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The control objective of the vertical plane underactuated manipulator (VPUM) is generally to swing up the end point (EP) from the vertical down equilibrium point (VDEP) to the vertical up equilibrium point (VUEP), and finally, to stabilize it at the VUEP. The zone control methods are usually used to achieve this control objective, but the problem of these methods is that they cannot find a unified zone range, and it is easy to appear singularity in the motion process. In this article, for two-link VPUMs, we propose a control strategy based on trajectory planning and optimization, which does not need to divide the zone range, avoids the singularity problem, and can achieve the control objective quickly and smoothly. We design the trajectory by using the time scale method for the active link according to the initial and target states. Then, we obtain the trajectory parameters by employing differential evolution algorithm to ensure that the passive link can also move from the initial states to the target states simultaneously. We design a sliding mode tracking controller to make the active link move along the designed trajectory, so the EP is moved to VUEP. Meantime, we design a sliding mode stabilization controller to ensure that the system is stable at VUEP. Finally, the universality and robustness of the proposed method are proved by simulations. [ABSTRACT FROM AUTHOR]

This article describes a topological approach to generating families of open- and closed-loop walking gaits for underactuated 2-D and 3-D biped walkers subject to configuration inequality constraints, physical holonomic constraints (e.g., closed-loop linkages), and virtual holonomic constraints (user-defined constraints enforced through feedback control). Our method constructs implicitly defined manifolds of feasible periodic gaits within a state-time-control space that parameterizes the biped’s hybrid trajectories. Since equilibrium configurations of the biped often belong to such manifolds, we use equilibria as “templates” from which to grow the gait families. Equilibria are reliable seeds for the construction of gait families, eliminating the need for random, intuited, or bio-inspired initial guesses at feasible trajectories in an optimization framework. We demonstrate the approach on several 2-D and 3-D biped walkers. [ABSTRACT FROM AUTHOR]

The installment of $LC$ filter between the voltage source inverter and motor terminal can reduce the value of $dv$ / $dt$ considerably, and further mitigate the surge voltage stress on the motor windings during the long-distance transmission. However, the sophisticated controller needs to be designed to solve the additional resonance problems caused by the filter. Conventional active damping (AD) scheme mainly introduce the multiloop feedback based on the analysis in $s$ -domain or $z$ -domain, which is realized with limited bandwidth and high tuning complexity. In this article, the finite-control-set model predictive control (FCS-MPC) is adopted to realize the $q$ -axis current reference tracking for motor and suppress the filter resonance simultaneously. Different from the transfer-function-based AD scheme, the mechanism of resonance generation is revealed in the time-domain, where the cost function of FCS-MPC is designed to directly regulate the multivariable trajectory of the system. Therefore, the proposed FCS-MPC controller expresses the intuitive design principle, a simple structure, and fewer tuning parameters, which could be an alternative to the existing AD scheme. To reduce the number of sensors, the Kalman-filter based state estimation is used by considering the one-step delay of the control input. The cost function is further optimized to a simplified form that suits the implementation of the digital platform, and the lower computational burden is obtained. The experimental results prove that the proposed FCS-MPC scheme can ensure the motor-friendly waveform and overcome the resonance problem effectively. The robustness of the controller to parameter variations of the filter is also verified. [ABSTRACT FROM AUTHOR]

On a grand scale, motion trajectories are usually defined by an origin, a sequence of waypoints, and a destination. A typical example is in air traffic management (ATM), where a flight from an origin passes several waypoints and arrives at a destination. The origin, the waypoints, and the destination contain useful information for trajectory modeling. On the other hand, due to trajectory design criteria and ATM restrictions and requirements, there are long-range dependencies in a flight trajectory. Such dependencies can be modeled by taking the origin, waypoints, and destination into account in trajectory modeling. In this article, we propose a class of conditionally Markov (CM) sequences to model such trajectories with long-range dependencies. First, we define a general CM sequence as a foundation. Then, we discuss its special cases for different scenarios. We derive dynamic models of these CM sequences in the Gaussian case. We show how parameters of the models can be learned from data or designed. We also justify the use of the proposed CM models for trajectory modeling. In addition, we obtain optimal filters and predictors for different models. Simulation demonstrations are given. [ABSTRACT FROM AUTHOR]

This paper presents a multi-stage series model predictive control (MS-MPC) for PMSM drives in order to further improve the control performance of MPC. Firstly, the basic principle of conventional MPC is introduced. Then, the multi-stage series MPC is proposed in this paper, in which the cost functions of different prediction instant are adopted to form series control structure. In this method, the current prediction trajectory of one voltage vector is extrapolated to multiple control periods, and the control performances of every voltage vector during multiple control periods are evaluated by multi-stage series cost functions. Additionally, the implementation process of the proposed method is described. Finally, the comparison experiments between the conventional MPC and the proposed method show that the proposed method can effectively reduce the switching frequency under the same control frequency. In addition, the improvement of current control performance can be achieved by the proposed method under the condition of the same switching frequency. [ABSTRACT FROM AUTHOR]

