Reference Trajectory Tracking Research Articles

Gradient-Based Predictive Pulse Pattern Control of Medium-Voltage Drives—Part I: Control, Concept, and Analysis

This article proposes a control and modulation strategy for medium-voltage (MV) drives that exhibits excellent steady-state and transient behavior. Specifically, optimized pulse patterns (OPPs) and direct model predictive control are employed so that the associated advantages of both, such as minimum stator current total demand distortion (TDD) and fast transients, respectively, are fully exploited. To do so, the current reference trajectory tracking and modulation problems are addressed in a coordinated manner in the form of a constrained optimization problem that utilizes the knowledge of the stator current evolution—as described by its gradient—within the prediction horizon. Solving this problem yields the optimal real-time modification of the offline-computed OPP, which guarantees that very low—and close to its theoretical minimum value—stator current TDD is produced at steady state, and very short settling times during transients. To highlight the effectiveness of the proposed strategy, a variable speed drive system consisting of a three-level neutral point clamped inverter and an MV induction machine serves as a case study.

Risk bounded nonlinear robot motion planning with integrated perception & control

Robust autonomy stacks require tight integration of perception, motion planning, and control layers, but these layers often inadequately incorporate inherent perception and prediction uncertainties, either ignoring them altogether or making questionable assumptions of Gaussianity. Robots with nonlinear dynamics and complex sensing modalities operating in an uncertain environment demand more careful consideration of how uncertainties propagate across stack layers. We propose a framework to integrate perception, motion planning, and control by explicitly incorporating perception and prediction uncertainties into planning so that risks of constraint violation can be mitigated. Specifically, we use a nonlinear model predictive control based steering law coupled with a decorrelation scheme based Unscented Kalman Filter for state and environment estimation to propagate the robot state and environment uncertainties. Subsequently, we use distributionally robust risk constraints to limit the risk in the presence of these uncertainties. Finally, we present a layered autonomy stack consisting of a nonlinear steering-based distributionally robust motion planning module and a reference trajectory tracking module. Our numerical experiments with nonlinear robot models and an urban driving simulator show the effectiveness of our proposed approaches.

Finite time fractional order ISMC with time delay estimation for re-entry phase of RLV with enhanced chattering suppression

This paper investigates the attitude controller design for the reusable launch vehicle (RLV) in its re-entry phase under the influence of model uncertainties and external disturbances. The navigation of RLV along a predefined safe trajectory is a challenging task since the RLV system dynamics has a complex nonlinear behaviour with uncertain environmental conditions. Therefore, this paper proposes a time-delay estimation technique with fractional order integral sliding mode control abbreviated as FOISMC-TDC, for efficient tracking of a pre-designed reference trajectory that ensures safe landing of the RLV. The time delay estimation method in the proposed research employs the input–output information of the immediate past instant to estimate any uncertainties and un-modelled dynamics. The estimated value is then fed to the composite control for disturbance compensation without primarily relying on the switching control of FOISMC approach. This in turn, eliminates the problem of high-frequency chattering in the control input. In addition, by using FOISMC philosophy finite time convergence of system states is achieved with desired error response. Furthermore, Lyapunov and homogeneity theories have been utilized to establish practical finite-time stability of the overall closed loop system. Numerical analysis with state-of-the-art techniques have also been presented to demonstrate effectiveness of the proposed methodology.

Distributed Path Tracking for Autonomous Underwater Vehicles Based on Pseudo Position Feedback

In this paper, we consider the distributed polynomial path tracking problem for a swarm of autonomous underwater vehicles (AUVs) modeled by second-order uncertain multi-agent systems. The application scenario of this paper has three distinguished characteristics. First, the communication network for the multi-agent system is unreliable and switching. Under the jointly connected condition, the communication network can be disconnected the entire time. Second, it is supposed that only the relative position between AUVs can be obtained for trajectory tracking control. Third, the AUV dynamics are subject to uncertain system parameters. By applying the cooperative output regulation control framework, a novel distributed robust control scheme is proposed to solve the distributed path tracking problem, which consists of three parts. First, to cope with communication network uncertainty, the distributed observer was invoked to recover the polynomial path for each AUV. Second, based on the relative position measurement between AUVs, a pseudo position estimator was adopted to generate the pseudo position for each AUV. Finally, based on the estimated polynomial path and the pseudo position, a certainty equivalent robust internal model control law was synthesized to achieve asymptotic reference trajectory tracking, where the internal model compensator aims to tackle uncertain system parameters. Numerical simulations are provided to validate the effectiveness of the proposed control scheme.

