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Robotics is an interdisciplinary field and there exist several well-known approaches to represent the dynamics model of a robot arm. The robot arm is an open kinematic chain of links connected through rotational and translational joints. In the general case, it is very difficult to obtain explicit expressions for the forces and the torques in the equations where the driving torques of the actuators produce desired motion of the gripper. The robot arm control depends significantly on the accuracy of the dynamic model. In the existing literature, the complexity of the dynamic model is reduced by linearization techniques or techniques like machine learning for the identification of unmodelled dynamics. This paper proposes a novel approach for deriving the equations of motion and the actuator torques of a robot arm with an arbitrary number of joints. The proposed approach for obtaining the dynamic model in closed form employs graph theory and the orthogonality principle, a powerful concept that serves as a generalization for the law of conservation of energy. The application of this approach is demonstrated using a 3D-printed planar robot arm with three degrees of freedom. Computer experiments for this robot are executed to validate the dynamic characteristics of the mathematical model of motion obtained by the application of the proposed approach. The results from the experiments are visualized and discussed in detail.

The orthopedic manipulation “bone drilling” is the most executed one in the orthopedic surgery concerning the operative treatment of bone fractures. The drilling process is characterized by a number of input and output parameters. The most important input parameters are the feed rate [mm/s] and the drill speed [rpm]. They play significant role for the final result (the output parameters): thermal and mechanical damages of the bone tissue as well as hole quality. During the manual drilling these parameters are controlled by the surgeon on the base of his practical skills. But the optimal results of the manipulations can be assured only when the input parameters are under control during an automatic execution of the drilling process. This work presents the functional characteristics of the handheld robotized system ODRO (Orthopedic Drilling Robot) for automatic bone drilling. Some experimental results are also shown. A comparison is made between the similar systems which are known in the literature, some of which are available on the market. The application areas of ODRO in the orthopedic surgery practice are underlined.

The orthopedic manipulation “bone drilling” is the most commonly used in the surgical treatment of bone fractures. The bone drilling process is characterized with a set of input and output parameters. The first ones define the conditions of the process execution and the second ones determine the outcome. The input parameters as feed rate [mm/s] and drill speed [rpm] have the most importance for the outcome, namely thermal and mechanical damages of the bone tissue.Many scientific researches related to the input parameters influence to the bone drilling process are published. The purpose is to find such an input parameters combination which is able to guarantee optimal result concerning the outcome parameters of the bone drilling process.The difference between the experimental results of many studies appears and even becomes bigger for the sake of wide variety of test conditions used by researchers. However, the following common dependencies stand out:-to avoid thermal osteonecrosis the drilling process must be executed with possibly maximal feed rate value together with possibly minimal drill speed value. -to avoid traumatic osteonecrosis the drilling process must be executed with possibly minimal feed rate value and possibly maximal drill speed value.So that the requirements concerning the drill speed and the feed rate values are contradictory and in the same time such values must be maintained during the bone drilling process aiming to obtain the optimal results. In manual drilling these parameters are controlled by the surgeon on the base of his practical experience. But the control of these parameters and the achievement of their optimal values can be successfully realized only under its robotized execution.Feed rate control during an automatic bone drilling process using an orthopedic drilling robot ODRO has already been introduced in our previous publications. The drill speed control is the next step in the development of ODRO.During bone drilling a significant amount of already done mechanical work directly converts into thermal heat elevated at the tool – bone interface. Since the critical temperature for thermal osteonecrosis is the most rigorously defined to be 47°C, the purpose of drill speed control during bone drilling process is to maintain the temperature below this critical threshold.Currently drill bit rotation in our case is realized on the base of MAXON BLDC controller/driver. With this type of controller, the motor speed is controlled entirely by hardware. It not allows software implementation of an algorithm for controlling the speed of the motor. The created and developed algorithm as well as the obtained and presented experimental results have a purpose to demonstrate the abilities of the controller TMCM 1630 for drill speed control during bone drilling process in dependence on the data characterizing the temperature deviation.This work presents basic characteristics of ODRO as well as a new drill speed control algorithm. It is one more additional step for improving the functionality of ODRO together with feed rate control during drilling and various specialized working regimes.

