Smooth Trajectory Tracking Research Articles

A Novel Robust Hybrid Control Strategy for a Quadrotor Trajectory Tracking Aided with Bioinspired Neural Dynamics

This paper introduces a novel hybrid control strategy for quadrotor UAVs inspired by neural dynamics. Our approach effectively addresses two common issues: the velocity jump problem in traditional backstepping control and the control signal chattering in conventional sliding mode control. The proposed system combines an outer-loop bioinspired backstepping controller with an inner-loop bioinspired sliding mode controller, ensuring smooth trajectory tracking even under external disturbances. We rigorously analyzed the system’s stability using Lyapunov stability theory. To validate our algorithm’s effectiveness, we conducted trajectory tracking experiments in both disturbance-free and step-disturbance conditions, comparing it with the traditional backstepping control, conventional sliding mode control, and saturated sliding mode control. The results demonstrate that our algorithm not only tracks trajectories more effectively but also significantly outperforms these methods in suppressing velocity jumps and signal chattering.

An adaptive framework for trajectory following in changing-contact robot manipulation tasks

We describe an adaptive control framework for changing-contact robot manipulation tasks that require the robot to make and break contacts with objects and surfaces. The piecewise continuous interaction dynamics of such tasks make it difficult to construct and use a single dynamics model or control strategy. Also, the nonlinear dynamics during contact changes can damage the robot or the domain objects. Our framework enables the robot to incrementally improve its prediction of contact changes in such tasks, efficiently learn models for the piecewise continuous interaction dynamics, and to provide smooth and accurate trajectory tracking based on a task-space variable impedance controller. We experimentally compare the performance of our framework against that of representative control methods to establish that the adaptive control, prediction, and incremental learning capabilities of our framework are essential to achieve the desired smooth control of changing-contact robot manipulation tasks.

Mixed-Integer Motion Planning on German Roads Within the Apollo Driving Stack

Traffic situations with interacting participants pose difficulties for today’s autonomous vehicles to interpret situations and eventually achieve their own mission goal. Interactive planning approaches are promising solutions for solving such situations. However, most approaches are only assessed in simulation, as researchers lack the resources to operate an autonomous vehicle. Likewise, open-source stacks for autonomous driving, such as Apollo, provide competitive and resource-efficient state-of-the-art planning algorithms. However, promising planning concepts from research are usually not included within a reasonable time, possibly due to resource restrictions or technical limitations. Without evaluating these novel algorithms in reality, the benefits and shortcomings of proposed approaches cannot be thoroughly assessed. This work aims to contribute methodology and implementation to integrate a novel mixed-integer optimization-based planning algorithm in Apollo’s planning component and assess its performance and real-time capability in theory and practice. It discusses the necessary modifications of Apollo for deployment on a different vehicle and presents three real-world driving experiments on a public road alongside a detailed experience report. The driving experiments show a smooth trajectory tracking performance operating robustly under varying perception data quality and the real-time capability of the closed-loop system.

Nonlinear Model Predictive Control of J2-perturbed impulsive transfer trajectories in long-range rendezvous missions

This paper develops a Nonlinear Model Predictive Control (NMPC) strategy for robust tracking of multi-impulse smooth transfer trajectories in J2-perturbed orbital environments. The reference trajectories are designed for long-range rendezvous of servicing satellites with orbiting targets. In the proposed NMPC, the control signals are velocity increments at the impulse times, and the prediction horizon is variable due to the impulsive nature of the reference trajectories. The reference control input and the impulse times are pre-specified by the reference trajectory. Then, the NMPC calculates the optimal correction control vector to track the trajectory with minimum deviation and control effort, during the time between two consecutive impulses. To arrive near the target at the end of the transfer, the optimization in the last horizon is modified to be free-final-time, with an added soft constraint to minimize the final distance between the servicer and the target satellite. To avoid singularities in the mean dynamics of the J2-perturbed servicer, the equinoctial orbital elements are used in the process model. We also include the first-order long-periodic effects in this model. We investigate the robustness of the proposed NMPC in a simulation environment that additionally models: (i) the first-order short-periodic effects, (ii) a bounded uncertain acceleration to capture unmodelled dynamics, and (iii) burning time for satellite thrusters. Finally, an evolutionary optimization algorithm is implemented and embedded in the controller to decrease the computational complexity and to handle impulsive control inputs. Simulation results are provided to illustrate the tracking effectiveness of the developed controller.

