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Weight-on-Bit is of vital importance to the drilling trajectory orientation in directional drilling. This paper concerns robust control of drilling trajectory with weight-on-bit uncertainty for the directional drilling process. The objective is to develop an equivalent-input-disturbance-based trajectory control scheme such that the drilling trajectory is precisely controlled by suppressing the fluctuations of weight-on-bit. The motion orientation of both the drill bit and a series of stabilizers is used to describe the evolution process of the drilling trajectory. A state-space model with weight-on-bit uncertainty is derived from the evolution equation through a variable transformation. An equivalent-input-disturbance-based trajectory control system is designed, and two control loops are to track and control the trajectory inclination and azimuth, respectively. Two internal models track the trajectory inclination and azimuth respectively to elevate the control accuracy in the trajectory system. Two observer models combined with two low-pass filters estimate the trajectory inclination and azimuth by measuring the bottom hole assembly’s inclination and azimuth. Some sufficient conditions are derived using linear-matrix-inequalities to obtain the control parameters by considering a reasonable fluctuation range of weight-on-bit. Finally, the control effects in the build-up and horizontal section of the drilling trajectory illustrate the proposed approach’s validity.

When a flexible link manipulator lacks a joint motor, how to use the remaining motors to achieve the control objective is a challenge, and the research in this direction is limited. This article presents a tip position control and vibration suppression approach for a planar two-link rigid-flexible (TLRF) underactuated manipulator with a passive first joint. First, we establish a dynamic model of the system by using the assumed mode method (AMM) and the Lagrangian modeling method. Then, we obtain the dynamic coupling relationship of the two links based on the dynamic model. According to this dynamic coupling relationship, we find that the passive rigid link can be controlled indirectly by controlling the active flexible link. Thus, we calculate the target angles of the two links by using the inverse kinematic method and design a controller for the active flexible link to stabilize it at its target angle and to suppress its vibration. Next, we optimize the parameters of this controller by using the genetic algorithm (GA). GA helps us simultaneously stabilize the passive rigid link at its target angle while realizing the control objective of the active flexible link. The simulation results demonstrate the effectiveness of the proposed control approach.

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.

For a three-link vertical underactuated manipulator with first active joint, few methods can swing its endpoint up from the vertical downward equilibrium point and stabilise it at the vertical upwa...

Zero residual vibration (RV) in the position control of a flexible system is difficult to achieve because this system has low stiffness and underactuated feature. In this paper, we present a position control strategy to achieve zero RV in the position control of two degrees-of-freedom (DOF) flexible systems. First, a general dynamic model for two-DOF flexible systems is established. Next, we transform the position control with zero RV to motion planning and tracking control. Based on the position control objective with zero RV, three constraints for the desired system trajectory are given. To make the desired system trajectory satisfy these three constraints, we propose a motion trajectory optimization method. Specifically, we plan a forward system trajectory and a reverse system trajectory based on bidirectional trajectory planning method. Then, the rewinding strategy and the trajectory optimization based on genetic algorithm are used to connect these two system trajectories and to obtain a complete desired system trajectory. Finally, a sliding mode tracking controller is designed to make the system track this desired system trajectory. In this way, the system can reach its target-rest-position with zero RV. The effectiveness and superiority of the proposed control strategy are demonstrated in simulations.

Unlike a fully-actuated manipulator, the position-posture control of a planar underactuated manipulator (PUM) is more difficult, but the research on it is significant due to the wide practical applications. The existing control methods consider no external disturbance and are involved in the staged control idea, bringing the problems of nonsmooth control torque and time-consuming. A novel one-stage control approach is proposed in this paper for the position-posture control of a three-link PUM with the first free joint under the external disturbance. By analyzing the coupling relationship between its active joints and free joint, the position-posture control is transformed into the trajectory tracking control. Unlike the general trajectory planning, the trajectories of the active joints are planned to include several parameters. Meanwhile, the parameters are solved using a chaos particle swarm optimization algorithm to guarantee that all joint angles can reach to their desired angles. Then, to obtain the high trajectory tracking accuracy at every moment under the external disturbance, the nonlinear disturbance observer is constructed and a nonlinear fast terminal sliding mode tracking controller is designed. Finally, the feasibility and superiority of this strategy are verified via two simulations.