The bone drilling process is characterised by various parameters, the most important of which are the feed rate (mm/s) and the drill speed (rpm). They highly reflect the final effects and results of the drilling process, such as mechanical and thermal damages of bone tissue and hole quality. During manual drilling, these parameters are controlled by the surgeon based on his practical skills. But automatic drilling can assure an optimal result of the manipulation where such parameters are under control. During bicortical automatic bone drilling such a process consists of several stages: searching the contact with the first cortex, cortex drilling and automatic stop; searching the contact with the second cortex, cortex drilling and automatic stop; drill bit extraction. This work presents a way to control the feed rate during different stages of the bone drilling process (an original feed rate control algorithm) using the orthopaedic drilling robot (ODRO). The feed rate control is based on a proposed algorithm created and realised by specific software. During bicortical bone drilling process the feed rate takes various values in any stage in the range 0.5–6 mm/s. These values depend on drill bit position and real time force sensor data. The novelty of this work is the synthesis of an original feed rate control algorithm to solve the main problems of bone drilling in orthopaedic surgery – minimisation the drilling time (the heat generation); eliminating of the drill bit slip at the first (near) cortex and the drill bit bending at the second (far) cortex; minimising the risk of micro cracks which causes Traumatic Osteonecrosis; improving hole quality of the drilled holes; eliminating of the drill bit slip and the drill bit bending at the second cortex; minimising the value of the second cortex drill bit penetration by bicortical bone drilling.

The advanced tendency in development of robots oriented to orthopedic manipulations is maximally simplification of their mechanics. So called Handheld Robotized Systems appear. Here handheld bone drilling robotized system ODRO (Orthopedic Drilling Robot) is considered. The purpose is to compare its functional characteristics with the similar systems known in the literature. Experimental results are presented for porcine femur drilling by new drill module. The stop drilling decision is taken automatically. The information about experiments concerning the different modes is shown on the display after the drilling end. Handheld robotized systems can perform the accuracy and precise work like the stationary multifunctional robots. They do not need special software, pre-operative planning procedures, calibration, registration and systems for intraoperative navigation. In the same time they are much cheaper, accessible for usage, convenient for work and maintenance which will facilitate their mass application in the orthopedic surgery practice.

Development of hand-held surgical robot for automatic bone drilling George Boiadjiev 1,2 , Kamen Delchev 2 ,Tony Boiadjiev 3 , Rumen Kastelov 4 , Kazimir Zagurski 5 1) Faculty of Mathematics and Informatics, Sofia University, Sofia, Bulgaria 2) Institute of Mechanics, Bulgarian Academy of Sciences, Sofia, Bulgaria 3) Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, Sofia, Bulgaria 4) Orthopaedic and Trauma Clinical Centre of Ministry of Domestic Affairs, Sofia, Bulgaria 5) Institute of system engineering and robotics, Bulgarian Academy of Sciences, Sofia, Bulgaria This paper represents the development of a prototype robotic system for automatic bone drilling in orthopedic surgery. Answering the surgical requirements for the robot dimensions and weight to be as small as possible a new design of the mechanical structure is proposed. The new structure design is based on idea of parallelism of the axis of the linear actuator and the axis of the rotary one. The control system is improved by using of a new micro-controller. A new type of linear drive and a new force sensor (load cell) are built in so that the quality characteristics of the “Orthopedic bone Drilling Robot” (ODRO) are not only the same as previous its versions [1, 2] but become better. An experimental setup is arranged and experiments are executed to test and verify the robot quality features and functional capabilities. References 1. G. Boiadjiev, T. Boiadjiev, V. Vitkov, K. Delchev, R. Kastelov, K. Zagurski, Robotizeed System for Automation of the Drilling in the Orthopedic Surgery. Control Algorithms and Experimental Results., Proceedings of the 9th IFAC International Symposium on Robot Control (SYROCO 2009), Gifu Japan, September 9-12, 2009, pp 633-637, (2009). 2. Boiadjiev, G., Kastelov, R., Boiadjiev, T., Kotev, V., Delchev, K., Zagurski, K., Vitkov, V., Design and performance study of an orthopaedic surgery robotized module for automatic bone drilling, International Journal of Medical Robotics and Computer Assisted Surgery, 9(4), pp. 455–463, (2013).