Optimal Control of Fish Growth Under Uncertainty Using Chance Constraint Model Predictive Controller

To achieve sustainability goals (social, economic and environmental), recirculation aquaculture systems (RAS) should be operated at optimal conditions. Recirculation aquaculture systems have various additive and unpredictable disturbances such as irregular temperature in big tanks, uneven distribution of feed and uncertain rate constants for nutrients utilization by fish. With such disturbance the performance of RAS cannot be met with probability one. Thus, the performance level should be attained under a desired probability (reliability) level. Therefore, in this paper we apply the chance-constraint model predictive control (CC-MPC) approach with state estimation using an Unscented Kalman Filter (UKF) to meet this requirement. The cost function is based on the feed conversion ratio metric, profit maximization with desired growth reference trajectory tracking. A bio-energetic and econometric model of fish growth in a RAS is utilized to illustrate the application of the formulation through simulations. Healthy fish growth is enabled by applying a health monitoring estimator based on artificial Intelligence (AI) in the feedback loop. The CC-MPC is compared to a deterministic MPC, with a focus on constraint breaching, computation time, and operational behavior. The simulations show similar performance for the fish growth for both types of MPC, while the computation time increases slightly for the CC-MPC, together with operational behaviors getting limited. In the case study, a final average fish weight of 433g is reached at a reliability level of 95% compared to 429g of the deterministic approach.

Practical Position Tracking for 3D Unicycle Model

This paper considers practical position tracking for the 3D unicycle model. In contrast to the existing hand position coordinate transformation, a novel modified hand position coordinate transformation is proposed for the 3D unicycle model which can guarantee that the induced velocity transformation matrix is nonsingular for all the possible orientations. By employing the proposed modified hand position coordinate transformation, the nonlinear 3D unicycle position kinematics can be converted into the single integrator form, which enables arbitrary position reference trajectory tracking given any prespecified upper bound for the steady-state tracking error. The control performance is examined by numerical examples.

Distributed fixed-time time-varying formation-containment control for networked underactuated quadrotor UAVs with unknown disturbances

This paper focuses on the fixed-time time-varying formation-containment (TVFC) control problem for multiple underactuated quadrotor unmanned aerial vehicles (QUAVs) with unknown disturbances. A two-layer control framework comprising reference trajectory generators and trajectory tracking controllers is proposed. Under undirected communication topology, the first layer includes two fixed-time distributed reference trajectory generators for leaders and followers. The generated trajectories can be in accordance with the TVFC control requirements. In the second layer, two fixed-time tracking controllers are proposed, and a fixed-time disturbance observer (FTDO) is developed to ensure the robustness and timeliness of the control system. Meanwhile, the intermediary control input developed in the translational controller can be used to obtain the desired attitude by the attitude extraction algorithm. To handle the derivative calculations of variables in the rotational controller, an exact tracking differentiator is adopted, and the closed-loop stability of the control system is proved mathematically. In the end, the proposed control methods are verified through simulations and two comparison simulations are presented to show the superiority.

Constrained Predictive Tracking Control for Unmanned Hexapod Robot with Tripod Gait

Since it is difficult to accurately track reference trajectories under the condition of stride constraints for an unmanned hexapod robot moving with rhythmic gait, an omnidirectional tracking strategy based on model predictive control and real-time replanning is proposed in this paper. Firstly, according to the characteristic that the stride dominates the rhythmic motion of an unmanned multi-legged robot, a body-level omnidirectional tracking model is established. Secondly, a quantification method of limb’s stretch and yaw constraints described by motion stride relying on a tripod gait is proposed, and then, a body-level accurate tracking controller based on constrained predictive control is designed. Then, in view of the low tracking efficiency of the robot under the guidance of common reference stride, a solution strategy of variable stride period and a real-time replanning scheme of reference stride are proposed based on the limb constraints and the integral mean, which effectively avoid the tracking deviation caused by the guidance of constant reference strides. Finally, the effectiveness and practicability of the proposed control strategy are demonstrated through the comparative analysis and simulation test of a hexapod robot WelCH with omnidirectional movement ability to continuously track the directed curve and the undirected polyline trajectory.

