Trajectory Tracking Task Research Articles

Robust sensorless low‐speed trajectory tracking for a permanent magnet synchronous motor: An extended state observer based backstepping control approach

This article deals with the low‐speed sensorless trajectory tracking control of a permanent magnet synchronous motor (PMSM). The rotor position and angular speed are obtained through back electromotive forces (back‐EMF), using extended state observers (ESOs) in the alpha‐beta coordinates. Additionally, the estimation of the back‐EMF is used by an algebraic module to reconstruct online the position and speed using an off‐line estimation of the back‐EMF parameter . The control law is derived using a robust recursive controller design methodology, namely; the backstepping design approach in the d‐q coordinates. Estimation schemes allow the adaptation of the angular position, angular speed, and the load torque parameters in the control law. With this adaptation, the controller achieves the necessary robustness to reduce the effects of endogenous and exogenous perturbations present in the PMSM system. The trajectory tracking task is achieved at low angular speed, with the presence of a load torque applied to the motor shaft. Experimental results at low‐speed and rated load/no‐load conditions are presented to demonstrate the effectiveness and robustness of the proposed scheme.

Finite-Time Terminal Sliding Mode Tracking Control of a VTOL UAV via the Generalized NDOB

In this paper, we propose a finite-time sliding mode trajectory tracking control methodology for the vertical takeoff and landing unmanned aerial vehicle (VTOL UAV). Firstly, a system error model of trajectory tracking task is established based on Rodrigues parameters by considering both external and internal uncertainties. According to the cascade property, the system model is divided into translational and rotational subsystems, and a hierarchical control structure is hence proposed. Then, a finite-time generalized nonlinear disturbance observer (NDOB) is proposed, based on which the finite-time convergence result of equivalent disturbance estimation can be acquired. Finally, by introducing a tan-type compensator into the traditional terminal sliding mode control (SMC), the finite-time convergence result of the closed-loop control system is acquired based on Lyapunov stability analysis. Simulation results show the effectiveness of the proposed methodology.

Neural Control of Robot Manipulators With Trajectory Tracking Constraints and Input Saturation.

This article presents a control scheme for the robot manipulator's trajectory tracking task considering output error constraints and control input saturation. We provide an alternative way to remove the feasibility condition that most BLF-based controllers should meet and design a control scheme on the premise that constraint violation possibly happens due to the control input saturation. A bounded barrier Lyapunov function is proposed and adopted to handle the output error constraints. Besides, to suppress the input saturation effect, an auxiliary system is designed and emerged into the control scheme. Moreover, a simplified RBFNN structure is adopted to approximate the lumped uncertainties. Simulation and experimental results demonstrate the effectiveness of the proposed control scheme.

Trajectory tracking control based on non-singular fractional derivatives for the PUMA 560 robot arm

In this paper, a novel hybrid fractional-order control strategy for the PUMA-560 robot manipulator is developed and presented, which combines the derivative of Caputo–Fabrizio and the integral of Atangana–Baleanu, both in the Caputo sense. The fractional-order dynamic model of the system (FODM) is also considered which consists of two models, the robot manipulator model, and the model of the induction motors which are the actuators that drive their joints. The fractional model of the manipulator is obtained using the Euler–Lagrange formulation. On the other hand, for controlling each one of the induction motors, fractional-order controllers ${{\mathop{\mathrm{PI}}\nolimits } ^{\vartheta }}$ based on Atangana–Baleanu in the Caputo sense integral were developed. And for the trajectory tracking control, fractional-order controllers ${{\mathop{\mathrm{PD}}\nolimits } ^{\xi }}$ were developed based on the fractional derivative of Caputo–Fabrizio in the Caputo sense. Also, ordinary PI and PD controllers were developed for the PUMA robot control to compare their performance with the fractional-order controllers. The results obtained demonstrated that the fractional-order controllers have a better capability for tracking trajectory tasks than the integer-order controllers, even when changes of the desired trajectory and external disturbances are considered. Additionally, an end-effector trajectory tracking task for manufacturing applications is also considered. All numerical simulations were performed by using the same orders and gains, demonstrating that the proposed fractional-order ${{\mathop{\mathrm{PI}}\nolimits } ^{\vartheta }}$ and ${{\mathop{\mathrm{PD}}\nolimits } ^{\xi }}$ controllers are robust, under different operating conditions, for tracking trajectory tasks. The fractional-order controllers and the integer-order controllers were tuned applying the cuckoo search optimization algorithm where the root-mean-square error (RMSE) was chosen as the cost function to minimize.

