Trajectory Tracking Applications Research Articles

Simplified Strategy for Trajectory Tracking Application of a Passive Suspension Rover-Type Mobile Robot

In the present work, based on an approximate modelling of a rover-type robot and a proportional control law, a simplified trajectory tracking strategy for a passive suspension rover-type mobile robot was developed. This strategy achieves trajectory tracking and the autonomous displacement of a rover, of which its configuration involves complex kinematics and dynamics. All these lineaments reduce the complexity of the analysis, the number of electronic components to implement, the computational requirements and the energy consumption. The robotic system used is based on the Shrimp rover, which is a robot with a passive suspension that is capable of carrying out displacements over rough terrain. The tests were performed using numerical simulations with different desired trajectories, and also using experimental tests using a passive suspension rover-type mobile robot.

Auxiliary Control to Avoid Undesirable Equilibria in Constrained Quadratic Programs for Trajectory Tracking Applications

Control Lyapunov function (CLF) and control barrier function (CBF) based quadratic programs (QPs) may create undesirable local equilibria in control systems. One recent solution utilizes a rotating nonradial CLF to avoid such equilibria in regulation applications. For trajectory tracking applications, a nominal feedback tracking control can be incorporated into the QP cost function to improve the tracking performance of the CLF–CBF–QP. However, the direction of the steepest descent curve of the CLF can differ from that of the nominal feedback control, which may compromise the tracking performance. Moreover, the design of a CLF is system-specific and generally not easy to realize. This article proposes a tracking–CBF–QP formulation, where a nominal tracking control is incorporated in the cost function of a CBF-based QP. If the nominal control conflicts with the CBF condition, undesirable local equilibria may be induced in the closed-loop system. This work theoretically investigates the occurrence of such undesirable local equilibria and provides an auxiliary control approach to prevent the system from falling into such equilibria. The auxiliary control is activated only when a conflict is projected between the nominal control and the CBF constraint, allowing the nominal control to guide the system otherwise. The proposed tracking–CBF–QP is utilized to design a novel leader–follower algorithm, and its effectiveness is verified experimentally.

Tracking control of a piezo-actuated compliant mechanism based on an improved Bouc–Wen hysteresis model with variable parameters

To deal with the challenges that the classical Bouc–Wen model fails to precisely characterize amplitude-dependent hysteresis and asymmetric hysteresis, an improved Bouc–Wen model with variable parameters is presented. The proposed model introduces asymmetric terms and parameter functions related to sinusoidal excitation amplitudes into the classical Bouc–Wen model. It has a relatively simple mathematic form and can be easily identified and applied for inverse feedforward compensation in real-time applications. By comparison with the classical Bouc–Wen model and other existing hysteresis models, the superiority of the proposed model has been verified. Furthermore, inverse hysteresis control and hybrid control combining the developed inverse control and proportional-integral feedback control are proposed. Several comparative experiments are conducted on a piezo-actuated micro-scanner. Results demonstrate that inverse control and hybrid control using the improved Bouc–Wen model with variable parameters can achieve better tracking performance and are meaningful in actual trajectory-tracking applications.

Trajectory tracking of Stanford robot manipulator by fractional-order sliding mode control

In this work, a fractional integral sliding-mode control scheme based on the Caputo–Fabrizio derivative and the Atangana–Baleanu integral of the Stanford robot for trajectory tracking tasks is developed and presented. The coupled system is composed of the robot manipulator and the induction motors that drive its joints. The mathematical model of the system is obtained by the Euler–Lagrange method and generalized to an arbitrary order via the Caputo–Fabrizio derivative. The actuators are controlled by fractional PI controllers based on the Atangana–Baleanu integral, while a fractional integral sliding mode control law is also developed for trajectory tracking control. In this context, a fractional version of the sliding surface via the Caputo–Fabrizio derivative is introduced to improve the performance of the control system. In addition, to attenuate the chattering effects, a fractional integral term, based on the Atangana–Baleanu integral, is introduced on the sliding surface further improving system performance with less power consumption. The conventional integral sliding mode control and an optimal super-twisting sliding mode control are also introduced for comparison with the proposed control strategy. The control schemes were tuned using the Cuckoo method. External disturbances are also considered in the system dynamics, as well as different end-effector reference trajectories, which were designed to carry out manufacturing tasks. Simulation results confirm the superiority of our control scheme for trajectory-tracking applications over its conventional version and the optimal super-twisting sliding mode control, even with external disturbances and trajectory changes. To show the robustness of the proposed control scheme under different operating conditions, all the numerical simulations were performed considering the same orders and gains. Finally, our control law introduces the fractional derivative and integral of Caputo–Fabrizio and Atangana–Baleanu respectively, which have not been used enough in the modeling and control of robotic systems. Therefore, it is interesting to analyze the contributions and advantages that arise when using them.