Proper burden distribution is an important way to improve conditions of a blast furnace, which indicate the stability and energy consumption. However, it is difficult for operators to recognize the stability and energy consumption at the same time and adjust them through burden distribution, due to complex iron-making mechanism. Therefore, this article presents a two-stage decision-making method for the burden distribution parameters based on recognizing the conditions. First, the stability and energy consumption are recognized, respectively, according to the classification of stability of slag crust (SSC) and the gas utilization rate (GUR). And then, two prediction models are presented for the SSC and GUR to predict the conditions. Finally, the burden distribution parameters are determined in two stages, where edge parameters of the burden distribution are determined at first according to the SSC, and then, center parameters are determined according to the GUR. Experimental results based on industrial data show that the proposed method provides an effective decision-making way for improving the conditions.

Single-link flexible-joint manipulator (FJM) is a kind of time-varying nonlinear system with underactuated characteristics. This paper takes the uncertain single-link FJM (USLFJM) as the object, and presents a novel robust control approach based on equivalent input disturbance (EID) method for motion control (i.e., position control and trajectory tracking control) of the USLFJM. Based on the uncertain dynamic model and desired target of this system, an error system is constructed. The error system is considered as a linear system with a nonlinear virtual disturbance. The motion control objective of the USLFJM can be realized by globally asymptotically stabilizing this linear system and compensating the influence of the nonlinear virtual disturbance. Then, an EID-based control system is designed to realize this control objective. Only position measurements are utilized in this paper, and the stability of the control system is proved. The simulation results are presented to illustrate the validity and the robustness of the proposed control method.

This paper concerns with trajectory azimuth control in directional drilling. The motion process of the drill bit and a series of stabilizers are described, and a state-space model of the trajectory azimuth is constructed. The scheme of the trajectory azimuth control system is designed based on the equivalent input disturbance approach. An internal model is inserted to track the drill bit to improve the quality of the drilling trajectory. A state observer is combined with a low-pass filter to estimate the trajectory azimuth by measuring the azimuth of the bottom hole assembly (BHA). The control parameters can be obtained by the condition of system stability, which is derived in terms of linear matrix inequalities. A typical case is used to illustrate the validity and robustness of our approach.

This paper presents a general control strategy based on the trajectory planning and tracking control for the planar 3-DoF underactuated manipulators with one passive joint at different position. According to the target position of the system, a set of target angles of all links are quickly obtained by using differential evolution algorithm. In order to achieve the control objective of the system from the initial position to the target position, we design the trajectory for each active link of the system, which is composed of two parts. The first part of the trajectory is designed according to the initial and target angle of the active link. The second part of the trajectory is designed based on the constraints between the passive joint and the active joints. Meanwhile, the parameters of the trajectories are optimized by the differential evolution algorithm to ensure that all links reach to their target angles eventually by tracking the designed trajectories. Then, the sliding mode variable structure controllers are designed to make all active links track their trajectories. The effectiveness of the proposed strategy is demonstrated through simulation results.

This paper develops a quick and effective continuous state feedback control strategy based on intelligent optimization for a planar three-link passive–active–active (PAA) underactuated system with first-order nonholonomic characteristic. We analyze the integral characteristic of the system and find the passive link will be stabilized at different angle when the two active links of the system are controlled to different angles. Therefore, we design a set of continuous state feedback controllers based on the control targets of the two active links, and then we optimize the target angles of all links and the design parameters of the above controllers by employing intelligent optimization algorithm. In this way, the system can be stabilized at the target point by using these controllers with optimized parameters. Finally, the simulation results demonstrate that the continuous control strategy based on intelligent optimization may make the planar PAA underactuated system be stabilized at any target point from any initial point.

This paper presents a position control strategy for a planar active-passive-active (APA) underactuated manipulator with second-order nonholonomic characteristics. According to the structural characteristics of the planar APA system, we divide the system into two parts: a planar virtual Pendubot (PVP) and a planar virtual Acrobot (PVA). For the PVP, we mainly fulfill the target angle of the first link, which is calculated through the geometry method, and make the system stable. In this stage, via keeping the states of the third link being zero, the system is reduced to the PVP. Meanwhile, we design an open-loop control law based on the nilpotent approximation (NA) model of the PVP to make the second link stable and the first link stabilize at its target angle. Then, the planar APA system is reduced to a PVA with all links’ angular velocities being zero. For the PVA, we mainly realize the other two links’ target angles obtained via the particle swarm optimization (PSO) algorithm. Thus, the control objective of the planar APA system is achieved. Finally, above control strategy is verified by simulation results.