Prescribed performance trajectory tracking control of dynamic positioning ship under input saturation

This paper investigates concentrates on the trajectory tracking control problem of dynamic positioning (DP) ship, in the presence of the time-varying disturbance and input saturation. Firstly, a simplified mathematical model of three degrees of freedom is established. According to the characteristics of the DP ship, an adaptive backstepping controller which combine the prescribed performance function with disturbance observer is proposed. The control scheme can guarantee the transient and steady state performance of the trajectory tracking and meet the prescribed performance criteria. In addition, an auxiliary dynamic system is introduced into the controller to deal with the input saturation problem of the actuator, so that the DP ship can accomplish the task of trajectory tracking under the condition of actuator constraint. Subsequently, in combination of barrier Lyapunov function (BLF), it is proved that the DP system can stabilize and converge rapidly to the small neighborhood of the equilibrium point, which can achieve the prescribed performance. Finally, the effectiveness of the DP control law is demonstrated by a series of simulation experiments.

On the Weighting of Control Signals in a Multi-robot System: A Formation-Based Analysis

This work presents a strategy to guide an n-robot convoy in a rigid virtual structure, split into $$n-2$$ triangular formations. Each set of three robots represents one formation, and transformation functions relate the robots’ position to the formation’s pose and shape, and vice versa. Each triangular formation has its own constructive sequence (clockwise or counterclockwise), which depends on the robots’ position, and is crucial for the control navigation. As first contribution, we propose a strategy based on cross-product concept to identify automatically the current and the desired triangle sequence. Furthermore, once knowing each robot can belong up to three formations, our second contribution is a control signals weighting, to improve simultaneous convergence of the whole formation. Finally, we present real experiments with four Pioneer-3DX robots performing a trajectory tracking task to validate our proposal.

Motion Planning and Coordinated Control of Underwater Vehicle-Manipulator Systems with Inertial Delay Control and Fuzzy Compensator

This paper presents new motion planning and robust coordinated control schemes for trajectory tracking of the underwater vehicle-manipulator system (UVMS) subjected to model uncertainties, time-varying external disturbances, payload and sensory noises. A redundancy resolution technique with a new secondary task and nonlinear function is proposed to generate trajectories for the vehicle and manipulator. In this way, the vehicle attitude and manipulator position are aligned in such a way that the interactive forces are reduced. To resist sensory measurement noises, an extended Kalman filter (EKF) is utilized to estimate the UVMS states. Using these estimates, a tracking controller based on feedback Linearization with both the joint-space and task-space tracking errors is proposed. Moreover, the inertial delay control (IDC) is incorporated in the proposed control scheme to estimate the lumped uncertainties and disturbances. In addition, a fuzzy compensator based on these estimates via IDC is introduced for reducing the undesired effects of perturbations. Trajectory tracking tasks on a five-degrees-of-freedom (5-DOF) underwater vehicle equipped with a 3-DOF manipulator are numerically simulated. The comparative results demonstrate the performance of the proposed controller in terms of tracking errors, energy consumption and robustness against uncertainties and disturbances.

Zero dynamics assignment and its applications to the stabilization of linear time-varying systems

An algorithm to select an output for desired vector relative degree, which is not restricted to be uniform (the same for all outputs), and zero dynamics in linear time-varying (LTV) multi-input multi-output (MIMO) systems is proposed. The proposed algorithm is developed under reasonable assumptions of uniform (with respect to time) and lexicography-fixed controllability (with some choice of fixed controllability indices) and is inspired by a generalization of the Ackermann’s formula. One application of the proposed algorithm is the context of higher-order sliding-mode control for perturbed LTV MIMO systems, achieving finite-time stability. The developed algorithm also provides an extension of the classical Ackermann–Utkin formula for outputs of uniform relative degree one and includes the design of flat outputs for LTV MIMO systems. Hence other application is the feedback controller design for trajectory tracking task. Finally, a complete HOSM methodology is provided and tested in an LTV model of the non-holonomic car.

