The article introduces a sophisticated control system for an ultrasonic probe designed to optimize contact measurements with viscoelastic materials. By integrating a precision force-torque sensor and an ultrasonic transducer, the probe can be controlled to maintain optimal force and orientation, enhancing ultrasound transmission and measurement accuracy. The proposed system uses a novel adaptive Fuzzy Rule-Based Emulated Network (FREN) controller, which combines neural networks and fuzzy logic to handle the complex dynamics of soft materials. This controller is designed to maximize energy transfer and minimize contact force error, making it a significant advancement in the field of medical imaging and robotics.
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Abstract
Ultrasound probes are widely employed for internal sonification, to detect anomalies and assess mechanical properties. Achieving precise contact and orientation control is crucial for optimizing the transmission of acoustic energy into the test material. This study investigates the contact control of a hemispherical probe against a viscoelastic gelatin (tissue-like) test object. For small applied loads, the signals from the force sensor are often contaminated with noise. To enhance contact measurements, an ultrasound hemispherical probe was designed for Hertzian contact with gelatin. The transmitted/reflected acoustic energy is known to be a function of the contact area, which can be related to the applied force. The transmitted and reflected acoustic energy, which depends on the contact area, is related to the applied force. The goal is to develop an adaptive, model-free algorithm to control the contact force and orientation of the probe to maximize energy transfer. This algorithm integrates reflected acoustic energy at the contact interface with force data as feedback. A multi-input fuzzy controller scheme that is robust to noise and operates in real time is proposed. Numerical and experimental results demonstrate the controller’s stability and its ability to rapidly converge to the desired force and orientation conditions.
Notes
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1 Introduction
For many ultrasound measurements of viscoelastic biological materials such as human tissue, the contact of the probe against the tissue is controlled freehand, with the operator intuitively adjusting the probe’s orientation and force until the target region, signal, or image is optimized. The quality and repeatability of signals and images can be significantly affected by the lack of effective control due to the operator-dependent nature of free-hand ultrasound systems.
Mechanical devises and robotic approaches has been developed. A hand-held force-controlled ultrasound probe was proposed for medical imaging applications in [7], by holding the probe-patient contact force constant. Also, robot-assisted US imaging systems have been proposed for scanning human body [13]. Telerobotic systems [27] have also been employed to perform remote ultrasound imaging and specific studies, such as in reference [25], where a force and positioning control was presented to track and explore stiff tissue within 3-D ultrasound volumes assuming a mathematical model of the system. In these systems, position tracking controllers were implemented sometimes with reflecting the tissue force [13, 25] to the sonographer.
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Soft material plays a key role in biomedicine ([12]), soft robotics ([29]), sensors ([37]), tapes ([33]) and printing industries ([19]). The contact mechanics of soft matter is not yet fully understood, due to its intrinsic viscoelasticity and rate-dependent adhesive features ([18, 34‐36]).
Beyond typical ultrasound imaging, techniques like ultrasound elastography, where a load is applied during ultrasound sonification require precise control of the applied force to measure tissue deformations to determine its elastic modulus [24, 30]. The compressive force must be minimized to determine the effective stiffness of the target region, e.g., a tumor, and its surrounding tissue [31].
Thus, determination of mechanical properties of soft material is a challenging task because they easily break, conventional tensile and bending tests are not suitable configurations. Uniaxial compression, shear strain oscillatory and indentation tests appear more appropriate. The contact between a sphere and a viscoelastic substrate has been of scientific and technological interest, because of the potential application to determine tissue properties and as a mean to transmit ultrasound into the tissue on small regions. The mechanics of Hertzian contact have been studied for decades, attracting attention due to its well-established relation between force and contact area during indentation in elastic materials. It has a gradual nonlinear increase in mechanical compliance, making this appropriate for application in robotics to simulate finger-object contact, in grasping and palpation tasks ([1‐3, 15, 17]. Hertzian contact has been also proposed to characterize elastic and viscoelastic properties of linear and nonlinear materials. In reference [23], Hertzian theory and photoelastic tomography were used to study the stress state inside gelatin material for small forces or contact areas (much smaller than the radius of a spherical indenter radius).
