Fuzzy position-velocity control of underactuated finger of FTN robot hand

1.1 State of the art

After few decades of significant progress in the field of artificial hand design, it is still an open problem with ongoing research. Development of new materials and new types of actuators is also promising for the next generation of robotic hands. Some state of the art solutions for the robotic hand design, characterized by great functionality and dexterity are the Robonaut hand, designed by NASA [4, 5], the series of DLR hands of different generations [6, 7], the GIFU hand III [8], the UB Hand III [9], Shadow Hand [10] and Elumotion Hand 2 [11]. A common drawback of these robotic hands is their complex design and extremely high price. Mostly they are still large and heavy, and they are not able to provide large grasp force, compared to the human hand. Robotic hands can be classified based on several criteria. Considering the type of actuation, most commonly used type of actuators are servos. The vast majority of robotic hands, including the one presented in this paper use this type of actuators [4–9, 11]. Servos are suitable for control but have poor mass/payload ratio. Pneumatic artificial muscles (PAMs) are lightweight and have much better mass/payload ratio than electric motors. PAMs have similar force characteristic as human muscles, but the characteristic is nonlinear. The great advantage of PAMs is their intrinsic compliance, but they need compressed air, which limits the mobility and manipulability of such robotic hands. Several dexterous robotic hands that use PAMs for actuation have been developed [10, 12]. Another solution of the lightweight artificial hand design, with special flexible fluidic actuators, is reported in [13]. An innovative design has been proposed for a robotic hand, which uses so-called hydraulic cluster actuators [14]. This electro-hydrostatic actuator generates great force, more than 260 N. Besides above-mentioned actuators, some other types of actuators might also be used like: piezoelectric actuators, memory alloys, and electro-active polymers.

1.2 Contribution of the paper

The main contribution of this paper is the development and implementation of the BDC motor position controller for actuating robotic hand’s joints. First, the fuzzy based position-velocity control algorithm is developed in Matlab/Simulink and the algorithm is later implemented on to the real-time embedded ARM Cortex M4 platform. The performance of the controller in simulation and the real world has been evaluated, and the fuzzy based controller has been compared with respect to the classical PID cascade position velocity controller.

This paper is organized as follows. In Section 2, first, the mechanical design of the FTN robotic hand is briefly described. After that, the proposed electronic system for actuation is introduced, with a special emphasis on the implementation issues and prototype design. The used methodology is briefly discussed in Section 3, where the model of actuators is introduced and the experimental platform is described. In Section 4, the comparison of the proposed fuzzy-based position controller and the traditional PID controller is presented, both in Simulink and on real hardware. At the end of the paper, in Section 5, a brief discussion of the obtained results is given, with a final conclusion.

2.1 Mechanical design of the hand

FTN robotic hand, with its biologically inspired design and kinematic structure, was originally presented in [15]. It has 5 fingers, where each finger has 3 joints (3 DOFs) which provide the flexion/extension movement.

The thumb has 3 DOFs for flexion/extension and additional DOF for the rotation in its base. Kinematic parameters of the hand are shown in Fig. 1a and CAD model is shown in Fig. 1b, c.

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Fig.1

FTN robotic hand: a) Structure of the hand and its kinematic parameters; b) CAD model of the robotic hand and c) actuation system embedded in the palm.

In order to provide a lightweight structure of the hand, all finger segments and the palm are supposed to be realized on a 3D printer. This production technique is suitable for rapid prototyping and allows complex shapes to be realized in order to provide anthropomorphic appearance and compact design. Unlike most robotic hands which have actuators located in the forearm, the hand proposed in this paper has 5 brushed DC motors embedded in the palm (Fig. 1c). Since only 5 motors are used for actuation of 16 joints, the hand is highly underactuated.

Middle finger and the index finger are actuated with one motor, each, while the thumb has one motor for flexion/extension movement and another one for the rotation in its base. The tendon-driven mechanism is used for the flexion/extension of each finger and these movements are actuated by the motors located in the palm. Each tendon goes from the pulley on the motor shaft in the palm, through the guiding holes in each finger’s segments to the fingertip, where it is fastened. Tendons and springs in joints impose constraints on finger motion and provide coupled motion in finger joints. In order to minimize the friction in the finger joints, small radial ball bearings are integrated into each joint. The rotation in the base of the thumb is also tendon driven. Two pulleys were used for power transmission in the base joint of the thumb. Unlike the other joints, tendon mechanism rotates the thumb joint in both directions, without a spring.