Comparison of Control Methods for Trajectory Tracking in Fully Actuated Unmanned Aerial Vehicles

In this article, recently proposed control methods, suitable for trajectory tracking in fully actuated unmanned aerial vehicles (UAVs), are reviewed and experimentally compared. We specifically focus on multirotor platforms with tiltable propellers, for which the thrust and torque delivered by each rotor can be oriented within the aircraft frame using servo actuators. First, the main assumptions underlying the control design model usually employed in the literature are discussed, pointing out the main limitations. Then, some recent control laws that have been proposed to address the trajectory tracking problem for these platforms are reviewed, placing emphasis on their tracking capabilities as well as on the ease of tuning and implementation. Finally, experimental results obtained by applying three control laws on a tilt-arm quadrotor UAV are shown to evaluate and compare their performance. Two experiments, representative of operating conditions for thrust-vectoring UAVs, have been performed: a set-point tracking with level attitude and a full-pose trajectory tracking task.

ANFIS controller design based on pigeon-inspired optimization to control an UAV trajectory tracking task

Unmanned aerial vehicles (UAVs) are flying platforms that have become increasingly used in a wide range of applications. However, the most recent research has aimed to improve the quality of UAV control to achieve its mission accurately. This paper proposes a robust and intelligent control method based on adaptive neuro-fuzzy inference system (ANFIS), and pigeon-inspired optimization algorithm (PIO) to govern the behavior of a three-degree of freedom (3-DOF) quadrotor UAV. The quadrotor was chosen due to its simple mechanical structure; nevertheless, these types of UAVs are highly nonlinear. Intelligent control that uses artificial intelligence computing approach such as fuzzy logic is a suitable choice to better control nonlinear systems. The ANFIS controller is proposed to control the movement of UAV to track a given reference trajectory in 2D vertical plane. The PIO is used to obtain the ANFIS optimal parameters with the aim of improving the quality of the controller and therefore, to minimize tracking error. To evaluate the performance of the ANFIS controller tuned by PIO, a comparison between the proposed ANFIS-PIO, ANFIS and proportional–integral–derivative controllers is illustrated, and comparative results demonstrate that the proposed controller is more effective.

Space manipulator trajectory tracking based on recursive decentralized finite-time control

In this paper, a novel decentralized control strategy with finite-time convergence is developed for the trajectory tracking of a space manipulator. The existing control schemes for a space manipulator can be classified into two main categories: centralized ones and decentralized ones. The former regards the robot as a high dimensional system with strong nonlinearity, thus the controllers are with multiple-input and multiple-output forms. The latter treats the system as a number of decoupled subsystems, each of which corresponds to a link of the manipulator. There are a set of decentralized single-input and single-output controllers for each subsystem. The centralized control has high performance and large calculation cost, whereas the decentralized control has relatively low control precision, but with high computational efficiency. This work combines the above two schemes to propose a compromised control strategy—recursive decentralized finite-time control. The space manipulator is viewed as a set of interconnected subsystems. The tracking error equations of each subsystem are firstly written based on the recursive dynamic model of the system. Then the decentralized non-singular terminal sliding mode (NTSM) control law is designed to make the tracking error converge to an arbitrarily small neighborhood of the origin within a finite time. Finally, numerical simulations of the trajectory tracking task for a space manipulator are given to verify the effectiveness and efficiency of the control scheme.

Nested Saturation Function Control of a Magnetic Levitation System

The trajectory tracking task of a magnetic levitation system connected to a beam mechanism is solved by means of a nested saturation control with a feedforward term. The flatness property of the system allows to use the nested saturation control technique and the feedforward control to stabilize the output tracking error around the equilibrium. The closed-loop error dynamics is proven to be locally exponentially stable. Numerical simulations prove the effectiveness of the proposal.

