Force/position control of a robotic system for transcranial magnetic stimulation W.N. Wan Zakaria School of Mechanical and System Engineering Newcastle University Abstract To develop a force control scheme for a Transcranial Magnetic Stimulation (TMS) robotic system, contact between the robot and subject s head is a challenge and crucial issue. Although this is the one of fundamental interactions that occur in manipulation, most current industrial robot systems inadequately sense or use contact information and rely on the precise pre-position of objects and joint information to guide the movement of the robot. This paper proposes combining force (and torque) information with positional data using hybrid force/position control to satisfy a related task in the control system. The correlation between the force/torque and position data will address the importance of the control system in solving the problem. An overview of the control algorithm as well as the architecture of the experimental robot control and the force/torque sensor data acquisition system (DAQ) is described. Keywords: Trascranial magnetic stimulation, force control, data acquisition system, robot control architecture 1. Introduction Robot manipulator arms are required to perform many tasks involving interaction with their environment, such as manufacturing, assembly, deburring, cutting, polishing and handling parts and also in non-industrial environments; for example, hospital, welfare, maintenance and space. Implementing these tasks require a robot to realize the predisposed position as well as provide the necessary force to either overcome the resistance from the environment or comply with the environment. Robot force control involves integration of task goals such as modelling the environment, position, velocity, and force feedback and adjustment of the applied torque to the robot joints. Zeng et al. [1] conclude that feedback of various measurement signals of the output of a robot such as position, velocity, force and the selection of command input signals to a robot result in different force control methods. A number of schemes have been proposed for force control [2]. This paper addresses the development of force control for a TMS robotic system. A Staubli TX60 six degree of freedom robot manipulator arm will be used to position the stimulating coil and allowing both coil location and orientation to be controlled. Furthermore, to maintain the coil in contact with the subject s head by a light force of no more than 2N, a six-axis ATI Gamma Force/Torque transducer will be mounted between the robot end-effector and the coil. The first step to define an appropriate force control scheme depends on two conditions: a force/torque sensor must be used
to measure the forces and torques exerted by the subject and there is no hardware modification on the original CS8C robot controller. Several force control schemes has been evaluated and it is proposed that the hybrid external force control scheme developed by De Schutter et al. [3,4] is considered to be the best solution regarding the safety constraints, simplicity and implementation efficiency [5,6,7,8]. 2. Hybrid position/force control scheme Railbert et al. [9] proposed the most well-known approach of compliant motions called hybrid position/force control. Numerous papers have been reported on this control scheme [1,2,3,4,10,11] that associates the constraints of a task requiring force feedback to the controller design. In hybrid position/force control the position and force can be separately controlled as shown in Figure 1. In Figure 1, S = diag (s j ) (j = 1 n) is called compliance selection matrix and the number of degree of freedom is defined by n. The subspaces for which force or position are to be controlled is determined using this matrix S. When s j = 1, the jth DOF must be force controlled, otherwise it must be position controlled. As shown in Figure 1 the hybrid controller consists of two complementary sets of position and force feedback loops controlling the manipulator arm. The position servo loop is already implemented in original robot controller and force control loop must be implemented which an action at the joint torque level. It is important to ensure orthogonality between the outputs of force controller and position controller to prevent any conflict at the actuator level. Furthermore, if disturbance occurs along the force controlled direction, the induced positioning cannot be corrected. Perdereau and Drouin s [5] comparative study showed that the determination of the position and force controllers is very difficult as a result of the burden same calculations to determinant equations of dynamic force and position responses which cannot be simplified. Moreover, this characteristic equation is totally non-linear because it depends not only on the mechanical structure but also on the task configuration through the selection matrix S as well as the operating point through Jacobian matrix J. The Railbert et al. [7] work can be classified as parallel hybrid position/force control since it satisfies simultaneously the desired position and force constraints of the task. De Schutter et al. [3,4] propose an external hybrid position/force control scheme which is composes of two embedded control loops: an inner loop (position controller) and outer loop (force controller) as illustrated in Figure 2. The output of the outer loop is transformed into a desired position input for the inner loop. Therond et al. [12] claim that this type of control scheme is relatively easy to implement on an industrial robot by retaining the robot conventional controllers and requires a rather small amount of computation. The study of this project is based on this control scheme. However, a conceptual scheme which is described above must be analyzed and modified to match the requirements for any real implementation.