Trajectory Tracking via Backstepping Controller with PID or SMC for Mobile Robots

Mobile robot concept is one of the most commonly used nonholonomic system for industrial and academic autonomous applications. There are many types of mobile robot design concepts and control strategies which have been continuously developed by researchers. In this study, two wheeled differential drive mobile robot (DDMR) is used for trajectory tracking study under different conditions. Reference trajectory, dynamic and kinematic motion models of DDMR are defined as mathematical expressions in computer software. For tracking the reference trajectory, error between current pose and reference pose was decreased by sliding mode controller (SMC) and proportional–integral–derivative controller (PID) with kinematic based backstepping controller (KBBC) respectively. A reference path which consists of sinusoidal and linear parts tracked by both controller combinations in first simulation to examine controller tracking performances. In order to examine and compare; responsiveness, stability and robustness of the controllers, an additional mass which affects motion dynamics of DDMR vertically added to the mobile robot body during trajectory tracking application. All results and discussions are comparatively stated at the end of the study with related error figures and evaluations.

Multi-Stage Estimation Algorithm for Vehicle Trajectory Tracking

This paper develops a multi-stage estimation algorithm for vehicle trajectory tracking applications. Previously designed nonlinear observers for vehicle trajectory tracking lack either the ability to handle variable velocity or have a high sensitivity to sensor noise. To overcome these shortcomings, the original model of the non-ego vehicle is translated into three separate models for speed, orientation, and position. Three stable observers are designed for these models which are all shown to be stable and robust to uncertainties. The new estimation algorithm outperforms previous high-gain and LMI-based nonlinear observers. The developed observer is useful for collision prediction and avoidance applications.

A fixed-time convergent and noise-tolerant zeroing neural network for online solution of time-varying matrix inversion

As a common mathematical operation, the time-varying matrix inversion (TVMI) is frequently arisen in many complex problems. It has been proved in a large number of studies that the zeroing neural network (ZNN) is a reliable tool to solve TVMI problems. However, the previous reported conventional zeroing neural network (CZNN) models only achieve undesirable exponential convergence or finite-time convergence, and they are difficult to be popularized in practical applications. Therefore, by introducing a novel activation function (NAF), a fixed-time convergence and noise-tolerant zeroing neural network (FTCNTZNN) model for solving TVMI problems is proposed in this paper. Different from existing CZNN models, the proposed FTCNTZNN model possesses both fixed-time convergence and anti-noise properties for TVMI solving. To comprehensively show the superiority of the proposed FTCNTZNN model for solving TVMI, a lot of theoretical demonstrations and comparative simulation experiments have been provided in this work. Firstly, the fixed-time convergence and robustness of the proposed FTCNTZNN model are verified by detailed theoretical analysis in noiseless and noisy environment, respectively. Then, the proposed FTCNTZNN model is applied to solve two different TVMI problems in a variety of situations. In addition, a successful manipulator trajectory tracking application using the proposed FTCNTZNN model in noisy environment further validates its practicability. Both of theoretical analysis and experimental results convincingly verify that the proposed FTCNTZNN model can effectively solve TVMI problems in noiseless and noisy environment.

Robust trajectory tracking control of non-holonomic wheeled mobile robots using an adaptive fractional order parallel fuzzy PID controller

Non-holonomic wheeled mobile robots (WMRs) are highly uncertain, multi-input multi-output (MIMO), non-linear dynamic systems that are expected to perform under varying environment and structural reservations. An Adaptive Fractional Order Parallel Fuzzy Proportional-Integral-Derivative (AFO−PFPID) controller is proposed and investigated on WMR to meet the above challenges. Computer simulations were carried out under the effects of dynamic parameter variations, noise, forced displacement, time delay, and uncertainty in the pose to thoroughly assess the controller's performance. Further, to evaluate its relative assessment, the AFO−PFPID controller's performance is compared with its integer counterpart Adaptive Integer Order Parallel Fuzzy Proportional-Integral-Derivative (AIO−PFPID) controller. Both the controllers were tuned with the Multi-Objective Grey Wolf Optimization Algorithm to minimize the positional and velocity profile errors with an overall goal to attain effective trajectory tracking. Though both the controllers effectively performed tracking goals, the AFO−PFPID controller has offered a significantly robust performance even under the model uncertainties and disturbances. Therefore, based on the presented investigations, it is concluded that the AFO−PFPID controller is a superior control technique for non-holonomic WMRs trajectory tracking application.