Optimization of ANFIS controllers using improved ant colony to control an UAV trajectory tracking task

Development of unmanned aerial vehicles (UAVs) has become the most important research areas in the field of autonomous aeronautical control. This paper proposes a robust and intelligent controller based on adaptive-network-based fuzzy inference system (ANFIS) and improved ant colony optimization (IACO) to govern the behavior of a three degree of freedom quadrotor UAV. The quadrotor was chosen due to its simple mechanical structure; nevertheless, these types of aircraft are highly nonlinear. Intelligent control such as fuzzy logic is a suitable choice for controlling nonlinear systems. The ANFIS controller is used to reproduce the desired trajectory of the quadrotor in 2D Vertical plane and the IACO algorithm aims is to facilitate convergence to the ANFIS’s optimal parameters in order to reduce learning errors and improve the quality of the controller. To evaluate the performance of the proposed IACO tuned ANFIS controller, a comparison between the proposed ANFIS-IACO controller and other controller’s performance such us ANFIS only and proportional–integral–derivative controllers is illustrated using the same system. As expected, the hybrid ANFIS-IACO controller gives very satisfactory results than the others methods already developed in the same study.

Fuzzy swarm trajectory tracking control of unmanned aerial vehicle

Abstract Accurate and precise trajectory tracking is crucial for unmanned aerial vehicles (UAVs) to operate in disturbed environments. This paper presents a novel tracking hybrid controller for a quadrotor UAV that combines the robust adaptive neuro-fuzzy inference system (ANFIS) and particle swarm optimization (PSO) algorithm. The ANFIS-PSO controller is implemented to govern the behavior of three degrees of freedom quadrotor UAV. The ANFIS controller allows controlling the movement of UAV to track a given trajectory in a 2D vertical plane. The PSO algorithm provides an automatic adjustment of the ANFIS parameters to reduce tracking error and improve the quality of the controller. The results showed perfect behavior for the control law to control a UAV trajectory tracking task. To show the effectiveness of the intelligent controller, simulation results are given to confirm the advantages of the proposed control method, compared with ANFIS and PID control methods.

Adaptive disturbance observer for trajectory tracking control of underwater vehicles

Complex and highly coupled dynamics, time-variance, unpredictable disturbances and lack of knowledge of hydrodynamic parameters, complicate the control of underwater vehicles. This paper deals with the adaptive disturbance observer design for the robust trajectory tracking problem for underwater vehicles in presence of unknown external disturbances and parametric uncertainties. First, the dynamics of the vehicle is transformed into the so-called regular form. Then, based on the Extended State Observer technique and High Order Sliding Modes Control, a disturbance observer is proposed. Furthermore, the gains of the observer are automatically adjusted by the introduction of an adaption law. The stability of the whole controller/observer scheme is proven using Lyapunov’s arguments. The adaptive disturbance observer aims to improve the Backstepping and nonlinear PD controllers. Real-Time experiments demonstrate the effectiveness of the proposed algorithm for the trajectory tracking task under several scenarios.

Human-in-the-Loop Assessment of an Ultralight, Low-Cost Body Posture Tracking Device.

In rehabilitation, assistive and space robotics, the capability to track the body posture of a user in real time is highly desirable. In more specific cases, such as teleoperated extra-vehicular activity, prosthetics and home service robotics, the ideal posture-tracking device must also be wearable, light and low-power, while still enforcing the best possible accuracy. Additionally, the device must be targeted at effective human-machine interaction. In this paper, we present and test such a device based upon commercial inertial measurement units: it weighs 575 g in total, lasts up to 10.5 h of continual operation, can be donned and doffed in under a minute and costs less than 290 EUR. We assess the attainable performance in terms of error in an online trajectory-tracking task in Virtual Reality using the device through an experiment involving 10 subjects, showing that an average user can attain a precision of 0.66 cm during a static precision task and 6.33 cm while tracking a moving trajectory, when tested in the full peri-personal space of a user.