A control strategy is proposed based on the model reduction and the chained structure for a planar four-link (Active-Active-Passive-Active, AAPA) underactuated manipulator to achieve its position-posture control objective. The whole control process is divided into three stages. In the first stage, the planar AAPA manipulator is reduced to the planar virtual three-link (Active-Active-Passive, AAP) manipulator by controlling the angle of the fourth link and rotating it to zero. In the second stage, the model of a planar virtual AAP manipulator is transformed into the standard chain structure form. Then, the corresponding controllers are designed to control the passive joint of the planar virtual AAP manipulator to its target position, and the posture angle of the passive link is controlled to its middle posture angle at the same time. At the end of this stage, the planar AAPA manipulator is reduced to the planar Acrobot. In the third stage, the angle of the active link of the planar Acrobot is controlled to its target angle. Also, the angle control of the passive link of the system is realized. Consequently, the position-posture control objective of the planar AAPA manipulator is recognized. Considering the angle constraint of the planar Acrobot, the genetic algorithm is used to coordinate and optimize the target angle of the passive joint, the middle posture angle of the passive link, the target angle of the fourth link, and the target posture angle of the passive link. These ensure the target angles of the planar Acrobot corresponding to the target position-posture of the system can be found. Finally, simulation results demonstrate the effectiveness of the proposed control strategy.

Stick–slip vibrations are widespread and hazardous phenomena in drilling practice. The objective of this paper is to develop a simple and general control strategy to minimise such vibrations togeth...

This paper presents a control strategy based on model reduction and online intelligent calculation for a planar ${n}$ -link underactuated manipulator with a passive first joint (PA $^{{n-1}}$ for short) to realize its control objective, which is to move its end-point from an initial position to a target position. First, two active links of the planar PA $^{{n-1}}$ manipulator are chosen to be the active links of a planar virtual passive–active–active (PAA) manipulator, which guarantees that the geometric reachable range of the planar virtual PAA manipulator is the same as that of the planar PA $^{{n-1}}$ manipulator. The planar PA $^{{n-1}}$ manipulator is reduced to the planar virtual PAA manipulator by keeping the states of two active links in their initial values and controlling the states of the remaining ${n-3}$ active links to zero. Then, the planar virtual PAA manipulator is equivalent to two planar virtual Acrobots by adopting two-stage control method. Based on two sets of angle constraint relationships corresponding to two planar virtual Acrobots, an online differential evolution algorithm is employed to obtain all link target angles of the planar virtual PAA manipulator. Next, two Lyapunov functions, each of which is constructed based on the active link angle of one planar virtual Acrobot, are used to design controllers to realize the system control objective. Finally, Simulation results of a planar PAA-active manipulator demonstrate the effectiveness of the proposed control strategy.

Convolutional neural network-based broad learning with efficient incremental reconstruction model (CNNBL) is proposed to recognize emotions in human-robot interaction. It aims to extract deep and abstract features from facial emotional images, and reduce the influence of the complex structure and slow network updates on facial emotion recognition in deep learning. Feature extraction is carried out by convolution and maximum pooling, and then the ridge regression algorithm is used for emotion recognition. When the network needs to expand, the network is dynamically updated by incremental learning algorithm. We verified the experimental performance through k-fold cross validation. According to the recognition results, the accuracy on JAFFE database of our proposal is greater than that of the state of the art, such as the Local Binary Patterns with Softmax and Deep Attentive Multi-path convolutional neural network.