Sliding Mode Control of a 2DOF Robot Manipulator: A Simulation Study Using Artificial Neural Networks with Minimum Parameter Learning

Background: In this paper we have developed an intelligent control law for the control of mobile manipulator robots by investigating the various techniques proposed in the literature. Thus, we have adopted a hybrid approach integrating part of classical and advanced automation in order to create an efficient control structure that can cope with a certain level of complexity. Our research logic is based on the process of keeping in mind that the control system must comply with the constraints imposed during the implementation of the control architecture. Objective: This paper aims to develop a control law in order to guarantee a certain level of performance and, more precisely, during a trajectory tracking application for mobile handling missions. The developed control law guarantees robustness with respect to external disturbances and parametric uncertainties due to the modelling of the system. Methods: In this paper, a study of the basic concepts of robotics and robot modelling is presented in order to set up the dynamic model used for the elaboration of the command. A sliding-mode controller based on a radial base function neural network with minimum parameter learning is developed for the Pelican robot as a two link robot manipulator. This approach, which combines a Radial Base Function Neuronal Network (RBFNN) and a Sliding Mode Control (SMC), is presented for the tracking control of this class of systems with unknown nonlinearities. The centres and outputs weights of the RBFNN are updated via online learning in accordance with the adaptive laws, allowing the control output of the neural network to approach the equivalent control in the sliding mode in the predetermined direction. The Lyapunov function is used to develop the adaptive control algorithm based on the RBFNN model. To reduce computational load and increase real-time arm performance, an RBFNN-based on the SMC with the Minimum Parameter Learning (MPL) method is designed. Results: Neural network sliding mode control is designed to underline the effectiveness of the approach to control the manipulator. This method of control ensure the tracking trajectories. Conclusion: The results of the simulation for the manipulator arm presented demonstrates the effectiveness of the modelling strategy, the correction and the robustness of the control approach.

Practical Nonlinear Model Predictive Controller Design for Trajectory Tracking of Unmanned Vehicles

The trajectory tracking issue of unmanned vehicles has attracted much attention recently, with the rapid development and implementation of sensing, communication, and computing technologies. This paper proposes a nonlinear model predictive controller (NMPC) for the trajectory tracking application of an unmanned vehicle (UV). First, a two-degree-of-freedom (2-DOF) kinematics model of this UV is used to derive the desirable controller with two control variables as forward velocity and yaw angle. Next, the one-step Euler method is employed to establish the nonlinear prediction model, then a nonlinear optimization objective function is formulated to minimize the tracking errors of forward velocity and yaw angle from a preset time-varying reference road. Finally, the effectiveness of the proposed NMPC scheme is assessed under two different driving scenarios via MATLAB simulations. The simulation results confirm that the proposed NMPC scheme reveals better control accuracy and computational efficiency than the standard MPC controller under two different prescribed roads. Moreover, an outdoor field test is conducted to verify the performance of the proposed NMPC scheme, and the results show that the proposed NMPC can be applied to the real vehicle and can improve the tracking accuracy and the driving stability of trajectory tracking.

A robust fast convergence zeroing neural network and its applications to dynamic Sylvester equation solving and robot trajectory tracking

In order to find the theoretical solution of a dynamic Sylvester equation (DSE) in noisy environment, a robust fast convergence zeroing neural network (RFCZNN) is proposed in this paper. Unlike the original zeroing neural network (ZNN) model with existing activation functions (AF), by introducing a new AF, the proposed RFCZNN model guarantees fixed-time convergence to theoretical solution of DSE and robustness against noise simultaneously. The effectiveness and robustness of the proposed RFCZNN model are investigated in theory and demonstrated through simulation results. In addition, its effectiveness and robustness are further verified by a successful robotic trajectory tracking application in noisy environment.

An Enhanced GRU Model With Application to Manipulator Trajectory Tracking

Service robots, e.g. massage robots, have attracted more and more attention in recent years and the most popular study within this field is trajectory tracking. Due to the actual demand for service robots, the solution of trajectory tracking requires fast convergence and high accuracy. In order to solve the above issues, this paper proposed an enhanced Gated recurrent unit (GRU) to deal with trajectory tracking tasks of robot manipulators. The main feature of enhanced GRU is utilizing cell states as well as various gate units to build a novel neural cell. Besides, the presented enhanced GRU resolves the problem of the general neural network model and large memory occupancy. Then the derivations about the computational process of cell state and mixed hidden state of the proposed model have been illustrated. Finally, three trajectory tracking applications, comparison, and visual simulation have verified feasibility as well as the superiority of the enhanced GRU model.

