In robot-assisted minimally invasive surgery, optimal camera positioning is crucial for effective visualization and manipulation of tissues, which impacts the success of procedures. Traditional camera control can increase cognitive workload, lead to suboptimal camera viewpoints, and complicate surgical tasks. We propose an autonomous camera system that uses situational awareness and real-time prediction of user intent from kinematic data, and adjusts the camera position dynamically during a simulated suturing task. Such a system reduces the need to manually adjust the camera, allowing users to stay focused on the procedure. We demonstrated the framework in a user study with eight non-expert participants. They used the da Vinci Research Kit to control a simulated camera and instruments in a suturing task. We compared the performances in the suturing task with the autonomous and the teleoperated camera control. The autonomous system reduced execution time by 43% , shortened path length by 30% , and decreased completion cost by 35%. These results serve as a proof of concept for a situationally aware camera system and suggest that autonomous camera control can improve efficiency and simplify surgical workflow.

This paper proposes a quality-driven adaptive control framework for robotic vascular anatomies scanning to facilitate the acquisition of high-quality ultrasound (US) images. Specifically, a novel probability-based US image quality evaluation metric for vascular anatomies is introduced, leveraging an image segmentation network to establish a mapping between the controlled variables of the robot (e.g., pose and force) and US image quality. Furthermore, an adaptive US probe control strategy driven by US image quality is developed to optimize real-time image acquisition, with its stability rigorously proven. To assess the effectiveness of the proposed framework, two experiments were conducted on a human tissue-mimicking phantom, encompassing both static and dynamic scenarios. The experimental results demonstrate that the proposed framework ensures stable contact force and significantly enhances US image quality for robot-assisted vascular anatomy imaging, even in the presence of external disturbances.

This work presents a compliant and passive shared control framework for teleoperated robot-assisted tasks. Inspired by the human operator's capability of continuously regulating the arm impedance to perform contact-rich tasks, a novel control schema, exploiting the variable impedance control framework for force tracking is proposed. Moreover, bilateral teleoperation and shared control strategies are implemented to alleviate the human operator's workload. Furthermore, a global energy tank-based approach is integrated to enforce the system's passivity. The proposed framework is first evaluated to assess the force-tracking capability when the robot autonomously performs contact-rich tasks, e.g., in an ultrasound scanning scenario. Then, a validation experiment is conducted utilizing the proposed shared control framework. Finally, the system's usability is investigated with 12 users. The experiment results in system assessment revealed a maximum median error of 0.25 N across all the force-tracking experiment setups, i.e., constant and time-varying ones. Then, the validation experiment demonstrated significant improvements regarding the force tracking tasks compared to conventional control methods, and the system passivity was preserved during the task execution. Finally, the usability experiment shows that the human operator workload is significantly reduced by$54.6 \%$compared to the other two control modalities. The proposed framework holds significant potential for the execution of remote robot-assisted medical procedures, such as palpation and ultrasound scanning, particularly in addressing deformation challenges while ensuring safety, compliance, and system passivity.

Lymphadenectomy generally accompanies various oncology surgeries to remove infected cancer cells. However, there are two limitations in robot-assisted lymphadenectomy: 1) lymph nodes are not visible during operation since they are hidden by the superficial fat layer; 2) intra-operative bleeding may occur during lymph node removal caused by collisions between surgical instruments and delicate blood vessels (arteries or veins) near the lymph nodes. Therefore, we propose a framework integrating augmented reality and virtual fixtures to address these limitations. Augmented reality intra-operatively visualizes the hidden lymph nodes by projecting the corresponding 3D pre-operative model, and virtual fixtures are used to provide force feedback to surgeons to avoid possible collisions when they operate the surgical instruments to resect the lymph nodes surrounding the blood vessel. Ten human subjects were invited to perform an emulated lymphadenectomy based on the da Vinci robot in a dry lab. Experimental results demonstrated that the proposed framework can keep localizing the hidden lymph nodes, and reduce the number of collisions (21% and 48% reduction rates using two different force models compared to the standard setup, respectively) between the instruments and the delicate blood vessel during lymph node resection. It shows the potential to enhance the safety of robot-assisted lymphadenectomy.