3. Force data acquisition system A six-axis ATI Gamma Force/Torque transducer has been mounted onto the endeffector of the Staubli TX60 manipulator robot to feed back forces/torques data occurring during simulation while robot maintaining the coil in contact to the subject s head. To improve the performance of the force/torque data gathering the ATI Force/Torque controller has been replaced with the Force/Torque data acquisition system developed by Po-ngaen[13] as shown in Figure 3. The sensor interface board consists of a high speed analog to digital converter (ADC) circuit and a PCI digital input/output interface card can effectively enhance system bandwidth with the acquisition and processing time requiring 0.7ms for each particular iteration process. 4. Force/torque signal processing In order to measure the forces and torques exerted by the manipulator arm on the subject s head, the weight of the coil beyond the F/T sensor must be compensated for. This section describes the transformation calculation of force/torque vector and gravity compensation used in control system. The notations called homogenous transformation describe the relationship between different frames and objects of a robotic cell are listed below. a - a leading superscript represents the reference frame b - a leading subscript represents the frame that relative to the reference frame c - a superscript represents a name for the vector d - a subscript represents a point in space while, F, N and R indicate force, torque and rotation respectively. There are three important frames which are world frame {W}, the F/T sensor frame {S} and the tool frame {T} at the center of gravity of the coil. As shown in Figure 4 the payload extending beyond the F/T sensor is modelled as a point of mass c, with the center of gravity at a distance d beyond the F/T sensor frame{s}. The distance d is measured along the positive z-axis of the sensor frame. First, the F/T sensor frame is assumed to be aligned with the tool frame. If the sensor is not aligned with the tool frame, an additional transformation can be applied to obtain the measured forces and torques in the sensor frame. Regardless of the position and the orientation of the coil in the space, the weight of the coil, W t can be expressed as a force vector as shown in equation (1) below. The equation indicates that the weight of coil, Wt exerted at a point c always acting along the gravity which is z-axis of the world frame {W}. In order to calculate the true contact forces and torques for gravity compensation, the force-torque transformation acts on the sensor measured in the sensor frame {S} is calculated as
follow. is the identity matrix since the {S} frame is assumed aligned with the {G} frame. Evaluating the first term of right side of the equation; is the vector of, thus The second term can be calculated as follows; where is rotation matrix defines the sensor frame {S} with respect to world frame {W} and is the third column of. The rotation matrix can be defined using forward kinematics of the manipulator and most cases the sensor frame has the same orientation of the robot s end-effector. Equally, This is because the tool does not rotate in free motion, thus and are zero. Whereas, the equation become; and Equations (3) and (4) can be described as the gravity compensation values. Now, the true forces and torques value can be determined by subtracting this gravity compensation values from force-torque data measured by for sensor expresses in sensor frame as shown below. Note that the weight of the tool, W t and the distance to the center of gravity, d can be determined experimentally by placing the sensor frame {S} and tool frame {T} aligns with the z-axis of the world frame {W}. In this configuration,
and. Thus, the measured force by the sensor is equal to weight of the tool. Then, the sensor frame z-axis is aligned with the world frame x-axis. In this case and. The d value can be calculated using (4) as; 5. Experimental programme In order to implement a force control scheme into the system several experiment is carried out to achieve the key requirement of the project. The first experiment involves the operation of the robot system in free space motion. Several tests were performed in world coordinates in x-axis direction where the force is applied to the force/torque sensor and the data measured is then routed to the robot controller. This generates incremental position demand for the robot system and the robot arm will move at a velocity proportional to the applied force as shown in Figure 5. The actual position of the robot x is proportional to force measured F by the gain K, where this situation can be modelled as a simple linear spring in Cartesian direction as described in equation (6). Determination of specific gain value for a conventional force controller in principle is relatively straightforward. However, the problem arises when the specific value of K is unknown or variable. Further experiment must be done to determine the ideal K value to avoid any serious consequences in practical robotic systems particularly in system stability. In TMS robotic system real implementation, this control approach can be used as manual mode for teaching. In this mode, the desired force is set to zero and the arm is compliant. The neurologist moves the robot from the initial position to the stimulating point and then the TMS procedure can be activated. A second experiment will be carried out using conventional PID control for force controller to improve stability performance and manoeuvrability of the manipulator arm in free space motion test as well as experiment in contact with the environment which is a key requirement of this project. This will be closed loop control system as shown in Figure 6. The sensed force between the robot arm and the environment will be processed by force/torque data acquisition system and this force is compared with the desired force at the set point regulation. The force control loop compensates the difference or error between the desired and actual force and then send the desired position to the robot controller. Further experiment will be done to develop force control scheme for TMS robotic system based on hybrid position/force control scheme.