IART: Learning From Demonstration for Assisted Robotic Therapy Using LSTM

In this paper, we present an intelligent Assistant for Robotic Therapy (iART), that provides robotic assistance during 3D trajectory tracking tasks. We propose a novel LSTM-based robot learning from demonstration (LfD) paradigm to mimic a therapist's assistance behavior. iART presents a trajectory agnostic LfD routine that can generalize learned behavior from a single trajectory to any 3D shape. Once the therapist's behavior has been learned, iART enables the patient to modify this behavior as per their preference. The system requires only a single demonstration of 2 minutes and exhibits a mean accuracy of 91.41% in predicting, and hence mimicking a therapist's assistance behavior. The system delivers stable assistance in realtime and successfully reproduces different types of assistance behaviors.

Collaboration and Task Planning of Turtle-Inspired Multiple Amphibious Spherical Robots.

Amphibious Spherical Robots (ASRs) use an electric field to communicate and collaborate effectively in a turbid water of confined spaces where other mode communication modalities failed. This paper proposes an embedded architecture formation strategy for a group of turtle-inspired amphibious robots to maintain a long distance-parameterized path based on dynamic visual servoing. Inspired by this biological phenomenon, we design an artificial multi-robot cooperative mode and explore an electronic communication and collaborate devices, the control method is based in particular on underwater environment and also conduct a detailed analysis of control motion module. The objectives of control strategies are divided into four categories: The first strategy is that the leader robot controls the action of the overall robots to maintain collaborate together during motion along a desired geometric path and to follow a timing law that the communication efficiency and the arrival times to assigned sites. Furthermore, we design an adaptive visual servoing controller for trajectory tracking task, taking into account system dynamics with environment interactions. After that, the third strategy is a centralized optimization algorithm for the redistribution of target mission changes. Finally, this paper also proposes a new method of control strategies in order to guarantee that each robot in the team moves together according to the preset target toward its location in the group formation based on communication and stability modules.

Intuitive Planning, Generation, and Tracking of Trajectory for WMR With Mobile Computing Device and Embedded System

With the intention of delivering an intuitive and simple platform to plan, generate, and track trajectories with a WMR, this paper presents a technological integration of hardware and software. This technological integration consists of a mobile computing device with an app developed by authors for the trajectory planning and a differential drive WMR that possesses an embedded system, in which a trajectory generation algorithm and a trajectory tracking control algorithm -both proposed by authors - are programmed. The mobile computing device wirelessly drives the WMR through the embedded system. The app is developed on the basis of the sketch approach, since it allows drawing sketches of the trajectory intuitively on the mobile device. Also, the app geometrically scales the sketch coordinates to match them with the real WMR workspace. For the trajectory generation, these scaled coordinates are wirelessly sent to the embedded system, where the trajectory generation algorithm joins them by using Bezier polynomials and concatenation of straight-lines. Hence, the tracking task is carried out with the control algorithm, which is proposed departing from the dynamic model of the WMR and whose asymptotic stability proof is performed with the Lyapunov method. Experimental results verify that the technological integration successfully plans, generates, and tracks trajectories, even when the WMR is far from the initial coordinate of the desired trajectory. These results, corroborate the good performance and robustness of the proposed control algorithm. Thus, the introduced technological integration is intuitive and simple since users only have to draw a sketch on the mobile device to carry out the trajectory tracking task.

Haptic Shared Control for Human-Robot Collaboration: A Game-Theoretical Approach

Abstract Complementing human and robot capabilities is essential for many tasks, e.g. rehabilitation and collaborative manufacturing. However, it is still not clear how control between humans and robots should be shared in order to ensure efficient task execution and intuitive interaction. Game theory seems as a promising mathematical framework that allows: i) posing this challenge as a dynamic negotiation (game) among human and robot (players) and ii) solving it to obtain optimal solution. In this work, we propose a differential game-theoretic shared control approach for human-robot haptic collaboration with Nash equilibrium optimal solution. We validate the proposed approach experimentally in a scenario where human is physically coupled with a haptic device and interacts with a virtual reality to perform a trajectory tracking task.