This work presents the development of a redundant planar robot created with a 3D printer. The mechanical structure and the main kinematic dependencies are discussed. The hardware and software implementation of the prototype are presented. An algorithm is presented to find solutions of the inverse kinematics problem in the presence of obstacles in the workspace of the robot. The algorithm gives results on possible solutions both in the Cartesian coordinates and joint angles. The proposed software and the obtained results are the basis for planning trajectories of the robot in complex environments with obstacles. The created prototype is used for education of students in robotics and mechatronics. The advantages of using 3D printing technology in modeling and design and its application in the education process are highlighted.

Bone drilling manipulation often occurs in the orthopaedic surgery. By statistics, nowadays, about one million people only in Europe need such an operation every year, where bone implants are inserted. Almost always, the drilling is performed handily, which cannot avoid the subjective factor influence. The question of subjective factor reduction has its answer - automatic bone drilling. The specific features and problems of orthopaedic drilling manipulation are considered in this work. The automatic drilling is presented according the possibilities of robotized system Orthopaedic Drilling Robot (ODRO) for assuring the manipulation accuracy, precision, reliability and safety.

The development of manipulative systems oriented to concrete orthopaedic manipulations is an advanced tendency aiming maximally simplification of robot mechanical system. As a result so called Handheld Robotized Systems appear. They have the accuracy like the universal multifunctional robots and in the same time they are much cheaper, user-friendly and easy for maintenance.

The need of the most precise manipulations in the orthopedic surgery concerns spine. The drilling takes place very often there. If spine cortices are broken by mistake then fatal problems appear as paralysis, block of breathing and death. Therefore in operation as pedicle drilling the far cortex perforation must be avoided. This paper shows that it can be done by bone drilling hand-hold robot ODRO. It is able to detect the bone far cortex and stops just before contact registration. Experimental results are presented. Also the results based on new algorithms and software are presented and discussed.

This paper discusses a problem appeared by drill bit bending during bone drilling in the orthopedic surgery, where precision is needed for screws to be implanted. The bone surface has a specific shape and the drill bit may slip a little along the bone before the process start, when a large thrust force is applied by hand-drilling. That could be seen and correct by the surgeon. But he can’t see inside – where the second cortex drilling starts. The drill bit bending leads to the worse screw fixation and even to the bone damage – if the drill bit stays off broken inside. To solve this problem an active force control is made by robot application. Experiments and results are presented.

This paper deals with the improvement of the stability of sampled-data (SD) feedback control for nonlinear multiple-input multiple-output time varying systems, such as robotic manipulators, by incorporating an off-line model based nonlinear iterative learning controller. The proposed scheme of nonlinear iterative learning control (NILC) with SD feedback is applicable to a large class of robots because the sampled-data feedback is required for model based feedback controllers, especially for robotic manipulators with complicated dynamics (6 or 7 DOF, or more), while the feedforward control from the off-line iterative learning controller should be assumed as a continuous one. The robustness and convergence of the proposed NILC law with SD feedback is proven, and the derived sufficient condition for convergence is the same as the condition for a NILC with a continuous feedback control input. With respect to the presented NILC algorithm applied to a virtual PUMA 560 robot, simulation results are presented in order to verify convergence and applicability of the proposed learning controller with SD feedback controller attached

This paper deals with an active force control for automatic bone drilling. Orthopedic surgery often requires precise bone drilling for screws to be implanted. The hole quality in drilling process strongly depends on the applied thrust force (resistance force). In particular, a relatively large thrust force, applied in hand-drilling process, could cause a bone trauma (thermo necrosis or bone damage). To solve this problem we apply an active force control in order to achieve constant and safety drilling thrust force. Moreover, we propose an algorithm for parameter tuning of the considered control system.

Bone drilling and cutting manipulations are widespread in the orthopedic surgery. In free hand performance of them some errors such as an inaccurate penetration and dilate of bone hole, overheating, harm soft tissues could be occurring. The goal of this study is to design and develop control concept for a bone drilling and cutting robotized system. The proposed orthopedic system consists of two executive modules for drilling and cutting and common control panel. The control algorithms and programs for drilling have done and given in the paper. We are developing the control algorithms for cutting manipulation.