6. Conclusions and future works This paper highlights the development of force control scheme of TMS robotics system. The Force/Torque DAQ had been improved to enhance the performance of forces and torques data gathering. Several experiments set up are designed to improve system performance as well as to achieve the key requirement of the project. The design of the robot end-effector to hold the TMS coil during the stimulation has been fabricated and ready to be used. In addition, the collision sensor is incorporated as a safety feature to prevent any exceeded applied force to the environment as shown in Figure 6. Work in the near future will focus on the development of force controller and implementation of safety system to the TMS robotic system. When this done, it will be possible to draw conclusions regarding to the force control and then will be combined with the navigation system in order to complete the whole TMS robotic system. References 1. Zeng, G.W. and A. Hemami, An overview of robot force control. Robotica, 1997. 15: p.473-482. 2. Whitney, D.E., Historical-Perspective and State-of-the-Art in Robot Force Control.International Journal of Robotics Research, 1987. 6(1): p. 3-14. 3. De Schutter, J., Van Brussel, H., COMPLIANT ROBOT MOTION I. A FORMALISM FOR SPECIFYING COMPLIANT MOTION TASKS. International Journal of Robotics Research 1988. 7(4): p. 3-17. 4. De Schutter, J. and H. Van Brussel, COMPLIANT ROBOT MOTION II. A CONTROL APPROACH BASED ON EXTERNAL CONTROL LOOPS. International Journal of Robotics Research 1988. 7(4): p. 18-33. 5. Perdereau, V. and M. Drouin, A New Scheme for Hybrid Force-Position Control. Robotica, 1993. 11: p. 453-464. 6. Pierrot, F., et al., Hippocrate: a safe robot arm for medical applications with force feedback. Med Image Anal, 1999. 3(3): p. 285-300. 7. Poignet, P., et al., Design and control issues for intrinsically safe medical robots. Industrial Robot-an International Journal, 2003. 30(1): p. 83-88. 8. Dombre, E., et al., Dermarob: A safe robot for reconstructive surgery. IEEE Transactions on Robotics and Automation, 2003. 19(5): p. 876-884. 9. Raibert, M.H. and J.J. Craig, Hybrid Position-Force Control of Manipulators. Journal of Dynamic Systems Measurement and Control-Transactions of the Asme, 1981. 103(2): p. 126-133.
10. Pujas, A., P. Dauchez, and F. Pierrot, Hybrid Position Force Control Task Description and Control Scheme Determination for a Real Implementation. Iros 93 : Proceedings of the 1993 Ieee/Rsj International Conference on Intelligent Robots and Systems, Vol 1-3, 1993: p. 841-846. 11. Yoshikawa, T. Force control of robot manipulators in Proceedings - IEEE International Conference on Robotics and Automation 2000. 12. Dombre, W.K.E., Compliant Motion Control, in Modelling, Identification & Control of Robots. 2002. p. 377-393. 13. Po-ngaen, W., Neuro-Fuzzy Control in Tele-Robotics, in School of Mechanical and System Engineering. 2006, Newcastle University: Newcastle upon Tyne.
Figure 1 Hybrid position/force control proposed by Railbert et al. [9] X - f(q) X d + dx f + X + - Position control law Γ Robot q f Force control law f d f + - Figure 2 External hybrid position/force control scheme [5,6]
Figure 3 Frame representation of the transformation calculation Figure 4 The analog to digital converter of the force/torque system [13]
Figure 5 Schematic diagram of the open loop control Figure 6 Schematic diagram of the closed loop control