In this article, a fast chance-constrained trajectory generation strategy incorporating convex optimization and convex approximation of chance constraints is designed so as to solve the unmanned vehicle path planning problem. A path-length-optimal unmanned vehicle trajectory optimization model is constructed with the consideration of the pitch angle constraint, the curvature radius constraint, the probabilistic control actuation constraint, and the probabilistic collision avoidance constraint. Subsequently, convexification technique is introduced to convert the nonlinear problem formulation into a convex form. To deal with the probabilistic constraints in the optimization model, convex approximation techniques are introduced such that the probabilistic constraints are replaced by deterministic ones while simultaneously preserving the convexity of the optimization model. Numerical results, obtained from a number of case studies, validate the effectiveness and reliability of the proposed approach. A number of comparative studies were also performed. The results confirm that the proposed design is able to produce more optimal flight paths and achieve enhanced computational performance than other chance-constrained optimization approaches investigated in this article. [ABSTRACT FROM AUTHOR]

This article presents a new and fast indirect method for solving fuel-optimal descent trajectories in the gravitational field of an irregularly-shaped asteroid. The costates associated with a two-impulse descent trajectory are used as approximate costates for the costate initialization of a finite-thrust fuel-optimal trajectory planning problem. The approximate solutions of the initial velocity and mass costates are given in analytical forms. A simple shooting equation is derived to solve the approximate position costates. The two-impulsive descent trajectory is solved by an irregular gravitational Lambert solver. Based on the Lambert solver and approximate costates, an algorithm is proposed for trajectory optimization with varying time of flight. The effectiveness and efficiency of the proposed method are tested through the simulation of landing on the asteroid 433 Eros. Additionally, a computationally efficient approximate model is employed to replace the polyhedral model, which greatly improves the computational speed and enhance the ability to address uncertainties. [ABSTRACT FROM AUTHOR]

The Kinematic Theory of rapid movements and its associated Sigma-Lognormal model have been extensively used in a large variety of applications. While the physical and biological meaning of the model have been widely tested and validated for rapid movements, some shortcomings have been detected when it is used with continuous long and complex movements. To alleviate such drawbacks, and inspired by the motor equivalence theory and a conceivable visual feedback, this paper proposes a novel framework to extract the Sigma-Lognormal parameters, namely iDeLog. Specifically, iDeLog consists of two steps. The first one, influenced by the motor equivalence model, separately derives an initial action plan defined by a set of virtual points and angles from the trajectory and a sequence of lognormals from the velocity. In the second step, based on a hypothetical visual feedback compatible with an open-loop motor control, the virtual target points of the action plan are iteratively moved to improve the matching between the observed and reconstructed trajectory and velocity. During experiments conducted with handwritten signatures, iDeLog obtained promising results as compared to the previous development of the Sigma-Lognormal. [ABSTRACT FROM AUTHOR]

The electric sail is an innovative concept for spacecraft propulsion, which can generate continuous thrust without propellant by reflecting solar wind ions. In previous studies, the thrust of an electric sail is described by a classical model that neglects the effects of the electric sail attitude on the propulsive thrust modulus and direction. This paper reappraised the performance of the electric sail in the Vesta and Ceres exploration mission with an advanced thrust model that considers the effect of the spacecraft attitude on both the thrust modulus and direction. By using a hybrid optimization method, the trajectory optimization of the electric-sail-based spacecraft from earth to Vesta and Ceres is implemented in an optimization framework. Numerical results show that the minimal flight time with the advanced thrust model is longer than that with the classical model. The difference in performance between the classical and advanced models is attributable to overestimation of the maximum thrust cone angle and the thrust modulus by the classical model. [ABSTRACT FROM AUTHOR]

We investigate and revisit the deployment of a directional time-varying (rotating) driving magnetic field to suppress the magneto-Rayleigh–Taylor (MRT) instability in dynamic Z-pinches. A rotational driving magnetic field is equivalent to two magnetic-field components, $\Theta $ and Z, that alternate in time, referred to as an alternate Theta-Z-pinch configuration. We consider a finitely thick cylindrical liner configuration in this paper. We numerically integrate the perturbation equation to stagnation time based on the optimal background unperturbed trajectories. We assess the cumulative growth of the dominant mode selected by some mechanism at the beginning of an implosion. The maximum e-folding number at the stagnation of the dominant mode of an optimized alternate Theta-Z-pinch is significantly lower than that of the standard Theta- or Z-pinch. The directional rotation of the magnetic field acts to suppress instabilities, independent of the finite thickness of the liner. The finite thickness effect plays a role only when the orientation of the magnetic field varies in time, whereas it does not play a role in the standard Theta- or Z-pinch. The rotating frequency of the magnetic field and the thickness of the liner both have a monotonic effect on suppression. Their synergistic effect can enhance the suppression of the MRT instability. Because the MRT instability can be well suppressed in this way, the alternate Theta-Z-pinch configuration has potential applications in liner inertial fusion that uses a magnetically driven liner to directly compress the fuel target to initiate fusion. [ABSTRACT FROM AUTHOR]

