The authors have declared that no competing interests exist.
Conceived and designed the experiments: NS TN. Performed the experiments: NS PD. Analyzed the data: NS TN PD. Contributed reagents/materials/analysis tools: NS. Wrote the paper: NS TN PD.
When people are asked to palpate a novel soft object to discern its physical properties such as texture, elasticity, and even nonhomogeneity, they not only regulate probing behaviors, but also the cocontraction level of antagonistic muscles to control the mechanical impedance of fingers. It is suspected that such behavior tries to enhance haptic perception by regulating the function of mechanoreceptors at different depths of the fingertips and proprioceptive sensors such as tendon and spindle sensors located in muscles. In this paper, we designed and fabricated a novel twodegree of freedom variable stiffness indentation probe to investigate whether the regulation of internal stiffness, indentation, and probe sweeping velocity (PSV) variables affect the accuracy of the depth estimation of stiff inclusions in an artificial silicon phantom using information gain metrics. Our experimental results provide new insights into not only the biological phenomena of haptic perception but also new opportunities to design and control soft robotic probes.
Physical examination of soft objects to identify hidden mechanical features can be seen in a variety of areas like minimally invasive surgery, medical physical examination, security, quality assurance in food industry, entertainment, etc. Manual examination involves variation of both behavioral and internal impedance levels of the fingers [
The system interacts with the environment through its embodiment. The internal impedance required for accurate perception through its embodied sensor can differ from that required to take appropriate action. Likewise an action taken with appropriate impedance could affect the quality of perception of the environment.
Recently, we have explored the role of internal impedance control for maximizing the information gain in robotic embodied perception [
In order to address this question, we designed and fabricated a new soft robotic probe with a controllable stiffness Mckibben type joint. The setup for probing experiments on a soft silicon phantom to estimate the depth of an embedded nodule is described in the following section. Then the dynamic simulations were carried out to explore the individual and collective role of internal impedance, indentation level, and PSV in the measured torque response. In the experimental section, we discuss experimental results derived from 5625 probing trials, where we explain our main contributions—1) Evidence to show that the internal stiffness of the soft probe plays a statistically significant role in the accuracy of nodule’s depth estimation, 2) A Bayesian learning framework to combine internal stiffness, indentation level, and PSV that maximizes the information gain, and 3) Experimental results to show that proposed algorithm can achieve on average 99% and 96% accuracy in estimating the nodule’s depth in both active and passive perception respectively.
The overall design of the probe used in this experiment is depicted in
(a) Shaded view of twolink probe’s design. (b) Two springs located inside the spring chambers are attached with the anchor ring and the pivot joint through a microfilament thread. (Note that the springs shown here are for illustrative purpose only). The stiffness of the joint can be represented by the distance of
The probe’s indentation level,
Here, we used soft silicon phantoms with an embedded hard nodule as the samples for the haptic perception experiments. Silicon phantom is made from a soft clear silicon elastomer gel RTV27905 from Techsil. The given chemical substances (Part A and B) were mixed in 1:1 ratio according to specification to fabricate the silicon phantom. According to the studies in human biology, the typical tumor in soft tissue has roughly spherical shape [
The exploded view of the variable stiffness joint is shown in
Hence, the torque generated from both springs due to the change of joint’s angular displacement and the position of the anchor ring is:
From Eqs
Torque (a) and the stiffness (b) produced at the pivot joint due to the changes in the displacement of the anchor ring,
The resulting joint torque due to the changes of both parameters,
The description of variables used in the system depicted in
The probe consists of two rigid manipulator links with a variable stiffness joint. In the experiment,
System  Variables  Descriptions 