Here, we propose a hemispheric probe equipped with an ultrasonic and a force sensor to control force and pose of the probe at low contact force to optimize transmission of ultrasound into a gelatin object. Ultrasound signals will be used, in conjunction with the force sensors, to control the pose and applied force on the surface of a viscoelastic gelatin test sample. Signals of the ultrasound and force sensors will be the feedback to a proposed data based fuzzy force controller.
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An orientation control based on a mathematical model assumes all system parameters as known or estimable. For example, in references [6, 21] algorithms based on inverse kinematics and divided surfaces to control a Computer Numerical Control (CNC) machine for cutting tasks of rigid materials were developed. However, orientation control of an end-effector in contact with a soft material involves a control design for which the system’s dynamics is not easy to determine [2]; it must take into account the nonlinear mechanical behavior during the contact and the environmental uncertainties, which cannot be modeled in a complete mathematical form.
Model-free control schemes, also known as Data-Driven Controllers (DDC) [10], can be designed without the need for a plant’s mathematical model [20]; only input–output data is required for the control design. This concept has led to the development of various model-free adaptive controllers, as seen in the literature [8, 26]. In control engineering, artificial intelligence techniques that integrate fuzzy logic and neural networks, termed Fuzzy Neural Networks (FNN), have gained significant attention due to their ability to approximate parameters to desired values through iterative processes [14, 28]. By combining the learning capabilities of neural networks with the human-like reasoning of fuzzy logic, FNN control techniques have been applied to diverse applications [11]. An adaptive controller based on similar principles, known as Fuzzy Rules Emulated Network (FREN), was proposed in [32]. This controller features a simple structure that facilitates intuitive selection of initial network parameters. FREN control has been implemented in various experimental systems; for instance, a model-free force control strategy for autonomous dry contact ultrasonic inspection of objects with rough surfaces was presented in [3]. Recently, a robust version of the FREN controller, incorporating sliding mode techniques, was introduced in [5] for positioning control of a nonlinear 3 degrees of freedom (DoF) robotic system. While these studies have successfully applied the control algorithm to nonlinear systems with uncertainties, the challenge of achieving simultaneous force and orientation control of a probe in contact with soft materials remains an area that requires further investigation.
The main contributions of this work are summarized as follows:
An ultrasound hemispherical probe has been developed for Hertzian contact with viscoelastic gelatin to enhance contact measurements. This probe integrates a precision force-torque sensor that provides accurate contact force measurements during operation. Furthermore, the design of the probe is suitable for use with industrial robotic arms.
The optimization problem involves both pose and contact force to maximize energy transfer and precisely regulate the force, ensuring that the probe is perpendicular to the surface of the test body (gelatin). If the probe is not perpendicular, it is adjusted to the normal position by simultaneously modifying the applied force and the probe’s orientation, thereby addressing the challenges associated with a soft, highly deformable substrate.
According to this comprehensive problem, an adaptive Fuzzy Rule-Based Emulated Network (FREN) controller is developed, incorporating a unique parallel structure. This controller is specifically designed to maximize the energy transfer of the ultrasonic signal while simultaneously minimizing the contact force error. The parallel structure allows for efficient processing of multiple input signals, enhancing the controller’s ability to optimize both energy transfer and force regulation.
The objectives are: first, to develop the ultrasound probe and carry out initial test on a gelatin material; second an algorithm based on neural networks is proposed to control force and orientation of an ultrasonic probe positioned on the surface of a gelatin test object using ultrasound signal as the primary feedback.; second, to test the controller numerically and experimentally on an autonomous robotic system.
2 Ultrasound tests on gelatine
2.1 Gelatine tissue preparation
A tissue-like material made of gelatine was used in the test. This material emulates ultrasonic properties of biological tissue such as sound velocity, attenuation and scattering [4, 16, 22]. The gelatine was prepared by combining type-A, 300-Bloom gelatin derived from acid-cured porcine skin (G2500, Sigma-Aldrich Corp.) with ultra-pure deionized water. The mixture was combined with formaldehyde (\(37 \%\) by weight, MERCK) to enhance cross-linking of the phantom and improve its long-term stability [9]. To enhance ultrasonic backscatter, 40-\(\mu \)m diameter silica particles (MIN-U-SIL-40, KOPRIMO) were added to the gelatin solution before the addition of the formaldehyde. The gelatin was contained on a petri box of 95 mm of diameter and 15 mm of high. The resulting sample is a homogeneous material with no visible internal defects.