A Provably Constrained Neural Control Architecture With Prescribed Performance for Fault-Tolerant Redundant Manipulators

In this paper, a novel neural control architecture is proposed and investigated for resolving redundancy in trajectory tracking applications for manipulators with joint velocity constraints. First, a nonlinear invertible map is invoked to transform the constrained system state into a set of unconstrained variables, which allows the proposed framework to realize solutions that rigorously adhere to the specified bound constraints. Next, a quadratic program (QP) architecture is synthesized by incorporating suitably prescribed performance constraints to ensure that the resulting system error achieves exponential convergence to the ground truth while also ensuring that the system states evolve along trajectories with good transient and steady-state behavior. Thus, in contrast with previous approaches that do not rigorously guarantee the satisfaction of the bound constraint in the transient phase and/or steady-state, the proposed scheme ensures that these constraints are rigorously satisfied while achieving prescribed performance both during the transient phase and in the steady-state. The novelty of the proposed scheme lies in the fusion of prescribed performance constraints with the state and input constraints within the QP framework, which offers the important advantage of higher computational efficiency compared to leading alternative designs. A detailed theoretical analysis is undertaken to prove the global stability and convergence of the proposed scheme. Simulation and experimental results with the KUKA LBR IIWA 14 R820 manipulator are used to verify the efficacy of the proposed scheme in accomplishing trajectory tracking for the fault-free and fault-tolerant cases with multiple joint failures. Finally, detailed performance comparison studies with leading alternative designs are further used to illustrate the advantages of the proposed scheme.

Model-Based Control Strategy for Autonomous Vehicle Path Tracking Task

Abstract Despite the advanced technologies used in recent years, the lack of robust systems still exists. The automated steering system is a critical and complex task in the domain of the autonomous vehicle’s applications. This paper is a part of project that deals with model-based control strategy as one of the most common control strategies. The main objective is to present the implementations of Model Predictive Control (MPC) for an autonomous vehicle steering system in regards to trajectory tracking application. The obtained results are analysed and the efficiency of the use of MPC controller were discussed based on its behaviour and performance.

Design and experimental implementation of a new robust observer-based nonlinear controller for DC-DC buck converters

DC-DC buck converters are extensively used in many industrial and end-user applications where significant attention highlights their power-conversion efficiency and robustness to load and source disturbances. This paper considers the problem of DC-DC buck converter control for Maximum Power Point (MPP) and voltage trajectory tracking applications in renewable energy systems. A new nonlinear robust controller is proposed for fast and robust output voltage tracking in the DC bus of the power source. New states are augmented in the design of a novel composite sliding mode controller. Furthermore, a nonlinear state observer is incorporated in the design for current estimation. Parameters of the overall approach are tuned using Particle Swarm Optimization (PSO) algorithm with an objective to ensure a good balance between fast transients, robustness, and dynamic performance in practical implementations. This novel strategy is cost-efficient and accounts for the switched and nonlinear aspects of the problem in addition to disturbances. The stability of the closed-loop system is analyzed and guaranteed through Lyapunov stability theory. The low complexity of the presented controller grants it a remarkable advantage for higher reliability in physical realization. Moreover, comparative simulation tests and experimental results from multiple scenarios show significant trajectory-tracking improvements in terms of faster convergence rate with short transients and effective disturbance rejection performance compared to the optimally tuned Proportional Integral (PI) controller that is widely adopted in industrial applications.

PD Tracking for a Class of Underactuated Robotic Systems With Kinetic Symmetry

In this letter, we study stability properties of Proportional-Derivative (PD) controlled underactuated robotic systems for trajectory tracking applications. Stability of PD control laws for fully actuated systems is an established result, and we extend it for the class of underactuated robotic systems. We will first show some well known examples where PD tracking control laws do not yield tracking; some of which can even lead to instability. We will then show that for a subclass of robotic systems, PD tracking control laws, indeed, yield desirable tracking guarantees. We will show that for a specified time interval, and for sufficiently large enough PD gains (input saturations permitting), local boundedness of the tracking error can be guaranteed. In addition, for a class of systems with the kinetic symmetry property, stronger conditions like convergence to desirable bounds can be guaranteed. This class is not restrictive and includes robots like the acrobot, the cart-pole, and the inertia-wheel pendulums. Towards the end, we will provide necessary simulation results in support of the theoretical guarantees presented.