Robot-assisted surgery is rapidly developing in the medical field, and the integration of augmented reality shows the potential to improve the operation performance of surgeons by providing more visual information. In this paper, we proposed a markerless augmented reality framework to enhance safety by avoiding intra-operative bleeding, which is a high risk caused by collision between surgical instruments and delicate blood vessels (arteries or veins). Advanced stereo reconstruction and segmentation networks are compared to find the best combination to reconstruct the intra-operative blood vessel in 3D space for registration with the pre-operative model, and the minimum distance detection between the instruments and the blood vessel is implemented. A robot-assisted lymphadenectomy is emulated on the da Vinci Research Kit in a dry lab, and ten human subjects perform this operation to explore the usability of the proposed framework. The result shows that the augmented reality framework can help the users to avoid the dangerous collision between the instruments and the delicate blood vessel while not introducing an extra load. It provides a flexible framework that integrates augmented reality into the medical robotic platform to enhance safety during surgery.

This paper presents an Augmented Reality (AR)assisted robot learning framework for Minimally Invasive Surgery (MIS) tasks. The proposed framework exploits an external optical tracking system to collect human demonstration. Gaussian Mixture Model (GMM) and Gaussian Mixture Regression (GMR) are utilized to encode and generate a robust desired trajectory for transferring to the real robot for the MIS task. The HoloLens 2 Head-Mounted-Display (HMD) is integrated for intuitive visualization of the robot configuration under the constraint of a small incision on the patient's abdominal cavity during the demonstration phase. Experiments are conducted to verify the feasibility and performance of the proposed framework and compared it with the kinesthetic teaching-based modality in a tumor resection MIS task. The results illustrate that the proposed AR-assisted robot learning framework requires lower workload demand, achieves higher performance and efficiency, and ensures the feasibility of the learned results for reproduction on a real robot for MIS tasks.

In this paper, a position-based visual-servoing control approach is introduced for a robotic camera holder to improve ergonomics and reduce mental stress during brain surgery. The visual tracking system controls and moves the robotic camera holder by following a selected surgical instrument without the need for artificial markers. The system was validated using a 7 Degree-of-Freedoms (DoFs) redundant robotic manipulator with an eye-in-hand stereo camera configuration and compared with conventional control methods using NASA TLX survey and four objective metrics, including execution time, time out of field of view (FoV), target score, and path length. Experimental results demonstrate that the proposed system can reduce the surgeon's workload during brain surgery-related task execution, improve ergonomics and achieve higher performance than traditional control methods.

Navigation inside luminal organs is an arduous task that requires non-intuitive coordination between the movement of the operator's hand and the information obtained from the endoscopic video. The development of tools to automate certain tasks could alleviate the physical and mental load of doctors during interventions allowing them to focus on diagnosis and decision-making tasks. In this paper we present a synergic solution for intraluminal navigation consisting of a 3D printed endoscopic soft robot that can move safely inside luminal structures. Visual servoing based on Convolutional Neural Networks (CNNs) is used to achieve the autonomous navigation task. The CNN is trained with phantoms and in-vivo data to segment the lumen and a model-less approach is presented to control the movement in constrained environments. The proposed robot is validated in anatomical phantoms in different path configurations. We analyze the movement of the robot using different metrics such as task completion time smoothness error in the steady-state mean and maximum error. We show that our method is suitable to navigate safely in hollow environments and conditions which are different than the ones the network was originally trained on.

Recently, the human-like behavior on the anthropomorphic robot manipulator is increasingly accomplished by the kinematic model establishing the relationship of an anthropomorphic manipulator and human arm motions. Notably, the growth and broad availability of advanced data science techniques facilitate the imitation learning process in anthropomorphic robotics. However, the enormous dataset causes the labeling and prediction burden. In this article, the swivel motion reconstruction approach was applied to imitate human-like behavior using the kinematic mapping in robot redundancy. For the sake of efficient computing, a novel incremental learning framework that combines an incremental learning approach with a deep convolutional neural network is proposed for fast and efficient learning. The algorithm exploits a novel approach to detect changes from human motion data streaming and then evolve its hierarchical representation of features. The incremental learning process can fine-tune the deep network only when model drifts detection mechanisms are triggered. Finally, we experimentally demonstrated this neural network's learning procedure and translated the trained human-like model to manage the redundancy optimization control of an anthropomorphic robot manipulator (LWR4+, KUKA, Germany). This approach can hold the anthropomorphic kinematic structure-based redundant robots. The experimental results showed that our architecture could not only enhance the regression accuracy but also significantly reduce the processing time of learning human motion data.