Fig. 1
Design and integration of the ultrasound probe
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2.2 Ultrasound probe design
The ultrasonic contact probe was built with a 5MHz ultrasonic transducer and a soft head made of elastomer material (dry couplant silicone manufactured by Sonemat Inc). The soft silicone properties are shown in Table 1. The probe is a hollow shell with a round probe tip. The probe is filled with water to form a water-column between the ultrasonic sensor and the interior curvature of the probe tip, as shown in Fig. 1a. This allows the piezoelectric transducer to generate the signals that interact at the interface between the probe and the soft surface of the object under test. The probe is attached to a force sensor and adapted to the robotic manipulator. The acquisition of ultrasonic data was implemented using a USB communication with a 100 Mega samples/sec digital oscilloscope Tektronix DPO 3012. A workstation (Intel (R) CPU @2.67 GHz) that performs all the control law computation and communication with the robot from MATLAB R2018a platform was used.
Table 1
Properties of silicon hemispherical probe
Name
Parameters
Value
Units
Radius of curvature
R
16
mm
Young modulus
E
0.173
MPa
Acoustic longitudinal velocity
L
1.03
\(mm/\mu s\)
Water column (length)
W
17.5
mm
2.3 Initial tests and ultrasound signals
Fig. 2
Relaxation of soft material under different applied loads
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In a set of preliminary tests, the mechanical contact response of the gelatin material to a vertical displacement (Z) of the developed probe was studied (see Fig. 2). A controlled vertical displacement of the probe was applied while the resulting force was monitored. The displacement was performed in steps of 0.5mm with an average duration of 190 s each. The results show that the force sensor is unable to detect small loads at the onset of the Hertzian contact[0-400 s]; also, there is an evident mechanical relaxation (creeping) of the material with increased displacement, and white noise on the monitored force signal is observed. Thus, a classical controller will be affected and be difficult to implement when using only force sensor signal as feedback.
In Fig. 3a examples of the recorded acoustic signals (used later as feedback in the controller) are given. In this case, the signals are reflections from the back of the gelatin test object formed in the shape of a thick solid disk (see Fig. 4). Time delay and a reduction in amplitude are observed as the probe indentation distance (\(\delta \)) increases (see Fig. 1b). The force was simultaneously recorded during the test. Figure 3b) shows experimental results (scatter points) of signal power P(k) versus measured value of force (related to the actual applied force). P(k) is estimated as
where x(k, l) is the amplitude value in volts [V], \(l=1,2,\ldots ,L\) is the time index that conform the k acquired signal.
Three phases on the data can be identified, phase A, for incipient or onset of indentation, the force sensor is insensitive to the progress of indentation, while ultrasound measurement can detect changes; a phase B, shows a proportional change in signal power with force; and finally, in the last phase C, for values near 1N, the contrary effect to phase A is observed, with a saturation or no change in the acoustic signal power.
Fig. 3
Ultrasonic signal amplitude and power estimation for various recorded values of applied force in Z- axis direction
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2.4 Effect of probe orientation on ultrasound signal
Figure 4 shows the orientation effect on ultrasonic reflected signals and power estimation. In this experiment, only one angle orientation, \(\theta _C\), was varied. The amplitude of signal in time domain is highly sensitive to misalignment. For example, a deviation of the normal position (probe is perpendicular to the surface) of \(\theta _C=10^{\circ }\) results in a total loss of signal amplitude. The distribution of ultrasound power \(P(\theta )\) in the range \(\theta _C=[-10,10]\) is symmetric (Fig. 4b). Similar results were found for \(\theta _B\). Using both distributions, a function resembling a Gaussian-like function can be reconstructed (Fig. 5). In this example, the scatter red points are recorded values and are located in the direction of the gradient \(\nabla P\). The maximum can be reach implementing iterative methods such as gradient ascendant.