In each finger joint, there is a torsional spring. Hence, the finger flexion is realized by DC motor, as a single active element, while the extension is realized by torsional springs, as antagonistic passive elements. The stiffness coefficients of these springs define the trajectory of the finger and the way it bends during unconstrained motion, in the absence of external forces and obstacles. This tendon-driven mechanism with springs provides certain passive adaptability to the shape of the object that is being gripped. If the first finger segment hits the obstacle, while bending, the second and third segment will continue to bend, until they hit the obstacle or reach their mechanical limits.

Mechanical design of the finger joints is shown in cross section in Fig. 2. There are two radial ball bearings in each joint and a torsional spring. Small lock washers are used to constrain the axial movement of the joint shafts. Flat cables for force sensors [16] and steel tendon for finger actuation are led through finger segments through guiding holes.

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Fig.2

Kinematic parameters of the fingers a) frontal view of a thumb; b) frontal and c) lateral view of other fingers.

One of the most important objectives is to design robotic hand that is highly anthropomorphic and biologically inspired by the human hand. This task is challenging from the implementation point of view, considering the necessary electronic system for the actuation of DC motors. In order to provide systematic design, the basic requirements that a system must meet are defined:

The system must support the actuation of eight BDC motors.

Since the available space for the installation of actuation printed circuit board (PCB) is very small, the last requirement is the most challenging [17–19]. In order to fulfill this requirement, along with other constraints and demands, an extensive analysis of available integrated circuit (IC) solutions has been performed. Besides the necessary functionality, other criteria for the IC selection process were: (i) its physical dimensions and (ii) the number of required external (mostly passive) components. Clearly, the smaller IC that requires less external components represents a better solution. Also, the dimensions of the external components were considered. In Fig. 3, a block diagram with selected ICs and their mutual connection is shown.

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Fig.3

Block diagram of electronic system for actuation of BDC motors with manufacturer part number of the main components.

For actuation of finger segments, a brushless DC motor from Maxon motor manufacturer is chosen. From the standpoint of electronic system design, the most important characteristics of the chosen BCD motor are the power of 1.2 W, the nominal voltage of 12 V, the maximum continuous current of 210 mA and starting current of 386 mA.

Specialized integrated component DRV8801 from Texas Instruments manufacturer was chosen as the optimal solution because it requires only a few external components. It is suitable for the selected BDC motor and has a lot of features that are extremely important for the intended application. IC contains a full H-bridge with integrated N-channel MOSFETs, the internal charge pump, 100% PWM support, wide supply voltage range (8 V to 36 V) and lot of important protection features such as: undervoltage lockout (UVLO), charge pump under-voltage (CPUV), over current protection (OCP), short-to-supply and short-to-ground protection, overtemperature warning (OTW), over-temperature shutdown (OTS) and fault condition indication pin (nFAULT). Typical application circuit and connections to the microcontroller are shown in Fig. 4. The microcontroller uses seven pins for full control of the driver circuit. Signal VPROPI represent voltage output proportional to winding current and it must be connected to ADC pin. Another feedback signal is nFAULT which pulls logic low in a fault condition. It is open-drain output so it must be pulled-up to the appropriate voltage. Signals MODE1, MODE2, PHASE, ENABLE and nSLEEP are used to program different functionality of the driver circuit.

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Fig.4

Schematic with DRV8801 BDC motor driver.

The electronic system for hand management is designed to perform most operations locally. However, for the proper operation of the entire robot system, it is necessary that the components mutually exchange information. The amount of information can be very large so it is necessary to provide fast and reliable communication. These are the main reasons for the selection of a full-duplex RS-485 standard for communication. For the implementation of this standard Texas Instrument’s SN65HVD1477 IC in a small package for demanding industrial applications has been chosen. The bus pins are robust to ESD events, with high levels of protection to human body model (HBM) and IEC contact discharge specifications.

For debugging purposes, a USB-to-UART serial converter is introduced. The MCP2200 IC from Microchip manufacturer is a serial converter which enables USB connectivity in the application that has a UART interface. The device reduces external components by integrating the USB termination resistors. In this way, it is possible to follow in real time the execution of the program in the microcontroller.