Learning manipulation skills from open surgery provides more flexible access to the organ targets in the abdomen cavity and this could make the surgical robot working in a highly intelligent and friendly manner. Teaching by demonstration (TbD) is capable of transferring the manipulation skills from human to humanoid robots by employing active learning of multiple demonstrated tasks. This work aims to transfer motion skills from multiple human demonstrations in open surgery to robot manipulators in robot-assisted minimally invasive surgery (RA-MIS) by using TbD. However, the kinematic constraint should be respected during the performing of the learned skills by using a robot for minimally invasive surgery. In this article, we propose a novel methodology by integrating the cognitive learning techniques and the developed control techniques, allowing the robot to be highly intelligent to learn senior surgeons' skills and to perform the learned surgical operations in semiautonomous surgery in the future. Finally, experiments are performed to verify the efficiency of the proposed strategy, and the results demonstrate the ability of the system to transfer human manipulation skills to a robot in RA-MIS and also shows that the remote center of motion (RCM) constraint can be guaranteed simultaneously. Note to Practitioners-This article is inspired by limited access to the manipulation of laparoscopic surgery under a kinematic constraint at the point of incision. Current commercial surgical robots are mostly operated by teleoperation, which is representing less autonomy on surgery. Assisting and enhancing the surgeon's performance by increasing the autonomy of surgical robots has fundamental importance. The technique of teaching by demonstration (TbD) is capable of transferring the manipulation skills from human to humanoid robots by employing active learning of multiple demonstrated tasks. With the improved ability to interact with humans, such as flexibility and compliance, the new generation of serial robots becomes more and more popular in nonclinical research. Thus, advanced control strategies are required by integrating cognitive functions and learning techniques into the processes of surgical operation between robots, surgeon, and minimally invasive surgery (MIS). In this article, we propose a novel methodology to model the manipulation skill from multiple demonstrations and execute the learned operations in robot-assisted minimally invasive surgery (RA-MIS) by using a decoupled controller to respect the remote center of motion (RCM) constraint exploiting the redundancy of the robot. The developed control scheme has the following functionalities: 1) it enables the 3-D manipulation skill modeling after multiple demonstrations of the surgical tasks in open surgery by integrating dynamic time warping (DTW) and Gaussian mixture model (GMM)-based dynamic movement primitive (DMP) and 2) it maintains the RCM constraint in a smaller safe area while performing the learned operation in RA-MIS. The developed control strategy can also be potentially used in other industrial applications with a similar scenario.

The complexity of surgical operation can be released significantly if surgical robots can learn the manipulation skills by imitation from complex tasks demonstrations such as puncture, suturing, and knotting, etc.. This paper proposes a reinforcement learning algorithm based manipulation skill transferring technique for robot-assisted Minimally Invasive Surgery by Teaching by Demonstration. It employed Gaussian mixture model and Gaussian mixture Regression based dynamic movement primitive to model the high-dimensional human-like manipulation skill after multiple demonstrations. Furthermore, this approach fascinates the learning and trial phase performed offline, which reduces the risks and cost for the practical surgical operation. Finally, it is demonstrated by transferring manipulation skills for reaching and puncture using a KUKA LWR4+ robot in a lab setup environment. The results show the effectiveness of the proposed approach for modelling and learning of human manipulation skill.

In this paper, an Internet of Things-based human-robot collaborative control scheme is developed in Robot-assisted Minimally Invasive Surgery scenario. A hierarchical operational space formulation is designed to exploit the redundancies of the 7-DoFs redundant manipulator to handle multiple operational tasks based on their priority levels, such as guaranteeing a remote center of motion constraint and avoiding collision with a swivel motion without influencing the undergoing surgical operation. Furthermore, the concept of the Internet of Robotic Things is exploited to facilitate the best action of the robot in human-robot interaction. Instead of utilizing compliant swivel motion, HTC VIVE PRO controllers, used as the Internet of Things technology, is adopted to detect the collision. A virtual force is applied to the robot elbow, enabling a smooth swivel motion for human-robot interaction. The effectiveness of the proposed strategy is validated using experiments performed on a patient phantom in a lab setup environment, with a KUKA LWR4+ slave robot and a SIGMA 7 master manipulator. By comparison with previous works, the results show improved performances in terms of the accuracy of the RCM constraint and surgical tip.