Considering input constraints and parameter uncertainty of the nonholonomic wheeled mobile robots, a new control law has been designed in this paper to solve the tracking and stabilization control problems simultaneously. The asymptotic convergence of the stabilization or tracking errors is achieved by a smooth controller with time-varying feedback parameters subject to set conditions. A geometric-based parameter design strategy is employed to overcome the difficulties resulting from input constraints. With the parameter design strategy, the designed parameters satisfy the set conditions and the control inputs stay in the constrained domain. Experimental studies have been conducted to verify the effectiveness of the proposed control law. [ABSTRACT FROM AUTHOR]

This paper proposes a new reentry trajectory generation method, which mainly comprises two parts: reentry profile design and trajectory optimization. Different from conventional methods that design angle-of-attack (AOA) and bank-angle profiles, a height-range profile is proposed in this paper. Using this profile, the AOA can be directly derived and the quasi-equilibrium glide condition is easily satisfied. In addition, the bank angle is analytically derived with the heading error, with only one reversal. Finally, the original problem is transformed into a parameter optimization problem and solved by an improved particle swarm optimization (PSO) method. In PSO, a comparison principle is proposed to tackle constraints and three modifications are applied to the swarm evolution to enhance the searching capacity. To conquer disturbances, an online profile updating strategy is developed based on the nominal profile, so complicated work of designing a trajectory tracker is avoided. Simulation validates the effectiveness of the proposed method and demonstrates that the improved PSO is comparable to the pseudospectral method and is better than the basic PSO. [ABSTRACT FROM AUTHOR]

Avionics and air traffic management (ATM) systems are evolving with the introduction of progressively higher levels of automation, toward attaining the ambitious operational, technical, and safety enhancements required to sustain the present growth of global air traffic. This paper presents novel 4-Dimensional Trajectory (4DT) functionalities that are being developed for integration in ATM and avionics systems to support trajectory based operations (TBO). The 4DT planning process, which is the main focus of the paper, is supported by a custom multiobjective variant of state-of-the-art optimal control algorithms, incorporating various operational, economic, and environmental factors. Capitalizing on the higher theoretical accuracy offered by optimal control algorithms compared to other methods, a key feature of the proposed approach is the introduction of a postprocessing stage to ensure that the mathematically optimal trajectories are translated into a set of standardized 4DT descriptors, which can be flown by state-of-the-art automatic flight control systems. Additionally, to support air-ground 4DT intent negotiation and validation in the TBO context, the 4DT postprocessing ensures that optimal trajectories are synthetically described by a limited number of parameters, minimizing the bandwidth requirements imposed on airborne data links. Simulation-based verification activities addressing operational efficiency improvements and computational performance in the terminal area ATM context support the viability of the proposed 4DT planning functionality for online tactical TBO. [ABSTRACT FROM AUTHOR]

Fixed-wing unmanned aerial vehicles (UAVs) can be an essential tool for low-cost aerial surveillance and mapping applications in remote regions. There is, however, a key limitation, which is the fact that low-cost UAVs have limited fuel capacity and, hence, require periodic refueling to accomplish a mission. Moreover, the usual mechanism of commanding the UAV to return to a stationary base station for refueling can result in the fuel wastage and inefficient mission operation time. Alternatively, one strategy could be the use of an unmanned ground vehicle (UGV) as a mobile refueling unit, where the UAV will rendezvous with the UGV for refueling. In order to accurately perform this task in the presence of wind disturbances, we need to determine an optimal trajectory in three-dimensional taking UAV and UGV dynamics and kinematics into account. In this paper, we propose an optimal control formulation to generate a tunable UAV trajectory for rendezvous on a moving UGV that also addresses the possibility of the presence of wind disturbances. By a suitable choice of the value of an aggressiveness index that we introduce in our problem setting, we are able to control the UAV rendezvous behavior. Several numerical results are presented to illustrate the reliability and effectiveness of our approach. [ABSTRACT FROM AUTHOR]