Fig. 4
Orientation effect on ultrasonic signal and power estimation
Fig. 5
Reconstructed Gaussian-like power distribution with superimposed experimental data (scatter points) indicating the path to reach the maximum value following the gradient of sound power \(\nabla P\)
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A practical implementation in a robotic system could be done by considering one plane of rotation at a time. That is, by fixing any of the orientation planes (\(\theta _{B,C}\)) and to perform gradient ascent on the free plane. In this, case, the controller needs to provide the switch of direction that assures the maximum ultrasonic signal power. The proposed control scheme will be discussed in detail in the next sections. As a result of these preliminary tests, it appears reasonable to fuse data from acoustic and force sensors into a neural-fuzzy controller to simultaneously control the force and pose of the probe.
3 Controlled plant
The robotic system to simultaneously achieve force and orientation control of an ultrasonic probe is presented in Fig. 7. The proposed control plant is integrated by a 6-DoF robot KUKA KRC1 manipulator, the developed ultrasound probe attached to a wrist force/torque sensor ATI Mini-40 and the test tissue-like gelatin.
Fig. 6
Matching between Cartesian reference frames of robotic arm and force sensor
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The described plant is considered as a class of unknown nonlinear discrete-time system. In this work, the inverse kinematics controller of KUKA robot is used, which allow us to control the manipulator by a set of six parameters, that is, three position parameters X, Y and Z corresponding to cartesian coordinates configuration for tool task space of robot, and \(\theta _A, \theta _B\) and \(\theta _C\) rotation angles, related to the tool orientation (rotations about Z, Y and X axis respectively). At initial contact of the probe with the test object, information of \(F_x\) and \(F_y\) force directions (see Fig. 6) provided by the force sensor are used to have a first estimate of the position of the ultrasonic probe. That requires a careful matching of the Cartesian reference frame attached to the 6-DoF robotic arm (see Fig. 6a) with the Cartesian reference frame of the wrist force sensor ATI Mini-40 (see Fig. 6b). Thus, \(F_x\) and \(F_y\), are used as an indicator of the probe’s orientation change at initial contact. For example, at initial contact, an orientation change of \(\theta _C\) can be correlated to the magnitude and direction of \(F_y\) as shown in Fig. 6c. The proposed controller is designed to provide the control signals \(u_{B}\) and \(u_{C}\) to set the orientation values in degrees, and \(u_z\) to set the vertical displacement in millimeters required to reach and keep a desired contact force of the probe. The measurable parameters are the ultrasonic signal power P, and the applied forces \(F_x, F_y\) and \(F_z\), which act as the feedback signals to the controller, designed for discrete time systems with unknown mathematical model.
Fig. 7
Ultrasonic robot-assisted system scheme
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4 Control algorithm
The proposed general force and orientation controller based on neuro-fuzzy networks (shown in Fig. 13) is divided into two control algorithms: force and orientation controls. The force control (Sect. 4.2.1) works under the conventional version of FREN (Sect. 4.1) which works by minimizing the error between a set or desired value and the current value. The orientation control (Sect. 4.3) uses a modified version of FREN, to optimize for the maximum ultrasonic power measurement, implementing a gradient ascent iterative technique.
4.1 Fuzzy rule emulated network
The Neural Network (NN) architecture of a conventional FREN is illustrated in Fig. 8. A characteristic of FREN is that prior knowledge regarding the controlled plant can be generalized within IF-THEN rules. Here is given a brief description of FREN’s architecture, for a detailed version see [32]. FREN is composed by four layers:
Fig. 8
Neural network of FREN controller
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Layer 1: The error \(e(k)=x_d(k)-x(k)\), where \(x_d(k)\) is the desired value, and x(k) is the current measurement, is the input of this layer which is directly sent to each node in the next layer.