Torque measured at the end of base link  
Torque at the pivot joint  
Angular displacement of pivot joint  
Length of the Indentation control link  
Total length of Base link  
Total length of Tip link  
Distance to center of mass of tip link  
Mass of Indent control, Base, and Tip link  
Indentation  
Gravitational Constant [9.81 ms^{−2}]  
Damping coefficient of variable stiffness joint  
Joint’s variable stiffness rating  
Distance from XY table to phantom’s surface  
Phantom’s deformation in y and zdirection  
Translational force in probing direction  
Damping coefficient of silicon phantom  
Stiffness of silicon phantom  
Restoring force from phantom in ydirection  
Restoring force from phantom in zdirection 
The interaction dynamics of the system can be derived as follows:
In order to simplify the dynamic equations of the system, the restoring force of the silicon phantom on the probe during the interaction can be modeled using a linear springdamper system, where the stiffness of the silicon depending on different depth levels of a hard nodule embedded in the sample phantom can be represented by varying the system’s spring constant.
Assume that:
At rest (no contact between probe and sample phantom) the probe has length of
The base of the probe is fixed directly above the sample phantom at distance
The probe has stiffness
The soft silicon phantom has uncertain stiffness
The restoring force from the soft silicon phantom is in both y and zdirection.
The friction between the tip and soft phantom’s surface is negligible.
The deformation of soft silicon phantom has a uniform curvature [
When the probe comes in contact with the sample phantom, both the probe and the phantom deform according to their relative stiffness as shown in
We denote the depth of phantom sample deformation in y and zdirections by
In the design of the probe shown in
According to Eqs
The expected value of the stiffness of the phantom,
The models of tissue’s stiffness, in which the nodule is present, are given by
System  Variables  Value 

80, 70 [mm]  
40, 35 [mm]  
0.2, 0.3 [kg]  
0.02 [Ns/m]  
{3, 5, 7, 9, 11} [mm]  
{10, 20, 30} [mm/s]  
6.8 [mm]  
{0, 4, 8, 12, 16} [mm]  
0.24 [N/mm]  
290 [mm]  

{75, 85, 95, 105} [N/m]  

65 [N/m]  

13.2 [N/m]  
0.1[Ns/m] 
The sample of torque responses,
The simulated spherical hard nodule of size 15 mm diameter is presented at location between 100 mm to 115 mm. The simulated interaction conditions for each subfigure are as follows: (a) The average stiffness of soft silicon phantom is varied with the other parameters fixed at
From each torque response profile measured during palpation, we extracted the maximum torque at the location of simulated hard nodule as shown in ‘circle’ in
These simulation results predict that the torque felt at the base of the probe can be controlled using probe stiffness, indentation level and PSV during the interaction with a soft tissue. The relationship between the torque felt and the combinations of probe’s stiffness, indentation level, and PSV are nonlinear. Furthermore, in reality the variability present in the system is nondeterministic and may arise from several sources such as the probing behavior, environment, and the probe itself. These raise the question as to how we can exploit these nonlinear relationships to enhance the interpretation of the features in the environment using proprioceptive feedback from the torque sensor mounted at the base of the probe (representing how the tendon sensor is located in natural muscles). Since the relationship is stochastic and nonlinear, the best way to preserve the interaction information is to present the relationship in the form of a probabilistic distribution. It provides us the opportunity to implement an appropriate stochastic machine learning technique to understand the role of individual factor in the interpretation of haptic perception.
In the experiment, we use the controllable stiffness robotic probe described earlier to derive deeper insights into the influence of the variation of combinations of probe’s internal stiffness, indentation level, and PSV on the realtime estimation of the depth of a hard nodule embedded in soft silicon phantom. We explore whether a probe with controllable stiffness, indentation level, and PSV can exploit its past experience of palpation by varying its own internal stiffness, indentation level, and PSV to estimate the depth of embedded nodule inside a soft silicon phantom.
The palpation experiences during interaction with the soft silicon phantoms with a nodule embedded at different depths can be presented in the form of a probabilistic representation, which hereafter is referred to as ‘memory primitives’. The memory primitives were built from torque measurements,
The probe mounted under the XYtable was programmed to palpate in a straight line along the probing path over the soft silicon phantom’s exposed surface shown in
In order to construct the primitives for this experiment, we conducted palpation experiments across 5 probe stiffness levels,
Experimental variables  Sym.  Values  Units 