The sensitivity of the initial guess in terms of optimizer based on an hp-adaptive pseudospectral method for solving a space maneuver vehicle's (SMV) trajectory optimization problem has long been recognized as a difficult problem. Because of the sensitivity with regard to the initial guess, it may cost the solver a large amount of time to do the Newton iteration and get the optimal solution or even the local optimal solution. In this paper, to provide the optimizer a better initial guess and solve the SMV trajectory optimization problem, an initial guess generator using a violation learning differential evolution algorithm is introduced. A new constraint-handling strategy without using penalty function is presented to modify the fitness values so that the performance of each candidate can be generalized. In addition, a learning strategy is designed to add diversity for the population in order to improve the convergency speed and avoid local optima. Several simulation results are conducted by using the combination algorithm; simulation results indicated that using limited computational efforts, the method proposed to generate initial guess can have better performance in terms of convergence ability and convergence speed compared with other approaches. By using the initial guess, the combinational method can also enhance the quality of the solution and reduce the number of Newton iteration and computational time. Therefore, the method is potentially feasible for solving the SMV trajectory optimization problem. [ABSTRACT FROM AUTHOR]

The research on the collision between a spinning ball and a table, as a general issue for the trajectory analysis of the spinning-flying objects, is important but complicated. Traditionally, it is studied either by simplifying the collision process as a black box in which the ball’s motion state changes abruptly before and after collision, or by assuming that the coefficient of restitution and the coefficient of friction are simply piecewise linear or even constant during the whole collision process. In this paper, we first analyze the mechanism of the collision dynamics and conclude from mathematical derivations that the collision between a ping-pong ball and a table is a continuous transition process and its collision duration is a constant irrelevant to the ball’s motion state. These two conclusions are also verified by the visual measurement using an ultrahigh-speed camera. Then, we propose a novel rebound model using the mean value theorem, momentum theorem, and angular momentum theorem. The novelty of the proposed model is that the forces and the parameters in it are formulated as the continuous functions related to the ball’s motion state, which is more accurate, rather than as constants. The integrations of these functions over time can be formulated by using the mean value theorem, and their expressions are learned using multilayer perception with a large data set collected by the position vision system and the pan-tilt vision system. The experimental results verify the effectiveness and accuracy of the proposed model. [ABSTRACT FROM AUTHOR]

When attempting to estimate parameters in a dynamical system, it is often beneficial to strategically design experimental trajectories that facilitate the estimation process. This paper presents an optimization algorithm which improves conditioning of estimation problems by modifying the experimental trajectory. An objective function which minimizes the condition number of the Hessian of the least-squares identification method is derived and a least-squares method is used to estimate parameters of the nonlinear system. A software-simulated example demonstrates that an arbitrarily designed trajectory can lead to an ill-conditioned least-squares estimation problem, which in turn leads to slower convergence to the best estimate and, in the presence of experimental uncertainties, may lead to no convergence at all. A physical experiment with a robot-controlled suspended mass also shows improved estimation results in practice in the presence of noise and uncertainty using the optimized trajectory. [ABSTRACT FROM PUBLISHER]

This paper presents a methodology of calculating the optimal torque and speed commands for the engine–generator system of a series hybrid electric vehicle (HEV). In series HEVs, the engine–generator subsystem provides electrical energy to the dc link. This paper proposes an optimal control strategy of the engine–generator subsystem to generate a desired amount of energy within a given period of time. The optimization algorithm, based on trajectory optimization, determines the torque and speed reference signals for the engine–generator subsystem that achieve maximum efficiency. A simplified version of the controller is also presented for online implementation. The proposed control strategy is compared with nonoptimized control techniques, and simulation results show the improvements in energy efficiency. [ABSTRACT FROM PUBLISHER]

This paper presents fast servo track writer seek control for unknown bias compensation and minimum resonance excitation. An add-on type discrete-time disturbance observer is also employed to obtain uniform settling performance in the presence of disturbance. To prevent a chattering effect due to the unstable zero dynamics of servo track writer, we propose a new disturbance observer dynamics. A two-degree-of-freedom control is used with the reference profile design based on the frequency shaped final-state control and compensation of phase mismatching. We analyze the experimental results of the servo track writer for fast seeking and settling. The proposed control scheme is validated by experimental results showing improvements in seeking and settling performance. [ABSTRACT FROM AUTHOR]

In this paper, a real-time walking trajectory generation method with three-mass models at constant body height for 3-D biped robots is extended for a diagonal walking. By realization of the diagonal walking, the availability is improved. The modeling of this method is more precise than that of conventional real-time walking trajectory generation methods. In this method, the zero-moment point equation of a body is derived, and an analytic solution of a body trajectory at a constant body height in a single support phase is obtained. Because the analytic solution is used, real-time trajectory generation can be realized. In addition, this method has advantages of the body trajectory at the constant body height. The validities are confirmed from simulations of the 2-D walking and an experiment of the 3-D diagonal walking. [ABSTRACT FROM AUTHOR]