Background Many orthopaedic operations involve drilling and tapping before the insertion of screws into a bone. This drilling is usually performed manually, thus introducing many problems. These include attaining a specific drilling accuracy, preventing blood vessels from breaking, and minimizing drill oscillations that would widen the hole. Bone overheating is the most important problem. To avoid such problems and reduce the subjective factor, automated drilling is recommended. Methods Because numerous parameters influence the drilling process, this study examined some experimental methods. These concerned the experimental identification of technical drilling parameters, including the bone resistance force and temperature in the drilling process. During the drilling process, the following parameters were monitored: time, linear velocity, angular velocity, resistance force, penetration depth, and temperature. Results Specific drilling effects were revealed during the experiments. The accuracy was improved at the starting point of the drilling, and the error for the entire process was less than 0.2 mm. The temperature deviations were kept within tolerable limits. The results of various experiments with different drilling velocities, drill bit diameters, and penetration depths are presented in tables, as well as the curves of the resistance force and temperature with respect to time. Real-time digital indications of the progress of the drilling process are shown. Conclusions Automatic bone drilling could entirely solve the problems that usually arise during manual drilling. An experimental setup was designed to identify bone drilling parameters such as the resistance force arising from variable bone density, appropriate mechanical drilling torque, linear speed of the drill, and electromechanical characteristics of the motors, drives, and corresponding controllers. Automatic drilling guarantees greater safety for the patient. Moreover, the robot presented is user-friendly because it is simple to set robot tasks, and process data are collected in real time. Copyright © 2013 John Wiley & Sons, Ltd.

Bone drilling manipulationstake placevery ofteninthe orthopedic surgery. The successful execution of bone drilling requires a high level of dexterity and experience. The patient’s recovering depends on the operation performance. This paper presents a design concept of a bone drilling hand-hold mechatronic system. It is based on the modified structure of the previous our robot ODRO. It isable to detect the bone breakthrough and the stops. It is intended to perform drilling a preliminary set depth. Resistantforce is measured and experimental results are shown.

Many surgical operations such as Total knee arthroplasty (TKA) and Total hip arthroplasty (THA) as well as bone fracture reposition require bone cutting manipulations. We have been developing a two degree of freedom robotized bone cutting hand-hold device. It is intended to execute cutting operation in order to avoid problems as accuracy errors, overheating and to obtain smooth bone surface. Surgeons have to orientate and hold the cutting robot, maintaining the contact with the bone during the operation all the time while the device executes manipulation automatically. Dynamical model based on graph theory and the orthogonally principle is derived for considered electromechanical system. Design of the mechanical part of bone cutting robotized device is provided

In orthopedic surgery the manipulation “bone drilling” is used very often and it is performed by hand drilling, which causes a lot of problems—getting the big outlets, breaking the tendons or blood vessels, protecting the rear bone wall (which brings one more cutting of the tissue), overheating, and so on. Automatic bone drilling could successfully solve these problems. The drilling orthopedic robot (DORO) is presented as a device for automatic bone drilling execution as well as its technical features and functional applications. The experimental results are shown for identification of the parameters of the drilling process, including the bone structure in part.

We proposed a new approach for redundant robots trajectories planning, based on the Null space (or Kernel) features. The Null space (Kernel) exists only in the case of redundant robots and it describes these joints motion which do not affect the robot end-effector motion in the sense of both position and orientation. Based on this “hidden motion” realized in the configuration space, which does not affect the motion in the working zone, we can control independently the robot end-effector position and orientation motions, or just maintain its state while some external force is applied to it. The proposed control strategy is simple, no additional penalty functions are used to restraint the end-effector motion as in the case of the conventional methods. No pseudo inverse kinematics calculations are required; the desired trajectories are generated directly in the configuration space. No complicated control schemes are introduced, the proposed method is based on solving algebraic systems of equations and finding eigenvectors and eigenvalues. In the paper the results from simulations and experiments based on the proposed method are presented and discussed.