In this paper, a bilateral teleoperation control of a serial robot manipulator, which guarantees a Remote Center of Motion (RCM) constraint in its kinematic level, is developed. A two-layered approach based on the energy tank model is proposed to achieve haptic feedback on the end effector with a pedal switch. The redundancy of the manipulator is exploited to maintain the RCM constraint using the decoupled Cartesian Admittance Control. Transparency and stability of the proposed bilateral teleoperation are demonstrated using a KUKA LWR4+ serial robot and a Sigma 7 haptic manipulator with an RCM constraint in augmented reality. The results prove that the control can achieve not only the bilateral teleoperation but also maintain the RCM constraint.

In this paper, an improved motion planning scheme is proposed for surgical robot control with multiple active constraints, including joint constraints, joint velocity constraints and remote center of motion constraints. It introduces an improved recurrent neural network (RNN) to optimize the online motion planning respect to multiple constraints. The demonstrated surgical operation trajectory is derived using teaching by demonstration. An improved motion planning scheme using the novel recurrent neural network is then designed to achieve the accurate task tracking under the multiple constraints. The general quadratic performance index is adopted to represent the constraints. Finally, the effectiveness of the proposed algorithm is demonstrated using KUKA LWR4+ robot in a lab setup environment.

For the time varying optimization problem, the tracking error cannot converge to zero at the finite time because of the optimal solution changing over time. This paper proposes a novel varying parameter recurrent neural network (VPRNN) based hierarchical optimization of a 7-DoF surgical manipulator for Robot-Assisted Minimally Invasive Surgery (RAMIS), which guarantees task tracking, Remote Center of Motion (RCM) and manipulability index optimization. A theoretically grounded hierarchical optimization framework based is introduced to control multiple tasks based on their priority. Finally, the effectiveness of the proposed control strategy is demonstrated with both simulation and experimental results. The results show that the proposed VPRNN-based method can optimal three tasks at the same time and have better performance than previous work.

This paper proposes a manipulability optimization control of a 7-DoF robot manipulator for Robot-Assisted Minimally Invasive Surgery (RAMIS), which at the same time guarantees a Remote Center of Motion (RCM). The first degree of redundancy of the manipulator is used to achieve an RCM constraint, the second one is adopted for manipulability optimization. A hierarchical operational space formulation is introduced to integrate all the control components, including a Cartesian compliance control involving the main surgical task, a first null-space controller for the RCM constraint, and a second null-space controller for manipulability optimization. Experiments with virtual surgical tasks, in an augmented reality environment, were performed to validate the proposed control strategy using the KUKA LWR 4 +. The results demonstrate that end-effector accuracy and RCM constraint can be guaranteed, along with improving the manipulability of the surgical tip.

Hands-on training is an indispensable part of surgical practice. As the tools used in the operating room become more intricate, the demand for efficient training methods increases. This work proposes a robotic assistance-as-needed method for training with surgical teleoperated robots. The method adapts the intensity of the assistance according to the trainee's current and past performance while gradually increasing the level of control of the trainee as the training progresses. The work includes an experiment comprising 160 acquisition sessions from 16 novice subjects performing a bimanual teleoperated exercise with a da Vinci Research Kit surgical console. Results capture the subtleties in the task's learning curve with and without robotic assistance and hint at the potential of robotic assistance for complex visuomotor training. Although robotic assistance for motor learning has received mixed results that range from beneficial to detrimental effects, this study shows such assistance may increase the rate of learning of certain skills in complex motor tasks.

In this paper, a teleoperation control of a 7-DoF robot manipulator for Minimally Invasive Surgery (MIS), which guarantees a safety-enhanced compliant behavior in the null space, is described. The redundancy of the manipulator is exploited to provide a flexible workspace for nurses or other staff (assisting physicians, patient support). The issue with safety and accurate surgical task execution may arise in the presence of human-robot interaction. Based on the implemented impedance control of tele-operated MIS tasks, a safety enhanced constraint is applied on the compliant null space motion. At the same time, the control approach integrates an adaptive fuzzy compensator to guarantee the accuracy of the surgical tasks during the uncertain human-robot interaction. The performance of the proposed algorithm is verified with virtual surgical tasks. The results showed that the compliant null space motion is constrained in a safe area, and also that the accuracy of tool tip is improved, providing a flexible and safe collaborative behavior in the null space for human-robot interaction during surgical tasks.