Robust proportional–integral control of submersible autonomous robotized vehicles by backstepping-averaged sub-gradient sliding mode control

This study presents a novel robust controller strategy for submersible autonomous robotized vehicles (SARV). This controller applies the averaged sub-gradient (ASG) descendant method to optimize the tracking of well-posed reference trajectories. The motion control form of the SARV is done in three stages (cascade-like control design). The phases consist of using the translation velocities as pseudo controllers to adjust the SARV position, regulating the angular velocities to attain the requested translation velocities, and using the proposed ASG to control the thrusters to get the needed angular velocities. ASG implementation optimizes a convex cost function depending on the integral of the tracking error using the ASG method. The application of Barbalat’s lemma justifies the tracking error is converging the origin asymptotically. A class of integral sliding mode controllers with a variable state-dependent gain solves the tracking of the designed reference trajectories in each of the three stages. The sliding surface depends on the tracking error for each pseudo-controller, its integral, and the cost function average. The optimization of the cost function can be done without complete knowledge of the SARV dynamics. A numerical example is presented in this study to confirm the suggested control design’s effectiveness based on the cost function’s time evolution analysis. The forced motion by the proposed controller is compared with the movement obtained by a proportional–integral–derivative (PID) controller. The proposed controller exhibits a better tracking of the reference trajectory than the PID version.

Mathematical Modeling and Robust Control of a Restricted State Suspended Biped Robot Implementing Linear Actuators for Articulation Mobilization

The aim of this study is to develop an adaptive automatic control method for solving the trajectory tracking problem for a biped robotic device (BRD) and taking into account that each articulation is mobilized by a linear actuator. Each extremity of the BRD has three articulations with a linear actuator enforcing the controlled motion for each articulation. The control problem considers the task of tracking reference trajectories that define a regular gait cycle. The suggested adaptive control form has state-dependent gains that drive the tracking error into an invariant and attractive ellipsoidal with a center at the origin; meanwhile, the articulation restrictions are satisfied permanently. The stability analysis based on a controlled Lyapunov function depending on the tracking error leads to the explicit design of the state-dependent adaptive gains. Taking into account the forward complete setting of the proposed BRD, an output feedback formulation of the given adaptive controller is also developed using a finite-time and robust convergent differentiator based on the super-twisting algorithm. A virtual dynamic representation of the BRD is used to test the proposed controller using a distributed implementation of the adaptive controller. Numerical simulations corroborate the convergence of the tracking error, while all the articulation restrictions are satisfied using the adaptive gains. With the purpose of characterizing the proposed controller, a sub-optimal tuned regular state feedback controller is used as a comparative approach for validating the suggested design. Among the compared controllers, the analysis of the convergence of the mean square error of the tracking error motivates the application of the designed adaptive variant.

Cooperative polynomial guidance law with collision avoidance and flight path angle coordination

In this paper, a cooperative polynomial guidance problem is investigated against a maneuvering target based on trajectory parameterization with collision avoidance and flight path angle coordination. To this end, a polynomial reference trajectory satisfying the initial and terminal constraints is introduced with its highest-order coefficient chosen as the guidance gain. Then, a safe distance criterion is enforced to coordinate parameters of the missiles for collision avoidance along the reference trajectories. Finally, the cooperative guidance law is developed by ensuring a smooth tracking of the polynomial reference trajectory. Numerical simulations verified performance of the proposed guidance strategy.

Reference-trajectory-planner–based integrated guidance and control under input saturation and impact angle constraint

This paper investigates the integrated guidance and control (IGC) problem for intercepting maneuvering targets subject to the impact angle and input saturation. In order to elegantly implement tracking control under constraints, the whole controller includes the reference trajectory planner for generating reference trajectory, and the reference trajectory tracking controller for tracking the generated reference trajectory. The trajectory tracking controller is based on the command filter backstepping design under the time-domain separation, and the reference trajectory planner with a kind of reference model governor takes into account the available regulation ability of the trajectory tracking controller, so as to improve the adaptability of the proposed control scheme. The two cooperate with each other to improve the stability of guidance interception system and come out a more reasonable interception path. The simulation comparison results are provided to illustrate the superiority of the reference-trajectory-planner–based IGC law.