Layer 2: This is called input membership function layer. Each node in this layer contains a membership function corresponding to one linguistic variable (e.g. negative, positive, zero, etc.). The output at the ith node of this layer is calculated by
where \(f_{i}\) denotes the membership function at the ith node (\(i=1,2,\ldots ,N\)), and N represents the number of linguistic variables, see Fig. 9. A set of Gaussian and sigmoid functions are used to cover the expected output error to be minimized. A set with an \(N=5\) is commonly sufficient, but it could be increased, considering its computational cost.
Fig. 9
Membership functions where: NL=negative large, NS=negative small, Z=zero, PS=positive small and PL=positive large
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Layer 3: This layer may be considered as a defuzzification step. It is called the linear consequence (LC) layer, where the parameters \(\beta _{i}\) are optimized by the steepest descent technique at each (k) iteration.
Layer 4: It is the output of the artificial neural network and is calculated as:
It is important to note that the control law (3) does not require an explicit mathematical model of the system being controlled. This is particularly advantageous for systems with complex, nonlinear, or poorly understood dynamics, such as the proposed ultrasound probe. Additionally, the parallel structure of the controller, which simultaneously handles both force regulation and maximum power seeking, is well-suited for the proposed application.
4.2 Force control algorithm
The FREN algorithm integrated into a force controller is shown in Fig. 10. It is expected that contact forces increase with contact area between the ultrasound probe (Fig. 1b) and soft gelatin test object. The signals that are fed into the controller are acoustic echoes taken from the bottom of the gelatin sample. Thus, variation in time of arrival and changes in amplitude of ultrasonic transmission (Fig. 3a) could occur before saturation conditions shown in Fig. 3b.
The force control algorithm aims to achieve and maintain a desired contact force, which ensures stable signal measurements and prevents damage to the soft material. The force \(F_{z}\) applied along the tool’s Z-axis serves as the feedback signal for the controller. The proposed force controller features four hidden layers, with the error \(e_z(k) = F_{zd} - F_{z}\) used as the input, where \(F_{zd}\) is the desired contact force and \(F_z\) is the current measurement of the contact force. The fourth hidden layer generates the control signal \(u_z(k)\) as follows
where the parameter \(\beta _{zi}\) with \(i=1,2,\ldots ,N\) and \(N=5\), represents the five time-varying control parameters of the force controller. The control scheme is depicted in Fig. 10. FREN receives the error signal \(e_z(k)\) as input to compute the nominal control signal \(u_z(k)\) according to eq. 3.
Fig. 10
Control scheme of force control based on FREN controller
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4.2.1 Adaptation algorithm
To obtain the learning laws of control gains to minimize the tracking error, the cost function J(k) is chosen as
having \(Y_p\) as the gradient of the plant that indicates the expected change of the output of the plant \(F_z(k+1)\) respect to the input \(u_z(k)\). Thus,
According to the proposed learning law in (10), the error \(e(k+1)\) is used together with \(A_z(k)\) from the control law u(k). This leads to an update of the parameter \(\beta _z\) aimed at minimizing the cost function \(J(k+1)\) in relation to u(k).
4.2.2 Stability analysis
For the force controller, the stability proof is analyzed with respect to the linear consequence parameters \(\beta _{zi}(k)\), which are updated at each time step as shown in equation 9. It is crucial to emphasize that the learning rate \(\eta _{z}\) plays a significant role in determining the convergence speed of the control. A value that is too large may compromise system stability, while a value that is too small can hinder the system’s adaptive performance. In this subsection, we discuss how to select an appropriate range for \(\eta _{z}\) to ensure stability in the Lyapunov sense. Consider the following Lyapunov function
By selecting the learning rate \(\eta _{z}\) in accordance with (16), the convergence of the internal parameters is guaranteed.
In this Sect. 4.2 the force control, adaptation algorithm and stability analysis were provided based on FREN controller and Lyapunov methodologies, having a reference value to estimate the error. In the next section 4.3, the orientation control using information of sound signal power as feedback is presented.