The aim of this paper is to present an autonomous control system for active ankle-foot orthoses (AFO). An ankle-foot orthosis is commonly used to help persons with weakness of ankle dorsiflexor muscles due to peripheral or central nervous system disorders. The proposed orthosis has one degree of freedom which foot segment is connected to the shank segment by a rotational joint. In order to assure automatic adaptation of the joint torque the joint is fitted with direct drive actuator attached laterally and controlled by a microcontroller ATmega128. Realizing flexion/extension the actuator applies a torque adequate to the joint position of the human ankle during level ground walking. The control signals are received from two tactile sensor arrays incorporated in the foot part of AFO and in the insole of the healthy leg. During each gait cycle a microcontroller estimates the forward speed and modulates the swing phase flexion and extension in order to achieve quite normal walking dynamics. A feedback with Proportional-Integral-Derivative control (PID control) was used to estimate the trajectory of the foot and positioning the actuated foot segment of the AFO when the foot rotates about the ankle. A graphical presentation of the mathematical model and simulation of the dynamic system is done building a Matlab Simulink block diagram model. The proposed intelligent system is oriented to control different models of personalized ankle-foot orthoses designed using reverse engineering and rapid prototyping by the joint team Bulgarian Academy of Sciences/Cardiff University.

A novel approach for learning control for robot-manipulators has been proposed. Real-time implementation on a five-degree of freedom chopsticks robot has been conducted to evaluate the performance of the repetitive controller. The repetitive controller is recommended when the desired trajectory is periodic. In such applications the proposed repetitive control scheme provides a very simple adaptation algorithm and is effective in removing any periodic tracking errors.

Background: Currently, applications of robotized systems in orthopedic trauma surgery steadily increase due to their functional abilities facilitating surgeon skills. The aim of this study is to present the functional advantages of a recently developed robot for bone drilling. Methods: Ex-vivo experiments were performed on fresh porcine and bovine bones, as well as on fresh and embalmed human bones such as femora, vertebrae and rips, by the use of the robot for bone drilling to identify diverse control parameters and analyse thrust force and drill bit temperature during drilling. Results: Experimental data during drilling is shown, control algorithms are described and bone drilling modes are characterized. Maximal values of thrust force and temperature are detected. Controlling thrust force seems to be the proper way to reduce force resistance and hence temperature during drilling. In automatic drilling mode, preliminary defined channel depth is drilled with accuracy of 0.1 mm, and far cortex end recognition is proved to work reliably for automatic stop with minimal controlled soft tissue penetration. Cortex and bone marrow thickness are measured and analysed in real time. Conclusion: The bone drilling robot is programmed to follow with high accuracy parameters defined by the surgeon. Enhancing surgeon’s freedom and responsibility to make decisions, it can perform precise manipulations, decreasing the influence of subjective factors and increasing patient’s safety.

Problems connected with the control of the local structure of manipulating robots type RRR are discussed in the paper. Mathematical model based on the graph theory and the orthogonality principle is used. The equations obtained for the motion of the analyzed object are in the base of the control synthesis. The method for servocontrol with standard corrections is used and the stability of the synthesized control of the motion of the manipulating robot is proved. Computer simulation of the control is done and the presented results are analyzed.

Bone drilling and cutting procedures are widely used in orthopedic surgery. Relatively high forces and temperatures experienced during bone drilling and cutting can cause significant damage to the bone as necrosis, widening of holes, breaking the tendons or blood vessels, which can make patient recovery long and painful. This paper presents a concept design of a hand-held robotized orthopedic system for bone drilling and cutting manipulations. The system consists of two executive modules for drilling and cutting, respectively. : bone drilling module detecting bone breakthrough is developed. It can monitor time, linear velocity, angular velocity, resistant force, depth of penetration and temperature during the drilling process. A design concept of a robotized oscillating saw for bone cutting is also presented. The saw is intended to perform cutting operations with preliminary setting of depth and stop automatically after the cutting process is completed. Cutting conditions will automatically change in accordance with bone density. Dynamical model using graph theory and the orthogonality principle is provided. CAD models of the prototype of the robotized bone cutting module are presented.