Design and practical implementation of a Neural Network self-tuned Inverse Dynamic Controller for a 3-DoF Delta parallel robot based on Arc Length Function for smooth trajectory tracking

This paper proposes an online Neural Network self-tuned Inverse Dynamic Controller (IDC) for high-speed and smooth trajectory tracking control of a 3-DoF Delta robot. The foregoing approaches provides a suitable controller for a wide range of nonlinear paths and reduce the end-effector oscillations at high speed. To this end, a compact and accurate dynamic model of the system is derived by taking into account actuators and gearbox dynamics. In order to alleviate some drawbacks of a velocity-based controller, such as not being able to track highly dynamic paths, an Inverse Dynamic Controller (IDC) is designed which can perform fast maneuvers accurately. The proposed IDC controller is practically implemented on the robot in following nonlinear paths comparing to the velocity-based controller. Afterward, controller parameters are tuned by resorting to the so-called Arc Length Function (ALF) in order to improve the smoothness of tracking the prescribed path. After that, a Feedforward Neural Network (NN) is trained with the help of the system’s model and Arc Length Function (ALF) to adjust controller coefficients in real-time implementation adaptively. By comparing the Root Mean Square Error (RMSE) results, it can be inferred that the proposed methods can reduce the end-effector oscillations up to 60 percent in practical implementation compared to other dynamic and kinematic methods. As a result, RMSE error is reduced from 0.00603 for the kinematic controller to 0.00063 by applying the NN-IDC.

Research on local trajectory planning of autonomous mobile robots

In the process of autonomous motion, the mobile robot needs real-time local trajectory planning based on the global smooth path and nominal local trajectory tracking. In this paper, the local trajectory planning problem of mobile robot is studied, and the local path represented by quintic polynomial is optimized in Frenet coordinate system with the global smooth path as reference path, then, according to the information of the robot’s pose, velocity and angular velocity, the robot’s velocity is planned according to all kinds of constraints. A LQR closed loop control law is designed to realize the precise tracking of local optimal trajectory, which makes the robot move safely and stably in the dynamic environment. In the “maze” simulation environment, using the Stageros simulator the local trajectory planning algorithm is tested, and the validity and correctness of the algorithm are verified.

Data-Driven Multiobjective Controller Optimization for a Magnetically Levitated Nanopositioning System

The performance achieved with traditional model-based control system design approaches typically relies heavily on accurate modeling of the motion dynamics. However, modeling the true dynamics of present-day increasingly complex systems can be an extremely challenging task; and the usually necessary practical approximations often renders the automation system to operate in a nonoptimal condition. This problem can be greatly aggravated in the case of a multiaxis magnetically levitated (maglev) nanopositioning system where the fully floating behavior and multiaxis coupling make extremely accurate identification of the motion dynamics largely impossible. On the other hand, in many related industrial automation applications, e.g., the scanning process with the maglev system, repetitive motions are involved which could generate a large amount of motion data under nonoptimal conditions. These motion data essentially contain rich information; therefore, the possibility exists to develop an intelligent automation system to learn from these motion data, and to drive the system to operate toward optimality in a data-driven manner. Along this line then, this article proposes a data-driven model-free controller optimization approach that learns from the past nonoptimal motion data to iteratively improve the motion control performance. Specifically, a novel data-driven multiobjective optimization approach is proposed that is able to automatically estimate the gradient and Hessian purely based on the measured motion data; the multiobjective cost function is suitably designed to take into account both smooth and accurate trajectory tracking. In this article, experiments are then conducted on the maglev nanopositioning system to demonstrate the effectiveness of the proposed method, and the results show rather clearly the practical appeal of our methodology for related complex robotic systems with no accurate model available.