For normal functioning of all parts of the electrical system, it is necessary to provide a stable supply of 3.3 V and 5 V. In order to avoid unnecessary waste of energy, a switched step-down power supply, that provides 12 V to 5 V voltage regulation, is designed. The MCP16311 IC from Microchip as a solution with the maximum output current of 1A, up to 95% efficiency, fast transient response, small PCB footprint is chosen. For 5 V to 3.3 V conversion, a low-dropout linear regulator TPS79601 from Texas Instruments is selected as a component that provides ultralow-noise support, up to 1 A current output, high power supply rejection ratio (PSRR) and very low quiescent current. The dimension of IC are 3×3 mm and with only a few external component makes the perfect solution for space required an application. The prototype PCB board is shown in Fig. 5.

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Fig.5

Prototype board for development of control algorithms for 8 BDC motors.

3.1 Modeling of the actuators

The custom made Maxon A-max brushed DC motor, used in the project to actuate the fingers of the robotic hand, is modeled in Simulink. The second order model of the brushed DC motor is used. It is described by the following equation: J θ ̈ + b θ ̇ = K m i L di dt + Ri = U - K e θ ̇ where J is rotor inertia, b is viscous friction, K _m is torque constant, L is terminal inductance, R is terminal resistance, and K _e is speed constant. The values of the parameters of the used motor [21] are given in Table 1.

Rotary incremental encoders (quadrature) connected to the rotor shaft convert rotational motion to digital information in the form of pulse signals. The encoder [22] is modeled using the following specifications:

counts per revolution: 512,

In Fig. 6 the experimental platform used for development and verification of control algorithms is shown. The setup is composed of a control board that is described in detail in Section 2.2., and a tendon-driven finger with 3 DOFs actuated by a BDC motor with incremental encoder. The parameters of the motor and encoder are equal to those used in modeling for the purpose of the simulation.

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Fig.6

Experimental prototyping platform.

Additionally, the experimental platform has a power supply, and a connection to a PC computer, for programming, debugging and communication with the control board.

4.1 PID controller

To compare the results obtained with the fuzzy controller, first, a classical position-velocity controller using PID rules is developed [23, 24]. For tuning the controller, a Ziegler-Nichols method is used. As a first demonstration example, position controller for a DC motor is described below. In this example, a PID controller is used to move a DC motor shaft from its initial position (0) to the final position (90 [rad]) 1 . Figure 7 shows the response of a Simulink model of PID control loop for the position control of a DC motor.

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Fig.7

Response of PID position controller tuned by Ziegler-Nichols method.

From the response it can be seen that the controller allows the DC motor to achieve its target position, but the velocity increases and decreases rapidly, causing an overshoot in the position before reaching the target position. Such transient behavior could cause problems in the real hardware implementation of the finger actuation system. The actuation has to be slow and controlled, and not fast with a significant jerk.

The problem with the previous position control system is that the velocity immediately spiked up and came down in order to achieve the target position. However, what is actually needed is a slower, and smoother movement from initial position to the desired position. One way to achieve this is to use a position-velocity controller with an embedded velocity profile. Thus, the Simulink model shown in Fig. 8 introduces a cascade position-velocity controller in order to achieve this controlled movement of the motor position.

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Fig.8

Simulink model of cascaded position-velocity control.

There are two controllers and two control loops in this model. The outer loop has the position controller and inner loop has the velocity controller. Parameters like the initial position, target position, maximum velocity, and acceleration provide a velocity profile for motor movement from initial to the final position. Figure 9 shows the obtained velocity profile in order to move the motor from its initial position (0 [rad]) to final position (30 [rad]) without a jerk at the beginning and at the end of the motion.

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Fig.9

Output of Position Control using cascaded PI controller.

It can be observed from the output that the measured velocity follows the trapezoidal velocity at the beginning of the motion and helps the motor reach its desired position in a controlled manner.

In this section, a Fuzzy Logic controller [25] is described for controlling the position of a motor [26] and it is compared with the classical PID control technique presented in Section 4.1. For implementing Fuzzy Logic controller, the following Simulink model shown in Fig. 10 was designed, following previous applications and theoretical aspects of fuzzy Control [27, 28].

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Fig.10

Position-velocity motor controller using Fuzzy Logic Controller.