4.3 Orientation control scheme
Due to the curvature of the probe (end-effector), contact forces on the surface of contact depend on orientation, making it challenging to control the probe’s orientation solely based on force measurements. Since the maximum power value depends on the applied force, it’s impossible to set a reference maximum power value. Additionally, optimization based on quadratic error cannot be implemented. However, there’s only one set of force and orientation values that results in maximum power. This value should include all potential nonlinearities and uncertainties of the system, such as deviations from the origin of the robot configuration and uncertainties in tool attachment or robot calibration. Despite these factors, there’s still only one maximum ultrasonic power for each applied contact force.
The orientation control algorithm is intended to find the optimal \(\beta _C\) parameters that assure normal position of the ultrasound probe with respect to the test object surface from any initial position. This controller requires force and ultrasonic power measurements as feedback signals. Initial signs of forces \(F_{x}\) and \(F_{y}\) give orientation information of probe as explained in section 2.2. The orientation control scheme shown in Fig. 11, is divided into two neural networks structures presented in Fig. 12: one for the control of \(\theta _B\) orientation parameter with the power measurement P(k) and the sign of the force value \(F_{x}(k=1)\) as inputs and, the second, for the control of \(\theta _C\) orientation parameter with P(k) and \(F_{y}(k=1)\) as inputs. Its
Fig. 11
Control scheme of orientation control based on two FREN controllers
Fig. 12
Neural networks structures of orientation controllers
where \(\Delta \theta _B\) and \(\Delta \theta _C\) are the changes of \(\theta _B\) and \(\theta _C\) orientation parameters, \(\beta _{Bi}\) and \(\beta _{Ci}\) are the time-varying control gains and \(f_{Bi}\) and \(f_{Ci}\), represents the sets of five membership function determined for each controller.
4.3.1 Adaptation algorithm
The control gains \(\beta _{Bi}\) and \(\beta _{Ci}\) are updated to seek for a maximum value of input based on the power feedback,
where \(\eta _{B}\) and \(\eta _{C}\) are the learning rates that determine the convergence speed. The back propagation algorithm is realized by the chain rule
In this subsection we discuss how to select an appropriate learning rate which guarantees algorithm’s stability. Consider the measurement of power P(k) as an always positive value. The change of power \(\Delta P(k)\) is given by
4.4 General force and orientation control structure
The control scheme of the proposed general adaptive contact force and orientation controller is illustrated in Fig. 13. An estimated maximum power value \(P_{max}\) in the contact condition is measured at a desired applied force and used as a reference. This value is then nearly normalized as \(P(k)/P_{max}\) and evaluated using a set of five membership functions, designed to cover the range from 0 to 1. The orientation controllers for the \(\theta _B\) and \(\theta _C\) parameters, along with the force controller for Z axis displacements, operate in a parallel structure to guide the ultrasound probe to a normal position at the desired contact force. The proposed algorithm is designed to handle the nonlinearities of the test object, such as relaxation and environmental uncertainties. The effectiveness of the proposed controller will be validated through experimental demonstrations.
Fig. 13
Description of the general force and orientation control scheme
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5 Results and discussion
Numerical and experimental results are given in this section. The numerical analysis to corroborate the theoretical convergence of the proposed orientation controller is developed. A set of experiments were carried out on the tissue mimicking gelatin to test the performance of the force and orientation controller.
5.1 Numerical results
For the numerical analysis, the distribution of power energy of ultrasound, \(P(\theta )\) was modeled as a Gaussian-like function. The aim of the controller is to reach the correct orientation finding the maximum of \(P(\theta )\). The analysis was applied for the one-dimensional (\(\theta _C\)) and two-dimensional (\(\theta _B\) and \(\theta _C\)) cases of orientation control. Both simulations reach the maximum value in only a few iterations, as shown in Fig. 14. For the one dimension case (see Fig. 14a) the initial random position was set 7 degrees out of the normal with a power value of 6 \(V^2\) approximately (red circle mark). Maximum power is reached at normal position \(\theta _C=0\) (red diamond mark) due to the orientation control. Similar results were found for the two-dimensional case (see Fig. 14b), where the synchronization of \(\beta _B\) and \(\beta _C\) orientation control parameters plays a relevant role during the maximum power optimization.