Many orthopaedic operations involve drilling and tapping before the insertion of screws into a bone. This drilling is usually performed manually, thus introducing many problems. These include attaining a specific drilling accuracy, preventing blood vessels from breaking, and minimizing drill oscillations that would widen the hole. Bone overheating is the most important problem. To avoid such problems and reduce the subjective factor, automated drilling is recommended.Because numerous parameters influence the drilling process, this study examined some experimental methods. These concerned the experimental identification of technical drilling parameters, including the bone resistance force and temperature in the drilling process. During the drilling process, the following parameters were monitored: time, linear velocity, angular velocity, resistance force, penetration depth, and temperature.Specific drilling effects were revealed during the experiments. The accuracy was improved at the starting point of the drilling, and the error for the entire process was less than 0.2 mm. The temperature deviations were kept within tolerable limits. The results of various experiments with different drilling velocities, drill bit diameters, and penetration depths are presented in tables, as well as the curves of the resistance force and temperature with respect to time. Real-time digital indications of the progress of the drilling process are shown.Automatic bone drilling could entirely solve the problems that usually arise during manual drilling. An experimental setup was designed to identify bone drilling parameters such as the resistance force arising from variable bone density, appropriate mechanical drilling torque, linear speed of the drill, and electromechanical characteristics of the motors, drives, and corresponding controllers. Automatic drilling guarantees greater safety for the patient. Moreover, the robot presented is user-friendly because it is simple to set robot tasks, and process data are collected in real time.

We propose a novel solution to the problem of path planning for redundant robot manipulators. The desired joint trajectories, generated according to the proposed approach allow the robot to change independently its end-effector position and orientation motions. The algorithm has successfully been used to make one 7 degrees of freedom robot with class-5 revolute joints track a desired image trajectory.

This paper introduces a control method for obstacle avoidance of a mobile robot. First, the mobile robot detects obstacles by information of both a CCD camera and ultrasonic sensors. Then, using information of both of camera and sensors, the mobile robot generates a dynamic trajectory to go to the goal point avoiding the obstacles. Through some experiments, a usefulness of proposed method is shown.

This work presents a modified computed torque method application for a 7 d.o.f. robot control. Generally it could be applied to any other robotics system. The effectiveness and stability of the proposed controller have been discussed and the results from experiments presented. The proposed control method introduces additional corrections for the joints positions, velocities and accelerations and can compensate uncertainties due to the inexactness of the dynamics, describing the system or some parameter variation.

This work is dedicated to accuracy control of redundant robot-manipulators using sensibility approach. A manifold structure is applied to realize bases transition at local robot level. This assures optimal choice of drive subsets or combination of drives realizing motion with desired sensibility. The formulated condition satisfaction in the robot configurational space leads to precise trajectory tracing in the working zone (coincidence of the sensibility direction with the trajectory tangent vector). An illustrative example is presented and the explicit results are shown. The group theory application completes the considerations and it is helpful for better mechanical interpretation

This work is dedicated to position control of redundant robots, realized with the help of the sensibility theory. The control method allows controlling the robot position following some working trajectory, and at the same time maintaining its orientation state unchanged or vice-versa. The latter is achieved by using the features of the four robot configuration space orthogonal fibrations. Their characteristics and role are clarified. A concept of robot image trajectories is formulated and its application is analyzed. The proposed method is going to be applied for a real-time control to a 7 d.o.f. robot, based on Puma type construction. Simulations have been done for it, taking into account its dynamics and sensibility models and also by applying the position control method. The results and conclusions are presented.

This work is dedicated to force control of redundant robot-manipulators using the sensibility approach. It allows the robot to react to external force appearance without changing its kinematics state. The sensibility factor-group is introduced for description and analysis of the robot configuration space orthogonal fibrations. They divide the robot configuration space into four sets, each responsible for separate motion realization - one for position, one for orientation, one for both and one which does not affect the kinematics state. A concept of robot kernel trajectories is formulated and its application is clarified. The proposed approach is aimed to be applied for real time control of 7 d.o.f. robot. Simulations have been done for that robot taking into account its dynamics and sensibility models and applying the force control method. The results are presented further.