Probe’s stiffness (anchor position)  {0,4,8,12,16}  mm  
Relative distance between the tip of the probe at rest and the surface of phantom, i.e. inwards the phantom (indentation)  {3,5,7,9,11}  mm  
Probe’s velocity  {10,20,30}  mm/s  
Nodule’s depth  {2,4,8}  mm  
Distance between the XYplate and bottom of phantom  320  mm 
Each measured torque signal from the F/T transducer is denoised for 5 levels using wavelet decomposition technique with a Daubechie’s
The sample of memory primitives shown here consist of those when the PSV,
The nonlinear relationship between the measured torque probability distribution and different combinations of probe’s stiffness, indentation level, and PSV can be used in an appropriate machine learning algorithms to enhance the accuracy in nodule’s depth estimation. In this paper, interpretation of realtime torque measurements during palpation was done using memory primitives (conditional probability density functions) in a Bayesian Inferencing framework as given by
Each plot depicts the distribution of depth estimation from the initially defined flat distribution at
The overall accuracy across 10 assessment trials in nodule depth estimation after each iteration and those for different nodule depth levels are shown in
The resulting overall nodule’s depth estimation accuracy is shown in black line. The estimation accuracy for each actual depth,
Further statistical analysis was performed to investigate the significance of
The average accuracy in the estimation of nodule’s depth given different probe’s stiffness,
0  4  8  12  16  

96.7%  98.7%  98.7%  99.3%  98.7%  
90.7%  97.3%  93.3%  98.7%  98%  
95.3%  83.3%  92.7%  100%  98%  
94.2%  93.1%  94.9%  99.3%  98.2% 
3  5  7  9  11  

94.7%  100%  100%  99.3%  98%  
96%  94.7%  90%  98.7%  98.7%  
89.3%  96%  90%  98.7%  95.3%  
93.3%  96.9%  93.3%  98.9%  97.3% 
10  20  30  