Nonsingular Fixed-Time Tracking Guidance for Mars Aerocapture With Neural Compensation

Mars aerocapture is one of the most concerned technologies for future Mars sample-return and manned exploration missions. This article investigates the challenging problem of the reference trajectory tracking guidance for Mars aerocapture under uncertainties. Based on an integral sliding surface, a fixed-time neural adaptive tracking guidance law is synthesized by incorporating the neural network (NN) approximation into the fixed-time integral sliding mode control approach. Benefiting from the integral sliding surface design, the proposed tracking guidance law has no singularity problem inherently existing in terminal sliding mode control. By adopting the NN approximation to compensate for the lumped uncertain term in the feedforward loop, the proposed tracking guidance law is strongly robust against aerodynamic coefficient uncertainties and atmospheric density uncertainty. Stability analysis shows that the radial distance tracking error and its time derivative can stabilize to the small neighborhoods around the origin in fixed time under the proposed tracking guidance law. Finally, the effectiveness and advantages of the proposed tracking guidance law are illustrated through simulations and comparisons.

A unified adaptive control approach of nonlinear continuous non‐parameterized systems with asymmetric control gains for trajectory tracking in different domains

AbstractIn this article, for nonlinear continuous non‐parameterized (NCNP) systems, an adaptive iterative learning control (ILC) algorithm, which can adjust the adaptive parameters in both iteration‐domain and time‐domain, is first proposed to track different reference trajectories repetitively over a finite time interval. As the NCNP system is required to asymptotically track reference trajectory in infinite time‐domain, by virtue of partitioning the reference trajectory and system signals with a fixed time interval, the proposed adaptive ILC controller is then extended to handle the asymptotic tracking issue in infinite time‐domain. Therefore, a unified adaptive control approach is practically presented for NCNP systems to track reference trajectories in different domains (the infinite iteration‐domain and the infinite time‐domain). A prominent feature of the unified adaptive control approach is that the unknown control gain matrices in the NCNP systems are assumed to be invertible only. As a result, the general requirement in conventional adaptive control and adaptive ILC that the control gain matrices of plants are real symmetric and positive‐definite (or negative‐definite) is greatly relaxed. In addition, only three adaptive variables are designed for adjusting or updating in the proposed unified adaptive control approach such that the structure of controller is very simple and the memory space for computing is saved.

Adaptive wavelet output regulation for nonlinear systems

Wavelet adaptive output regulation design procedure is developed for highly uncertain nonlinear system. We consider uncertainties, tracking reference trajectories (or) rejecting disturbance are unknown but bounded which are exists in exosystem whose output error are known, but it has arbitrary relative degree. We present wavelet adaptive controller is the principal controller while output regulation design to achieve the desired performance by attenuating the effect of output error to maintaining stability. Wavelet adaptations are derived for system linearization and wavelet identifiers are used synchronize the controller to system dynamics from input/output data. Practical and approximate regulation results are derived from Lyapunov function to guarantying system with uncertainties, tracking reference trajectories (or) rejecting disturbance is stable and tracking errors are bounded. Finally, specific examples are shown in order to demonstrate the applicability of the result.

Finite‐time disturbance rejection for nonlinear systems using an adaptive disturbance observer based on experience‐replay

SummaryControl systems are inevitably affected by external disturbances, and a major challenge of control design approaches is to attenuate or eliminate their adverse effects on the system performance. This article presents a disturbance rejection control approach with two main improvements over existing results: (1) it relaxes the requirement of calculating or measuring the state derivatives, which are not available for measurement, and their calculation is corrupted by noise, and (2) it guarantees finite‐time disturbance rejection and finite‐time reference trajectory tracking when disturbances are generated from exosystem models with unknown dynamics. To this end, a filtered regressor form is leveraged to model the nonlinear system dynamics as well as the unknown disturbance dynamics. It is shown that the presented filtered regressor form allows us to estimate the disturbance using only measured state of the regressor and without requiring any state derivative measurements. First, an adaptive controller combined with the adaptive disturbance observer is presented for the case where the disturbance is bounded. Second, an adaptive controller combined with the experience‐replay based adaptive disturbance observer is presented for the case where the disturbance can be unbounded. In both cases, it is guaranteed that the reference tracking error as well as the disturbance estimation error and its dynamic error converge to zero in finite time. A simulation example illustrates the effectiveness of the proposed approach.