Barrier Lyapunov Function Based Controller Design for Euler-Lagrange Systems with Reduced Control Effort

In this paper, a novel nonlinear controller is designed for Euler- Lagrange (EL) systems while satisfying user-defined safety-constraints in position variables. The EL systems, which are highly popular for modeling a variety of non-linear mechanical plants like aircraft, spacecraft, quad-rotors, robotic manipulators, etc., critically demand safety-constraint satisfaction during trajectory tracking applications. Barrier Lyapunov Function (BLF) is widely used for systematically designing the controller to prevent safety-constraint violation during trajectory tracking. By proving the boundedness of BLF in a closed loop, safety-constraint satisfaction is analytically guaranteed. The fundamental principle of BLF is that if the states are reaching close to the boundary of a safe region, the high control input is applied to the system to push states far inside the boundary. In practical scenarios, such a high control effort requirement may lead to the critical problem of actuator saturation. This work alleviates the issue of high control effort requirements in the BLF framework. The proposed BLF-based controller is capable of guaranteeing safety-constraint satisfaction with less control effort, making the design practically viable. Simulation results validate significant improvement in terms of reduction in control input magnitude of the proposed algorithm in contrast to conventional BLF-based control algorithms.

Two-Stage Robot Controller Auto-Tuning Methodology for Trajectory Tracking Applications

Autonomy is increasingly demanded of industrial manipulators. Robots have to be capable of regulating their behavior to different operational conditions, without requiring high time/resource-consuming human intervention. Achieving an automated tuning of the control parameters of a manipulator is still a challenging task. This paper addresses the problem of automated tuning of the manipulator controller for trajectory tracking. A Bayesian optimization algorithm is proposed to tune firstly the low-level controller parameters (i.e., robot dynamics compensation), then the high-level controller parameters (i.e., the joint PID gains), providing a two-stage robot controller auto-tuning methodology. In both the optimization phases, the algorithm adapts the control parameters through a data-driven procedure, optimizing a user-defined trajectory tracking cost. Safety constraints ensuring, e.g., closed-loop stability and bounds on the maximum joint position errors, are also included. The performance of the proposed approach is demonstrated on a torque-controlled 7-degree-of-freedom FRANKA Emika robot manipulator. The 4 robot dynamics parameters (i.e., 4 link-mass parameters) are tuned in 40 iterations, while the robot control parameters (i.e., 21 PID gains) are tuned in 90 iterations. Comparable trajectory tracking-errors results with respect to the FRANKA Emika embedded position controller are achieved.

Design of a Feedforward-Feedback Controller for a Piezoelectric-Driven Mechanism to Achieve High-Frequency Nonperiodic Motion Tracking

Piezoelectric-driven mechanisms have several advantages like high stiffness, rapid response, and good resolution. Therefore, they are widely used for many micro/nano trajectory-tracking applications. However, the existence of the hysteretic nonlinearity behavior makes it challenging to use in practice. In addition, the hysteresis changes with frequency and is dependent on environmental parameters like temperature and load. Finding a method that can track both continuous periodic and nonperiodic motion under wide frequency range with high precision is nontrivial. In this study, a feedforward-feedback control strategy is proposed to bridge this gap, where a direct inverse rate-dependent Prandtl–Ishlinskii model based on radial basis function neural network to compensate rate-dependent hysteresis and a proportional-integral controller with an inner-loop disturbance observer to further attenuate tracking error (caused by the imperfect modeling, unknown lumped disturbance). The proposed method can perform a wide-bandwidth tracking control of periodic and nonperiodic motion of a piezoelectric-driven mechanism. Experiments are then conducted to demonstrate the capability of the proposed controller.

A new on-line observer-based controller for leader-follower formation of multiple nonholonomic mobile robots

In this paper, a novel on-line observer-based trajectory tracking strategy for leader-follower formation of multiple nonholonomic mobile robots is developed. In the proposed strategy, a leader robot follows a certain trajectory whereas a number of followers track the leader as specified by a formation protocol. Unlike other techniques in the literature, a predefined trajectory is not required, and it can be changed on-line. Moreover, this strategy aims to have a fast transient response without showing undesired overshoots. To achieve this feature, a new observer is introduced. Based on the output of that observer, a control strategy with two components is derived. The first control component is responsible for tracking the desired trajectory, whereas the second control component is used to regulate the robot to its desired steady state position. The stability of the closed loop control system is investigated. Applications of the proposed observer-based controller to different case studies are presented to illustrate the effectiveness, robustness and applicability of the developed technique. To show the superiority of proposed controller, its performance in a trajectory tracking application is compared to that of a Lyapunov-based controller.