For a three-link vertical underactuated manipulator (TVUM) with only one active joint, the control target is to swing up its endpoint from the straight-down equilibrium point (SDEP) and to stabilize the endpoint at the straight-up equilibrium point (SUEP) eventually. Up to now, there are few effective control strategies to achieve the above control target. In this article, we propose an effective control method based on the trajectory optimization to realize the system control target, and the main steps of this article are: 1) a continuous trajectory that consists of two segments with design parameters is planned for the actuated link, along which the actuated link can be swung up from the initial states to the final states; 2) the design parameters are optimized by using the intelligent optimization algorithm to guarantee that the states of the underactuated links are continuous at the junction. In this way, the underactuated links are also moved to their final states with the actuated link simultaneously; 3) a tracking controller is designed by using the sliding-mode method to track the trajectory with optimized design parameters, so the endpoint is swung up from the SDEP to the SUEP directly; and 4) a stabilizing controller is further devised through the LQR method to keep the endpoint being stable at the SUEP. Finally, simulation results show that the proposed control method achieves the swing-up and stable control target of the system, and the control performance of the proposed method is superior than that of the existing control methods through the comparisons.

Complicated geological environments lead to a high risk of drilling incidents. Incident early warning for drilling process is in demand for industry field. An incident early warning method for loss and kick based on sparse autoencoder and decision fusion is proposed in this paper. Sparse autoencoder is employed to detect the abnormality of the drilling parameter time series. Mann-Kendall trend test approach is performed to extract the trend of the time series that is detected as abnormal. The abnormality detection and trend extraction results of each drilling parameter are fused to get the final incident early warning result. Experiments are executed with the actual data collected from a practical drilling process. The experiment results indicate the effectiveness of the proposed method.

The safe and efficient operation of geological drilling systems is critically dependent on proper process monitoring. A monitoring model based on probabilistic principal component analysis is presented to deeply exploit performance feature information hidden among the process data in this paper. First, the offline monitoring model is established with historical process data collected from different sources to reveal different characteristics, and the monitoring statistics as a benchmark are obtained. Then, actual operating data are introduced to the established model to realize online monitoring. Finally, the monitoring effect is discussed, and the causes of inefficient drilling are tracked. The experimental results indicate that the proposed method can effectively monitor the operating performance of the drilling process.

Planar underactuated mechanical systems are unaffected by gravity and therefore widely used in aerospace robots and underwater vehicles. However, the stable control is quite difficult since any position that the system can reach is its equilibrium point where it is linearly uncontrollable. In this paper, considering a planar three-link passive-active-active underactuated manipulator, a novel control approach using intelligent optimization is developed for its asymptotic stability at a target position. In the first stage, we develop controllers for stabilizing one active link at its target angle obtained by inverse kinematic method and the other two links at their transitional angles obtained by the Genetic Algorithm (GA), where the angles need to satisfy the angle constraint. Meanwhile, the GA is also utilized to optimize controllers’ parameters to ensure this stable control. Then in next stage, under the control of the angle constraint, the remaining two links are moved to the target angles simultaneously. Besides, we also improve the optimization criterion to include the control error, control time and input torque, thereby selecting better parameters of the controllers to obtain better control performance. Four simulations are implemented to prove the validity and feasibility of the proposed control and optimization algorithm.

This paper presents a stable control strategy for a planar four-link active–passive–active–active (APAA) underactuated mechanical system. The control objective is to move its end-point from any ini...

The research on the robust control of uncertain planar underactuated manipulators is almost nonexistent due to the lack of actuator and the uncontrollability at equilibrium points. Taking an uncertain planar three-link passive-active-active underactuated manipulator as an example, this paper develops a robust control scheme including motion planning and adaptive tracking control to realize its position control. According to the constraints between the passive link and active links and the target position of the manipulator, differential evolution algorithm is used to solve the target angles and ratio between the angular velocities. Then, a set of motion trajectories is planned based on the target values. Considering the uncertain parameter perturbation and external disturbance exist, we use RBF neural network to online approximate the uncertainty. Meanwhile, we develop a set of fast terminal sliding mode controllers to track the planned trajectories, and design adaptive laws to guarantee the stability and convergence of the tracking system. Next, an online iteration algorithm is presented to correct the deviations of all link angles caused by the parameter perturbation, which makes the manipulator gradually approach to its target position. Finally, the simulation results verify the effectiveness of the proposed method.