97.6%  100%  97.6%  
96.4%  94.4%  96%  
88%  96%  97.6%  
94%  96.8%  97.1% 
Furthermore,
In general, the common influences of multiple coupled systems and factors can be quantified through the directed information exchanges by measuring the information transfer entropy, also known as relative entropy [
To be more specific, KLdivergence can be used to assess whether further information regarding the nodule’s depth estimation can be gained by taking another action (further iteration in Bayesian nodule’s depth estimation procedure). If we consider a set of
In addition to the Bayesian Inference method for estimating the depth of the nodule from the realtime captured torque data, here KLdivergence is implemented at the end of each Bayesian iteration to determine whether further measurement is required to accurately estimate the nodule’s depth. This additional process is carried out by computing the correlation distance,
With the implementation of KLdivergence in addition to the Bayesian Inference algorithm, the nodule’s depth estimation process requires on average of only 2.8 iterations with standard deviation of 1.2 iterations to converge. While the number of iterations required for convergence is kept to minimum; the nodule’s depth estimation accuracy still reaches within the comparable range to that with fixed 5iterations in the inferencing algorithm presented in Algorithm 1. On average the overall depth estimation accuracy is approximately 96.2% as shown in
1) 5iteration Bayesian inference without KLdivergence (shown in green), 2) the Bayesian Inference together with the KLTransfer Entropy with fixed probe’s stiffness, indentation level, and PSV (shown in orange), and 3) the Bayesian Inference together with the KLTransfer Entropy with random probe’s stiffness, indentation level, and PSV (shown in blue).
Therefore, we can conclude that Bayesian Inference together with KLdivergence provides a realtime framework to estimate the convergence to an optimal estimate of nodule depth in the sense of information gain.
So far, the experiments involved keeping
In order to address this, we repeated a similar estimation algorithm to that shown in Algorithm 2. However, instead of the static combination of probe’s stiffness, indentation level, and palpation velocity; these variables were allowed to randomly vary across iterations in the nodule’s depth estimation process. We repeated this process for 100 trials for each artificial soft silicon phantom with nodule embedded at
The nodule’s depth estimation result from the implementation of the Bayesian Inference with dynamic probing shown in Algorithm 3 are shown in blue bar in
A preliminary experiment was carried out with 1 human subject in the same probing task. In order to have comparative basis between human and robotic experiments, the subject was blindfolded and asked to palpate the same set of soft phantoms to estimate the depth of the embedded hard nodule. The muscle activity caused by the stiffness regulation of the finger was captured using electromyography (EMG) signal at Flexor digitorum superficialis (FDS) and Extensor digitorum communis (EDC) [
The FDS (a) and EDC (b) muscle activities were quantified by the EMG signal during manual palpation trial to estimate the depth of a hard nodule embedded inside a silicon phantom. The combination of the activities contributed from both muscles can be described as the cocontraction. The normalised cocontraction is shown in magenta curve in (c); whereas the red circles indicate the peaks extracted from this signal.
This paper investigated both individual and collective role of the probe’s internal stiffness, indentation level, and PSV in the accuracy in interpreting and estimating an environmental feature (depth of a nodule) by controlling a soft probe. The soft robotic probe comprised of a variable stiffness joint and an indentation level control mechanism. The probe structure was mounted under an XYstage allowing the planar movement. Firstly, we simulated the dynamics of palpation using the designed probe on a simulated soft silicon phantom to observe the interaction between them under different combinations of probe’s internal stiffness, indentation level, and PSV.
The results from the simulation suggest that 1) the torque felt at the base of the probe can be controlled using different combinations of probe’s stiffness, indentation level, and probing speed and 2) the relationships between the torque measured, the stiffness of the soft silicon phantom, and the combination of probe’s internal stiffness, indentation level, and PSV are nonlinear. While a variability in the simulated system from the Gaussian distribution of the phantom’s stiffness is predefined; the variability in such a system in reality is nondeterministic and can arise from multiple sources. These brought into a question as to how we can use these nonlinear relationships in the experiment to enhance the estimation of the environmental features.
In the experiment, we investigated the question as to how the probe with controllable stiffness, indentation level, and PSV can exploit its past experience of palpation to estimate the depth of a nodule embedded inside a soft tissue in real time. The nonlinear relationship between the probe’s measured torque, its internal variables, and the environment (depth of nodule in silicon phantom) were presented in the form of a probabilistic distribution given different combinations of probe’s internal stiffness, indentation level, and PSV. In this paper, we referred to these conditional probability distributions as ‘memory primitives’. These ‘memory primitives’ functioned as likelihood functions in a Bayesian framework to estimate the depth of a nodule in the soft tissue phantom. The memory primitives were constructed from three levels of PSV, five levels of indentation, and five levels of joint stiffness, for three nodule’s depth levels. In total 5625 probing trials were performed using this automated experimental setup.
In conclusion, the implementation of Bayesian Inference allows the algorithm to accurately estimate the depth of a nodule from the measured torque realtime. Furthermore, KLdivergence was introduced to determine whether further iteration of measurement is required to make an accurate estimation by comparing the information gained in the current iteration to that of the previous iteration. It was shown that on average the estimation processes using Algorithm 2 and 3 require approximately 3 iterations to converge in order to obtain comparable and better (in the latter) estimation accuracy. Finally, allowing the combination of probe’s internal stiffness, indentation level, and PSV to randomly vary across iterations (allowing exploration in multiple memory primitives in each nodule’s depth estimation process), resulted in a convergence to the global optimum with a minimum number of iterations. We showed that, this could enhance the average depth estimation accuracy to almost 100% with higher repeatability (smaller standard deviation).
The insights from this study sheds light on the practice of manual and robotic assisted palpation of soft tissue to locate T1 stage tumors in biological tissues [
This paper has provided important explanations about the role of morphological computation in haptic based probing of a soft object, as well as providing guidelines to design and control variable stiffness probes for physical examination. Certainly, the operational implementation of this probe should be further developed depending on different applications. However, the fact that controllable internal stiffness helps to gain proprioception information is still valid in such a tool. However, additional complexities arising from factors such as variable friction and irregular surface conditions not addressed in this paper should be further examined. Future studies will also involve temporal control of probe stiffness, indentation, and speed to better understand diverse probing strategies used by different classes of human participants as seen in [