Distributed adaptive optimization-based formation tracking with double parameter projections for multi-agent systems

In this paper, a distributed adaptive optimization-based formation tracking strategy with double parameter projections for multi-agent systems is addressed under a centralized task allocation and distributed task execution (CTA-DTE) framework. Since a pre-described formation strategy is unable to adapt to a complex and dynamic environment, an optimization-based approach is proposed to transfer the formation tracking problem into a time-varying optimization one, subject to some constraints with several time-varying parameters which determine the rule of formation configuration change adaptively. These parameters are computed by a centralized unit and allocated to each agent as a global mission. Furthermore, each agent cooperates with others to execute this mission under a distributed optimization-based strategy, which combines a geometric center observer technology and a novel double parameter projections technology. The former ensures accurate tracking of a continuous reference trajectory. The latter guarantees that all agents enter into a time-varying security region and never escape from it, and meanwhile, all agents are attracted towards the best time-varying formation configuration via a gradient descent with a compensation. Finally, some simulation results are illustrated to verify the effectiveness of the strategy.

Trajectory Control Algorithm of Flexible Joint Manipulator Based on Random Matrix and Screw Theory

Flexible articulated manipulators are often used for the task of tracking reference trajectories in space and have attracted much attention. Aiming at the uncertainty of the robot system, based on random matrix and screw theory, this paper constructs a trajectory control model of a flexible joint manipulator. In order to reduce the steady-state tracking error, a random matrix variable structure control method is introduced into the model, and a nonlinear spinor-like random matrix function is designed to improve the traditional random matrix surface. In the simulation process, the dynamic model of the series robot is firstly obtained according to the screw and random matrix equation, and the dynamic characteristics are analyzed. Combined with dynamic surface control technology, a neural network controller is designed to solve the problem of dimensional explosion and ensure that the tracking error converges to a small neighborhood of zero. The experimental results show that by using the observation value to replace the unmeasurable state of the system, combining it with the random matrix network to identify the unknown dynamics of the system, and designing the random matrix network controller, the tracking control of the system can be realized, and the tracking error can be ensured to converge to a small neighborhood of zero. The control system has a better control effect than traditional PID, the peak time is shortened by 45.83%, the adjustment time is shortened by 46.91%, the maximum overshoot is reduced by 51.35%, and the steady-state error after filtering is only 0.049, which is reduced by 47.31%. Effective interference signal and measurement noise are suppressed, and the quantitative observation performance of the flexible joint manipulator system is improved.

Hierarchic Controllability Analysis in High-Dynamic Guidance for Autonomous Vehicle Landing

Controllability analysis is significant for guidance law optimization and control system synthesis during atmospheric landing of hypersonic flight vehicles. This article concerns the problem of quantifying the controllability and developing a novel controllability measure, i.e., the degree of controllability (DOC), for linear (or linearized) time-varying systems, and conducts the hierarchically quantitative controllability analysis in high-dynamic guidance for autonomous vehicle landing. In particular, a novel DOC criterion is derived via analyzing the characteristics of singular values and the condition number of the controllability Gramian. The proposed DOC criterion can offer a deep insight into the controllability of both the system and each state subspace, and thus, it possesses a clear physical meaning in practice. Furthermore, a certain normalization and modification method is designed to make the criterion more applicable in aerospace engineering. To validate the derived criterion, the scenario of 3-DOF Mars entry guidance is simulated based on a reference-trajectory tracking scheme with active disturbance rejection control algorithm. According to the simulation results, the optimality of different reference trajectories can be evaluated and compared via the DOC criterion. Therefore, the DOC criterion can function as an indicator to analyze the influence of trajectory parameters on the landing process from the perspective of controllability analysis.

Trajectory tracking for quadrotors: An optimization‐based planning followed by controlling approach

AbstractWe present an optimization‐based reference trajectory tracking method for quadrotor robots for slow‐speed maneuvers. The proposed method uses planning followed by the controlling paradigm. The basic concept of the proposed method is an analogy with linear quadratic Gaussian in which nonlinear model predictive control (NMPC) is employed for predicting optimal control policy in each iteration. Multiple‐shooting is suggested over direct‐collocation for imposing constraints when modeling the NMPC. Incremental Euclidean distance transformation map is constructed for obtaining the closest free distances relative to the predicted trajectory; these distances are considered obstacle constraints. The reference trajectory is generated ensuring dynamic feasibility. The objective is to minimize the error between the quadrotor's current pose and the desired reference trajectory pose in each iteration. Finally, we compared the proposed method with two other approaches and showed that the proposed method outperforms the said approaches in terms of reaching the goal without any collision. Additionally, we published a new data set that can be used for evaluating the performance of trajectory tracking algorithms.