipulators based on self-adaptive differential evolution.

This article presents an approach to solve the inverse kinematics of cooperative mobile manipulators for coordinate manipulation tasks. A self-adaptive differential evolution algorithm is used to solve the inverse kinematics as a global constrained optimization problem. A kinematics model of the cooperative mobile manipulators system is proposed, considering a system with two omnidirectional platform manipulators with n DOF. An objective function is formulated based on the forward kinematics equations. Consequently, the proposed approach does not suffer from singularities because it does not require the inversion of any Jacobian matrix. The design of the objective function also contains penalty functions to handle the joint limits constraints. Simulation experiments are performed to test the proposed approach for solving coordinate path tracking tasks. The solutions of the inverse kinematics show precise and accurate results. The experimental setup considers two mobile manipulators based on the KUKA Youbot system to demonstrate the applicability of the proposed approach.

A robust path tracking algorithm for connected and automated vehicles under i-VICS

Connected and automated vehicle (CAV) can obtain the precise vehicle location information via vehicle to infrastructure (V2I) communication to achieve the path tracking task under the intelligent vehicle-infrastructure cooperative system (i-VICS). However, in some special scenarios, the location information of vehicles might become inaccurate or lost, e.g., the vehicle loses contact with the road-side unit (RSU). To improve the reliability of vehicle location information, we concentrate on solving two kinds of tracking problems, i.e., vehicle location information is inaccurate and lost in this paper. First, a predicted method using vehicle dynamics is presented to recognize the scenarios in which the vehicle location information becomes inaccurate when the vehicle moves. Then, a modified Kalman filter is employed to adapt to a more complex scenario with variable position error. After that, a multilayer perceptron (MLP) model is designed to predict vehicle location information when vehicle location information is lost. At last, simulation results demonstrate that the proposed methods have a marked influence on handling the driving scenario and make our path tracking algorithm more robust.

Deep reinforcement learning based path tracking controller for autonomous vehicle

Path tracking is an essential task for autonomous vehicles (AV), for which controllers are designed to issue commands so that the AV will follow the planned path properly to ensure operational safety, comfort, and efficiency. While solving the time-varying nonlinear vehicle dynamic problem is still challenging today, deep neural network (NN) methods, with their capability to deal with nonlinear systems, provide an alternative approach to tackle the difficulties. This study explores the potential of using deep reinforcement learning (DRL) for vehicle control and applies it to the path tracking task. In this study, proximal policy optimization (PPO) is selected as the DRL algorithm and is combined with the conventional pure pursuit (PP) method to structure the vehicle controller architecture. The PP method is used to generate a baseline steering control command, and the PPO is used to derive a correction command to mitigate the inaccuracy associated with the baseline from PP. The blend of the two controllers makes the overall operation more robust and adaptive and attains the optimality to improve tracking performance. In this paper, the structure, settings and training process of the PPO are described. Simulation experiments are carried out based on the proposed methodology, and the results show that the path tracking capability in a low-speed driving condition is significantly enhanced.

Development of a Hybrid Path Planning Algorithm and a Bio-Inspired Control for an Omni-Wheel Mobile Robot.

This research presents a control structure for an omni-wheel mobile robot (OWMR). The control structure includes the path planning module and the motion control module. In order to secure the robustness and fast control performance required in the operating environment of OWMR, a bio-inspired control method, brain limbic system (BLS)-based control, was applied. Based on the derived OWMR kinematic model, a motion controller was designed. Additionally, an optimal path planning module is suggested by combining the advantages of A* algorithm and the fuzzy analytic hierarchy process (FAHP). In order to verify the performance of the proposed motion control strategy and path planning algorithm, numerical simulations were conducted. Through a point-to-point movement task, circular path tracking task, and randomly moving target tracking task, it was confirmed that the suggesting motion controller is superior to the existing controllers, such as PID. In addition, A*–FAHP was applied to the OWMR to verify the performance of the proposed path planning algorithm, and it was simulated based on the static warehouse environment, dynamic warehouse environment, and autonomous ballet parking scenarios. The simulation results demonstrated that the proposed algorithm generates the optimal path in a short time without collision with stop and moving obstacles.