Robust representation of actions and its sequences for complex robotic tasks would transform robot's understanding to execute robotic tasks efficiently. The challenge is to understand action sequences for highly unstructured environments and to represent and construct action and action sequences. In this manuscript, we present a review of literature dealing with representation of action and action sequences for robot task planning and execution. The methodological review was conducted using Google Scholar and IEEE Xplore, searching the specific keywords. This manuscript gives an overview of current approaches for representing action sequences in robotics. We propose a classification of different methodologies used for action sequences representation and describe the most important aspects of the reviewed publications. This review allows the reader to understand several options that do exist in the research community, to represent and deploy such action representations in real robots.

Surgical workflow modeling is becoming increasingly useful to train surgical residents for complex surgical procedures. Rule-based surgical workflows have shown to be useful to create context-aware systems. However, manually constructing production rules is a time-intensive and laborious task. With the expansion of new technologies, large video archive can be created and annotated exploiting and storing the experts knowledge. This paper presents a prototypical study of automatic generation of production rules, in the Horn-clause, using the First Order Inductive Learner (FOIL) algorithm applied to annotated surgical videos of Thoracentesis procedure and of its feasibility to use in context-aware system framework. The algorithm was able to learn 18 rules for surgical workflow model with 0.88 precision, and 0.94 F1 score on the standard video annotation data, representing entities of the surgical workflow, which was used to retrieve contextual information on Thoracentesis workflow for its application to surgical training.

Prostate cancer is the most common non-cutaneous cancer in America. Tumor detection involves non-invasive screening tests, but positive results must be confirmed by a prostate biopsy. About twelve random samples are obtained during the biopsy, which is a systematic procedure traditionally performed with trans-rectal ultrasound (TRUS) guidance to determine prostate location. Recently, methods of fusion between TRUS and preoperative MRI have been introduced in order to perform targeted biopsies aimed to reduce the number of samples to few suspicious areas. Since the TRUS displaces the prostate during the procedure, the preoperative MRI does not match patient anatomy. Therefore, complex MRI deformation algorithms are needed. However, despite the substantial increase in complexity and cost, there is no strong evidence that the TRUS-MRI fusion actually improves accuracy and surgical outcomes.

Haptically enabled hands-on or tele-operated surgical robotic systems provide a unique opportunity to integrate pre- and intra-operative information into physical actions through active constraints (also known as virtual fixtures). In many surgical procedures, including cardiac interventions, where physiological motion complicates tissue manipulation, dynamic active constraints can improve the performance of the intervention in terms of safety and accuracy. The non-energy-storing class of dynamic guidance constraints attempt to assist the clinician in following a reference path, while guaranteeing that the control system will not generate undesired motion due to stored potential energy. An important aspect that has not received much attention from the researchers is that while these methods help increase the performance, they should by no means distract the user systematically. In this paper, a viscosity-based dynamic guidance constraint is introduced that continuously redirects the tool's motion towards the reference path. The proportionality and continuity of generated forces make the method less distracting and subjectively appealing. The performance is validated and compared with two existing non-energy-storing methods through extensive experimentation.

Surgeons can benefit from the cooperation with a robotic assistant during the repetitive execution of precise targeting tasks on soft tissues, such as during brain cortex stimulation procedures in open-skull neurosurgery. Position-based force-to-motion control schemes may not be suitable solution to provide the manipulator with the high compliance desirable during guidance along wide trajectories. A new torque controller with non-linear force feedback (FFE) is presented to provide augmented haptic perception to the operator, during the instrument's placement on the tissue. The FFE controller was experimentally validated with a pool of non-expert users using brain-mimicking gelatin phantoms (8%-16% concentration). Besides providing hand tremor rejection for a stable holding of the tool, the FFE controller was proved to allow for a safer tissue contact with respect to both robotic assistance without force feedback and freehand executions (50% and 75% reduction of the indentation depth, respectively). Future work will address the evaluation of the safety features of the FFE controller with expert surgeons on a realistic brain phantom, also accounting for unpredictable tissue motions as during seizures due to cortex stimulation.