It can be observed from the figure that for achieving the desired position, a position controller is used in the outer loop and a Fuzzy velocity controller is used in the inner loop. The output from the position controller along with the desired acceleration and maximum velocity generates the velocity profile similar as in the case of a controller shown in Fig. 9. The Fuzzy controller has to control the output speed along this generated velocity profile in order to achieve the desired position.

For the Simulink model of the Fuzzy Logic controller described in Fig. 10, two input parameters are required. The two parameters are “Error” and “Change in Error”. A Mamdani Fuzzy Inference System was used for modeling this controller. The Triangular membership functions are used to define the degree of membership of the input and output variables as described in Fig. 11.

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Fig.11

Membership Function plot of input variable a) ‘Error’, input variable b) ‘ChangeInError’, and output variable c) ‘output’.

A rule base was formulated in order to define the controller functionality. It is of the “If - Then” format, where the “if” part represents the condition and the “then” part represents the conclusion. The various measured inputs are compared against each other using this rule base and the output is generated according to the rule base described below in Fig. 12.

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Fig.12

Rule base.

This is a control system which has 2 inputs E (error) and CE (change in Error) and 5 membership functions NB (Negative Big), NS (Negative Small), ZE (Zero Error), PS (Positive Small) and PB (Positive Big). The rules of this system can be read as: “If E is NB and CE is NB then the output is NB”, “If E is NS and CE is NB then the output is NB” etc. After Fuzzification is completed, we use the rule base to map the input variables to linguistic output variables. But the linguistic output variables cannot be fed into the device and hence has to be converted back into a numeric value and this process is called Defuzzification. The Defuzzification method used here was the center of gravity method.

It can be observed from the output in Fig. 13 that the measured velocity follows the trapezoidal velocity profile at the beginning of the motion and helps the motor reach its desired position in a controlled manner.

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Fig.13

Output of motor position control using Fuzzy Logic Controller.

For the purpose of experimental verification, both, the PID and a Fuzzy Logic controller are implemented on real hardware. In the chosen case study, the controller was set to move the motor shaft position from 0 to 100 [rad], with a maximum acceleration of 0.75 [rad/s²], and a maximum velocity of 6 [rad/s]. Both controllers were first tested in a simulation environment and later on an embedded platform. The obtained results are discussed at the end of this section. The output from the PID controller and Fuzzy controller in simulation environment are shown in Figs. 14 and 15.

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Fig.14

Output of cascaded PID controller in a simulation environment.

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Fig.15

Output of cascaded Fuzzy Logic Controller in a simulation environment.

The result obtained from the cascaded PID controller while testing on hardware is shown in Fig. 16. The resulting graph was generated by plotting the values of the reference velocity, measured velocity and measured position obtained from experimental platform every 1 ms. The result obtained from the cascaded Fuzzy Logic controller while testing on the experimental platform is shown in Fig. 17. The resulting graph was also generated by plotting the values of reference velocity, measured velocity and measured position obtained from experimental platform every 1 ms.

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Fig.16

Output of the implementation of PID controller on an experimental platform.

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Fig.17

Output of the implementation of Fuzzy Logic controller on an experimental platform.

From the results of both PID controller and Fuzzy Logic controller on the experimental platform, it can be observed that there is not much of a difference in the characteristics of both types of controllers in the time domain, however, it could be observed that the Fuzzy logic controller displayed slightly better rise time and settling time.

The PID controller performed well in controlling the velocity of the motor along the desired velocity profile in order to achieve the target position from its initial position. The performance of the PID controller could be improved a bit more by additional tuning of the parameters manually.

The Fuzzy Logic controller showed good performance in controlling the velocity along a similar velocity profile generated by setting the initial position, desired position, desired velocity and maximum acceleration. The main advantage of a Fuzzy Logic controller is that an exact mathematical model is not required for designing a Fuzzy controller. Also since it is expressed in a linguistic manner [29], it is easily understandable.

Fuzzy Logic Controller has the advantage that it can work well with nonlinear systems [30]. However, compared to PID controller which has only three parameters, the Fuzzy controller has a lot of parameters to be taken into account. The number of membership functions and the rule base plays a vital role in how the controller responds. It was observed that the shape of the membership function selected didn’t make much difference, but specifying the degree of membership of the inputs and the outputs accurately makes a lot of difference.

One problem observed with the Fuzzy controller is that the computational time needed to obtain the new control variable was much greater for the FLC than the PID controller due to the Fuzzification and Defuzzification involved.