Trajectory Tracking of Wheeled Mobile Robots Using Z-Number Based Fuzzy Logic

Being trajectory tracking key for safe mobile robot navigation, Fuzzy Logic (FL) has been useful in tackling uncertainty and imprecision to realize robust and smooth trajectory tracking. In this paper, we present the Z-number based Fuzzy Logic control for trajectory tracking of differential wheeled mobile robots. The unique point of our approach lies in the ability to encode constraint and reliability in multi-input and multi-output rules, whose antecedent universe considers only the instantaneous measurements of distance and the orientation gaps, and whose consequent universe is computed by the interpolative reasoning and the graded mean integration approach. As a consequence, not only our approach avoids the complexity of encoding error gradients, but also is advantageous to model versatile control rules able to cope with missing observations and noisy inducements on actuators. Our experiments using both physics-based simulations and real-world tests based on a Pioneer 3DX robot architecture have elucidated the superior efficacy and the feasibility of the proposed controller regarding accuracy, robustness, and smoothness compared to other well-known related frameworks such as Fuzzy Logic Type 1, Fuzzy Logic Type 2 and Fuzzy Logic with PID. Our results provide unique insights to realize generalizable algorithms aided by FL and Z-number towards robust trajectory tracking.

Fault-Tolerant Adaptive Model Inversion Control for Vision-Based Autonomous Air Refueling

The practical autonomous air refueling of unmanned air system tanker aircraft to unmanned air system receiver aircraft will require an integrated relative navigation system and controller that is tolerant to faults. This paper develops and demonstrates a fault-tolerant structured-adaptive-model-inversion controller integrated with a reliable relative-position sensor for this autonomous air-refueling scenario using the probe-and-drogue method. The structured-adaptive-model-inversion controller does not depend on fault-detection information, yet reconfigures and provides smooth trajectory tracking and probe docking in the presence of control-effector failure. The controller also handles parameter uncertainty in the receiver-aircraft model. In this paper, the controller is integrated with a vision-based relative-position sensor, which tracks the relative position of the drogue, and a reference-trajectory generator. The feasibility and performance of the controller and integrated system are demonstrated with simulated docking maneuvers with a nonstationary drogue, in the presence of system uncertainties and control-effector failures. The results presented in the paper demonstrate that the integrated controller/sensor system can provide successful docking in the presence of system uncertainties for a specified class of control-effector failures.

Maximum Torque-per-Amp Control for Traction IM Drives: Theory and Experimental Results

A novel maximum torque per Ampere (MTPA) controller for the induction motor (IM) drives is presented. It is shown to be highly suited to applications that do not demand an extremely fast dynamic response, for example, electric vehicle drives. The proposed MTPA field oriented controller guarantees asymptotic torque (speed) tracking of smooth reference trajectories and maximizes the torque per Ampere ratio when the developed torque is constant or slow varying. An output-feedback linearizing concept is employed for the design of torque and flux subsystems to compensate for the torque-dependent flux variations required to satisfy the MTPA condition. As a first step, a linear approximation of the IM magnetic system is considered. Then, based on a standard saturated IM model, the nonlinear MTPA relationship for the rotor flux are derived as a function of the desired torque, and a modified torque–flux controller for the saturated machine is developed. The static and dynamic flux reference calculation methods to achieve simultaneously an asymptotic field orientation, a torque–flux decoupling, and an MTPA optimization in a steady state, is proposed. The method guarantees a singularity free operation and can be used as means to improve stator current transients. Experimental tests prove the accuracy of the control over a full torque range and show successful compensation of the magnetizing inductance variations caused by saturation. The proposed MTPA control algorithm also demonstrates a decoupling of the torque (speed) and flux dynamics to ensure asymptotic torque tracking. In addition, a higher torque per Ampere ratio is achieved together with an improved efficiency of electromechanical energy conversion.

Modelling and Trajectory Tracking of Wheeled Mobile Robots

Differential drive mobile robots are widely used due to their simplicity, easiness of control and flexibility. This paper discuss a detailed modeling of a differential drive robot taking into account the kinematics, actuator dynamics and rolling resistances of the wheels. Controllers have been designed for smooth trajectory tracking. Different trajectories similar to real life scenarios have been created and the model and control algorithm are seen to give accurate trajectory tracking.