This paper presents a continuous control strategy based on the differential evolution (DE) algorithm for a planar four-link underactuated manipulator with a passive first joint to realize its position-posture control objective. First, we obtain the coupling equation in integral form between the angle of the passive link and the states (angles and angular velocities) of three active links according to the angular velocity constraint of the system. Then, according to this coupling equation, we construct a Lyapunov function only based on the control targets of three active links, and use the Lyapunov function to design the PD controllers. In addition, these general PD controllers are modified to be the step PD controllers to overcome the sudden change in the initial torques. Next, we use the DE algorithm to optimize the target angles of all links and the design parameters of the step PD controllers, which ensures that the angle of the passive link converges to its target angle when the angles of three active links converge to their target angles. Finally, simulation results demonstrate the effectiveness of the proposed control strategy.

This article deals with an uncertain two-link rigid-flexible manipulator with vibration amplitude constraint, intending to achieve its position control via motion planning and adaptive tracking approach. In motion planning, the motion trajectories for the two links of the manipulator are planned based on virtual damping and online trajectories correction techniques. The planned trajectories can not only guarantee that the two links can reach their desired angles, but also have the ability to suppress vibration, which can be adjusted to meet the vibration amplitude constraint by limiting the parameters of the planned trajectories. Then, the adaptive tracking controller is designed using the radial basis function neural network and the sliding mode control technique. The developed controller makes the two links of the manipulator track the planned trajectories under the uncertainties including unmodeled dynamics, parameter perturbations, and persistent external disturbances acting on the joint motors. The simulation results verify the effectiveness of the proposed control strategy and also demonstrate the superior performance of the motion planning and the tracking controller.

In this chapter, we present the control methods for the multi-link planar underactuated manipulator (PUM) with one passive joint. Firstly, we present a continuous control strategy based on the differential evolution algorithm for the system with passive first joint to quickly realize its position-posture control objective. The angular velocity constraint of the system is used to obtain the coupling equation in integral form between the angle of the passive joint and the states of the active joints. The step PD controllers are used to overcome the sudden change of the initial torques. The differential evolution algorithm is used to optimize the target angles of all joints and the design parameters of the step PD controllers corresponding to the target position-posture. Secondly, we present a unified trajectory planning and tracking control strategy for the multi-link PUMs with a passive joint at a different location. In addition, we employ intelligent optimization algorithm to optimize the parameters of the trajectories. The effectiveness of such strategies is demonstrated through simulation results.

This paper presents an adaptive robust control strategy based on a radial basis function neural network (RBFNN) and an online iterative correction method (OICM) for a planar n-link underactuated manipulator with a passive first joint to realize its position control objective. An uncertain model of the planar n-link underactuated manipulator is built, which contains the parameter perturbation and the external disturbance. The adaptive robust controllers based on the RBFNN are designed to realize the model reduction, which makes the system reduce to a planar virtual three-link underactuated manipulator (PVTUM) and simplifies the complexity of the system control. An online differential evolution (DE) algorithm is used to calculate the target angles of the PVTUM based on the nominal model parameters. The control of the PVTUM is divided into two stages, and the adaptive robust controllers are still employed to realize the control objective of each stage. Then, the OICM is used to correct the deviations of all link angles of the PVTUM caused by the parameter perturbation, which makes the end-point of the system gradually approach to its target position. Finally, simulation results of a planar four-link underactuated manipulator demonstrate the effectiveness of the proposed adaptive robust control strategy.

In this paper, we develop a quick and effective position control strategy based on the differential evolution (DE) algorithm for a planar three-link passive-active-active (PAA) underactuated system with first-order nonholonomic constraint. Due to the existence of the constraint, when the angular velocities of the two active links are proportional, the planar PAA system is transformed from a first-order nonholonomic system to a holonomic system like an Acrobot. Making full use of the angular constraint of the like-Acrobot, we employ the DE algorithm to calculate the target angles of all links and the target ratio between the angular velocities of the two active links. After that, one continuous controller for one active link is designed to ensure the target ratio in the whole control process; meantime, the other continuous controller for the other active link is designed to make its angle asymptotically converge to the corresponding target value. In this way, the angles of all links can asymptotically converge to the corresponding target values according to the angular constraint, and thus the position control of the system is realized using the continuous control method. Finally, the simulation results demonstrate the quickness and effectiveness of our proposed control method.