In present days, the number of application in which robots and users share the same workspace is increasing, as long as the need of cooperation between them. To achieve a smooth cooperation, in particular in surgical applications, the robot needs to timely change its behavior to adapt to the needs of the user. In this work, a simplified scenario for neurosurgery was defined in which the user interacts with the robot through a Graphical User Interface (GUI) and by touching the robot links and, based to those events and on the current status, different control modes are enabled in the high level controller we developed, such as autonomous, cooperative and teleoperation. Experiments were performed to measure the performances and safety of the developed high level controller in handling the transitions between two states by checking the continuity of data from the robot and from an external measurement system. Results proved that the trajectories of the end effector and links during the switching phase are continuous and thus the modular high level controller developed switches control safely without undesired deviation from desired course.

Robotic systems have been introduced in surgery to increase the intervention accuracy. In this framework, the ROBOCAST system is an optically controlled multi-robot chain aimed at enhancing the accuracy of surgical probe insertion during keyhole neurosurgery procedures. The system is composed by three robots, connected as a multiple kinematic chain (serial, parallel and linear) totaling 13 degrees of freedom (DoFs) and is it is used to automatically align the probe onto the desired trajectory. This paper presents an iterative approach for aligning the surgical probe with the planned target pose, reducing both the translation and the rotation errors. An experimental protocol was designed, in order to assess the system performances in terms of residual targeting errors and convergence ratio. The proposed targeting procedures allows obtaining (0.06 ± 0.02) mm and (0.8 ± 0.2) × 10-3rad as residual median errors, thus satisfying the operational requirements (1 mm). The performances proved to be independent upon the robots calibration accuracy.

Modern scanners are able to deliver huge quantities of three-dimensional (3-D) data points sampled on an object's surface, in a short time. These data have to be filtered and their cardinality reduced to come up with a mesh manageable at interactive rates. We introduce here a novel procedure to accomplish these two tasks, which is based on an optimized version of soft vector quantization (VQ). The resulting technique has been termed enhanced vector quantization (EVQ) since it introduces several improvements with respect to the classical soft VQ approaches. These are based on computationally expensive iterative optimization; local computation is introduced here, by means of an adequate partitioning of the data space called hyperbox (HB), to reduce the computational time so as to be linear in the number of data points N, saving more than 80% of time in real applications. Moreover, the algorithm can be fully parallelized, thus leading to an implementation that is sublinear in N. The voxel side and the other parameters are automatically determined from data distribution on the basis of the Zador's criterion. This makes the algorithm completely automatic. Because the only parameter to be specified is the compression rate, the procedure is suitable even for nontrained users. Results obtained in reconstructing faces of both humans and puppets as well as artifacts from point clouds publicly available on the web are reported and discussed, in comparison with other methods available in the literature. EVQ has been conceived as a general procedure, suited for VQ applications with large data sets whose data space has relatively low dimensionality.

We present a new algorithm, called the soft-tissue filter, that can make both soft and bone tissue clearly visible in digital cephalic radiographies under a wide range of exposures. It uses a mixture model made up of two Gaussian distributions and one inverted lognormal distribution to analyze the image histogram. The image is clustered in three parts: background, soft tissue, and bone using this model. Improvement in the visibility of both structures is achieved through a local transformation based on gamma correction, stretching, and saturation, which is applied using different parameters for bone and soft-tissue pixels. A processing time of 1 s for 5 Mpixel images allows the filter to operate in real time. Although the default value of the filter parameters is adequate for most images, real-time operation allows adjustment to recover under- and overexposed images or to obtain the best quality subjectively. The filter was extensively clinically tested: quantitative and qualitative results are reported here.

One of the major problems which arises in the field of virtual design is the realization of virtual mannequins able to move in a human like way. This work focuses on the analysis of the human sitting working posture, which is described by a 30-DOF mannequin, modeling the upper part of the body (pelvis, trunk, arms, and head). Trajectories formation in point to point reaching movements represents the main topic. Our approach is based on the acquisition of real human kinematics data, collected by means of an automatic motion analyzer. Starting from the kinematics database of one subject, sit in front of a desk, a neural network was trained in order to generate the movements of the virtual mannequin. The work is divided into four parts: mannequin modeling, 3D human data collection, data preprocessing according to the biomechanical model, and design and training of a multilayer perceptron neural network.