Experience mapping based prediction controller for the smooth trajectory tracking of DC motors

Experience mapping based prediction controller (EMPC) is a novel controller based on the human motor control mechanism. The application of EMPC for the precise position control of PMDC motors and the performance analysis using step responses is present in literature. However, the performance of the EMPC control concepts in trajectory tracking applications is not studied. This paper investigates the trajectory control of a PMDC motor using EMPC. The ability of EMPC to control the position along an arbitrarily selected trajectory and the limitations of the quasi-open-loop control structure of EMPC in trajectory tracking applications are studied. A modification to the control strategy which retains the quasi-open-loop control structure is suggested to improve the performance. Further, a novel method is developed within the existing framework of EMPC in this paper for the prediction of duty-cycle to achieve the required steady-state velocity output of the DC motor system and this is employed for smooth trajectory tracking. The proposed method is tested in simulation and the results are analyzed and compared with that of MRAC and LQG techniques. The robustness of the proposed technique to changes in system parameters is also studied. All the proposed techniques are also implemented on a practical laboratory setup and the results are provided. The proposed methods are used for plotting and drawing on a XY plotter and the results are presented and discussed.

Modeling and Sliding Mode Control of a Micro Helicopter-Airplane System

This paper presents the regulation and trajectory tracking for a Micro Coaxial Rocket Helicopter (MCR UAV), as well as the control of a mini aircraft. The former vehicle has the characteristic of performing hover and forward flight while the latter vehicle is considered as an external air transporter for the MCR UAV. For control purposes, the helicopter stabilization is based on sliding mode controllers which avoid the chattering generated during the flight and allow the MCR UAV to perform tracking of smooth trajectories, Furthermore a PD controller stabilizes the aircraft in order to execute semi-autonomous flight. A flight computer for these aerial vehicles consists of a homemade embedded system, low-cost sensors, and signal conditioning circuits, analog filters and actuator. The proposed control algorithms are implemented on the embedded system. Simulation and experimental results show the good performance of the developed system during the flight.

Adaptive backstepping control of a speed-sensorless induction motor under time-varying load torque and rotor resistance uncertainty

A new global adaptive backstepping controller is designed for induction motor speed control based on measurements of stator current and estimation of rotor speed. The designed partial state feedback controller is singularity free and guarantees asymptotic tracking of smooth reference trajectories for the speed of the motor under time varying load torque and rotor resistance uncertainty. The new control algorithm generates estimates for unknown time varying load torque, rotor resistance and rotor speed, which asymptotically tracks and converges to their true values. The rotor flux modulus asymptotically tracks a desired reference signal which allows the motor to operate within its specifications. As in the field-oriented control scheme; the control algorithm generates references for the magnetising flux component and for the speed component of the stator current. The control strategy yields decoupled rotor speed and rotor flux amplitude tracking control goals which allow the selection of an appropriate flu...

Adaptive backstepping control of an induction motor under time-varying load torque and rotor resistance uncertainty

A new global adaptive controller is designed for induction motor speed control based on measurements of speed and stator current. The designed partial state feedback controller is singularity free, and guarantees asymptotic tracking of smooth reference trajectories for the speed of the motor under time-varying load torque and rotor resistance uncertainty, for any initial condition. The new control algorithm generates estimates for unknown time-varying load torque, rotor resistance and unmeasured state variables (rotor fluxes) which asymptotically tracks and converges to their true values. The rotor flux modulus asymptotically tracks a desired reference signal which allows the motor to operate within its specifications. The control strategy yields decoupled rotor speed and rotor flux amplitude tracking control goals which allows the selection of an appropriate flux modulus for the rotor to maximise efficiency.