Fig. 14
Numerical simulations results for a one dimension and b two dimensions
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5.2 Experimental results
The objective of this experiment is to verify the performance of the proposed controller in reaching the normal orientation of the robotic ultrasonic probe at a desired contact force when interacting with a soft material. The monitored parameters are the positive ultrasonic signal power P(k) and the exerted contact forces \(F_x\), \(F_y\) and \(F_z\). The sign of forces \(F_x(k=1)\) and \(F_y(k=1)\) at initial condition given by the force sensor allow having an initial guess of the orientation of the probe, and to set the positive or negative initial direction that should be applied to \(\beta _B\) and \(\beta _C\) orientation control parameters.
A frontal view of the experimental setup is shown in Fig. 15. The experiment consists of applying a misalignment of the probe in \(\theta _B\) and \(\theta _C\) of 4, 5, 6, and 7 degrees with respect to normal position. Autonomous alignment to normal position is controlled by force and orientation controllers working simultaneously.
Fig. 15
Experimental setup for tests
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5.2.1 Force control results
The force control signal \(u_z \), the error measurement \(e_Z\) and the contact force \(F_z\) due to Z axis displacement, are shown in Fig. 16. Initially, an overshoot correlated with the degree of the orientation angles \(\theta _B\) and \(\theta _C\) appears, since the controller reacts with higher values. On the other hand, force measurement \(F_z\) overshoots are due to drastic orientation change, which applied more force during restoration.
Fig. 16
Control signal \(u_z\) and applied force \(F_z\) behavior
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5.2.2 Orientation control results
For the orientation controller, five membership functions were designed based on the normalized allowable maximum power values measured at a set contact force, as shown in Fig. 17. To account for any unexpected variation in the value of the set maximum force, the range of the membership functions was set slightly larger (15%) which was estimated experimentally.
Fig. 17
Membership functions for nearly normalized power
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The behavior of the control signals \(u_B \), the robot positioning \(\theta _B \) and the ultrasonic signal power measurements P(k) are shown in Fig. 18a and same parameters for \(\theta _C\) orientation in Fig. 18b. It is shown that less of ten iterations are enough to converge at the desired position. Same power measurement P(K) is used as input for both, \(\theta _B\) and \(\theta _C\) orientation controllers, however, the restoration performing is different for each one.
Fig. 18
Behavior of controls signals, robot positioning and ultrasonic signal power
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In Fig. 19 a visual representation experimental results is shown. It can bee seen, that for the initial \(7^\circ \) out of the normal for \(\theta _B\) and \(\theta _C\) the value of power P(k) is minimal and for the final position the power increases rapidly until reach its maximum value of \(0.46V^2\) approximately.
Fig. 19
Visualization of orientation control using ultrasonic signals as a feedback
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6 Conclusions
In this work, a hemispherical probe for Hertzian contact with tissue-like gelatin was developed to enhance contact measurements. This probe integrates a precision force sensor and an ultrasonic sensor, designed for integration into a robotic arm. Initial tests demonstrated high sensitivity of the ultrasonic signals to contact and orientation, particularly in the low range of applied loads where force sensors are limited. The signals from both acoustic and force sensors were fed back to a proposed neuro-fuzzy controller. An adaptive model-free algorithm based on neuro-fuzzy networks and ultrasonic power measurements is introduced. This controller, which operates without a mathematical model of the plant, relies on IF-THEN rules derived from human knowledge. It was tested on a soft material with varying initial orientations of the ultrasonic probe. The control scheme features two separate controllers-one for contact force and one for orientation-working together to maintain the probe’s desired orientation and contact force on a nonlinear elastic gel. Feedback inputs of ultrasonic signal power and reaction forces were used to optimize control parameters. The controller achieved a constant ultrasound signal, correlating with the contact area and necessary for accurate testing. The adaptive algorithm demonstrated effective parameter tuning, with stability and convergence ensured through analysis. The approach overcame technical complexities without needing a deterministic model of the surface or contact mechanics. The proposed method addressed the simultaneous control of force and orientation at a probe/gelatin interface using artificial intelligence with ultrasonic feedback. Future work will explore the use of a flat-end probe, as well as the implementation of the developed system for scanning and image reconstruction using information of the ultrasonic signals.
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