Robust Smooth-Trajectory Control of Nonlinear Servo Systems Based on Neural Networks

The electromagnetic torque introduces ripples into the electromechanical motion system due to nonlinearities, such as uncertain changes of magnet field, load, and friction, which generate speed oscillations and deteriorate the tracking performance of servo system. Furthermore, the minimum time response and smooth trajectory tracking are cruces in servo control. In this paper, an available method is proposed to solve them by using neural networks (NNs) and a nonlinear smooth trajectory filter (STF) for the robust smoothing feedforward control of a class of general nonlinear systems. First, the online weight-tuning scheme based on Lyapunov function can guarantee the boundedness of tracking error by good performance of NNs modeling nonlinear functions. Second, a feedforward controller based on the output of nonlinear STF is designed to guarantee minimum time response and smooth trajectory tracking. Finally, as a example, the motion system can be equivalent to the two-order system under the linear closed-loop current control in view of the (d,q) mathematic model for PM synchronous motor, so that this robust smoothing control method using neutral networks can be applied into position servo control. Moreover, the validity and effectiveness of this control method are verified through simulations and experiments

Nonlinear Predictive Control With End Point Constraints

The optimal nonlinear predictive control structure with end point constraints is presented, which provides asymptotic tracking of smooth reference trajectories. The controller is based on a finite horizon continuous time minimization of nonlinear predicted tracking errors. A key feature of the control law is that its implementation does not need to perform an online optimization, and asymptotic tracking of smooth reference signal is guaranteed. The proposed control scheme is applied to planning motions problem of a mobile robot. Simulations results are performed to validate the tracking performance of the proposed controller.

Autonomous control of multi-fingered hand*

Abstract This paper describes a novel autonomous control strategy of multi-fingered hand based on a modular control system of dexterous manipulation. A simple proportional-integral-derivative(PID) position control with friction compensation, which requires few friction parameters, is used to realize accurate and smooth trajectory tracking in pregrasp phase. In grasp and manipulation phases, an event-driven switcher is adopted to determine the switching between unconstrained position control and constrained torque control, and an improved explicit integral force control strategy is implemented to realize simultaneously stable contact transition and accurate force tracking. Experimental results have verified the effectiveness of the proposed autonomous control strategy of multi-fingered hand. * Supported by National Natural Science Foundation of China (Grant No. 60275032)

Application of a multi-DOF ultrasonic servomotor in an auditory tele-existence robot

A multi-degree-of-freedom (DOF) ultrasonic motor can rotate in three DOFs and does not generate noise. In addition, with an appropriate preloading mechanism, it can generate high torque for its size. The multi-DOF ultrasonic motor is, therefore, anticipated for use as a servomotor in the next generation of robots. However, for several reasons, there have been few applications of multi-DOF ultrasonic motors. One reason is the difficulty in designing a proper preloading mechanism for the motor and the limitation of the size of the stators. Another is the difficulty in developing a control algorithm, due to the motor's complex and changing dynamical characteristics, and the serious jaggy motion caused by its very quick response. This paper proposes a preloading mechanism and control algorithm for a multi-DOF ultrasonic motor, considering the motor's application to an actual auditory tele-existence robot, TeleHead. TeleHead is an elaborate dummy head robot that has a 3-DOF neck mechanism. The proposed methods achieve smooth and fast multi-DOF rotating motion of the dummy head with little time delay. In the preloading method, tensioned springs generate high preloading force and make up for the lack of torque by compensating for the resistance torque generated by the inclining motion of the dummy head. In the control algorithm, high-DOF motion is managed by high-frequency switching of the rotating axis, and smooth and quick trajectory tracking motion is achieved by introducing feed-forward control using an inverse model, with multiresolution acquired by feedback-error learning. Experimental results verify the high performance of these methods.

Nonlinear Receding-Horizon Control of Rigid Link Robot Manipulators

The approximate nonlinear receding-horizon control law is used to treat the trajectory tracking control problem of rigid link robot manipulators. The derived nonlinear predictive law uses a quadratic performance index of the predicted tracking error and the predicted control effort. A key feature of this control law is that, for their implementation, there is no need to perform an online optimization, and asymptotic tracking of smooth reference trajectories is guaranteed. It is shown that this controller achieves the positions tracking objectives via link position measurements. The stability convergence of the output tracking error to the origin is proved. To enhance the robustness of the closed loop system with respect to payload uncertainties and viscous friction, an integral action is introduced in the loop. A nonlinear observer is used to estimate velocity. Simulation results for a two-link rigid robot are performed to validate the performance of the proposed controller.