Observability-Informed Optimal Sensor Placement for Soft Robots

Samuel Smocot; James Richard Forbes; Audrey Sedal

cs.ROSep 27, 2026

Observability-Informed Optimal Sensor Placement for Soft Robots

Authors: Samuel Smocot, James Richard Forbes, Audrey Sedal

Organizations: Dept. of Mechanical Engineering, McGill University, Montreal, Canada. · Mila – Québec AI Institute, Montreal, Canada.

Abstract

This paper presents the application and experimental evaluation of a systematic method for optimal sensor placement in soft robots. Existing methods either lack generalizability across different soft robot morphologies or do not account for system dynamics. The applied method uses convex optimization to find the optimal sensor configuration that maximizes an observability Gramian-based metric. The framework is experimentally evaluated using position and strain measurements on a soft continuum arm. Kalman filter state estimates using optimal sensor placements yield lower reconstruction error than a baseline across all sinusoidal input trials, with improvements on the order of millimeters. This case study shows that linear control theory tools can guide optimal sensor placement in soft robots, suggesting an interpretable approach to sensor placement that may extend to other morphologies.

Figures & tables

DOI:	10.1109/RoboSoft67810.2026.11522828
IEEE Xplore:	https://ieeexplore.ieee.org/document/11522828

Table 1

Fig. 1: Overview of the sensor placement framework: starting from candidate sensor locations, the method selects an optimal configuration to maximize observability. The shape reconstruction comparison illustrates the quality of the selected placement.

Fig. 2: Marker and centroid positions on the soft robot captured by the mocap system. Left: 3D positions of markers placed along the three chambers and their computed centroids. Right: 2D projection of the centroids onto a plane-of-best-fit, enabling planar modelling of the continuum arm.

$\mathcal{J}(\mbf{W}_{\mathrm{o}})$	$p=1$	$p=2$	$p=3$
$\lambda_{\min}(\mbf{W}_{\mathrm{o}})$	N.A.	N.A.	N.A.
${\mathrm{tr}}(\mbf{W}_{\mathrm{o}})$	$\{7\}$	$\{6,7\}$	$\{5,6,7\}$
$\log(\det(\mbf{W}_{\mathrm{o}}))$	$\{7\}$	$\{4,7\}$	$\{4,6,7\}$
Baseline	$\{4\}$	$\{4,7\}$	$\{3,5,7\}$

TABLE I: Placement for

p

position sensors and different

\mathcal{J}(\mbf{W}_{\mathrm{o}})

$\mathcal{J}(\mbf{W}_{\mathrm{o}})$	Step Input			Sinusoidal Input
$\mathcal{J}(\mbf{W}_{\mathrm{o}})$	$p=1$	$p=2$	$p=3$	$p=1$	$p=2$	$p=3$
${\mathrm{tr}}(\mbf{W}_{\mathrm{o}})$	1.82 ∗∗∗ (1.00, 3.27)	1.05 ∗ (0.69, 1.97)	0.62 ∗∗∗ (0.20, 1.17)	1.34 ∗∗∗ (0.86, 2.08)	0.81 ∗∗ (0.57, 1.09)	0.52 (0.32, 0.65)
$\log(\det(\mbf{W}_{\mathrm{o}}))$	1.82 ∗∗∗ (1.00, 3.27)	0.97 (0.66, 1.55)	0.59 ∗∗∗ (0.51, 1.04)	1.34 ∗∗∗ (0.86, 2.08)	0.59 (0.39, 1.11)	0.4 (0.29, 0.59)
Baseline	3.45 (1.23, 6.83)	0.97 (0.66, 1.55)	0.53 (0.14, 0.96)	3.01 (2.04, 3.69)	0.59 (0.39, 1.11)	0.44 (0.27, 0.75)

TABLE II: Total trajectory RMSE for position sensor placements from Table I , grouped by actuation input type

Fig. 3: Time evolution of RMSE for representative trials from Section IV-A . Top:

p=1

, step input

p_{\text{set}}=

90\text{\,}\mathrm{kPa}

. Bottom:

p=3

, sinusoidal input

p_{\text{set}}=40(\sin(3t)+1)

\text{\,}\mathrm{kPa}

\mathcal{J}(\mbf{W}_{\mathrm{o}})~=~\log(\det(\mbf{W}_{\mathrm{o}}))

Fig. 4: Total trajectory RMSE for different actuation amplitudes

A

[

\text{\,}\mathrm{kPa}

] and frequencies

\omega

[

\text{\,}\mathrm{rad}\text{/}\mathrm{s}

] in

p_{\text{set}}=A(\sin(\omega t)+1)

. Box plots show RMSE distributions across all sinusoidal trials. Left column:

p=3

position measurements with

\log(\det(\mbf{W}_{\mathrm{o}}))

placement vs. baseline. Middle column:

p=3

strain measurements with

{\mathrm{tr}}(\mbf{W}_{\mathrm{o}})

placement vs. baseline. Right column:

p_{1}=1

and

p_{2}=3

combined measurements with

{\mathrm{tr}}(\mbf{W}_{\mathrm{o}})

placement vs. baseline.

$\mathcal{J}(\mbf{W}_{\mathrm{o}})$	$p=1$	$p=2$	$p=3$
$\lambda_{\min}(\mbf{W}_{\mathrm{o}})$	$\{1\}$	$\{1,7\}$	$\{1,7,8\}$
${\mathrm{tr}}(\mbf{W}_{\mathrm{o}})$	$\{1\}$	$\{1,2\}$	$\{1,2,3\}$
$\log(\det(\mbf{W}_{\mathrm{o}}))$	$\{1\}$	$\{1,2\}$	$\{1,2,7\}$
Baseline	$\{7\}$	$\{1,7\}$	$\{1,5,9\}$

TABLE III: Sensor placement for

p

strain sensors and different

\mathcal{J}(\mbf{W}_{\mathrm{o}})

$\mathcal{J}(\mbf{W}_{\mathrm{o}})$	Step Input			Sinusoidal Input
$\mathcal{J}(\mbf{W}_{\mathrm{o}})$	$p=1$	$p=2$	$p=3$	$p=1$	$p=2$	$p=3$
$\lambda_{\min}(\mbf{W}_{\mathrm{o}})$	11.46 ∗∗∗ (5.24, 20.98)	11.55 (5.28, 21.15)	12.12 ∗∗∗ (5.54, 22.20)	8.82 ∗∗∗ (5.50, 12.15)	8.88 (5.52, 12.23)	9.31 ∗∗∗ (5.78, 12.83)
${\mathrm{tr}}(\mbf{W}_{\mathrm{o}})$	11.46 ∗∗∗ (5.24, 20.98)	10.14 ∗∗∗ (4.63, 18.56)	8.88 ∗∗∗ (4.06, 16.26)	8.82 ∗∗∗ (5.50, 12.15)	7.80 ∗∗∗ (4.86, 10.74)	6.83 ∗∗∗ (4.25, 9.41)
$\log(\det(\mbf{W}_{\mathrm{o}}))$	11.46 ∗∗∗ (5.24, 20.98)	10.14 ∗∗∗ (4.63, 18.56)	10.26 ∗∗∗ (4.68, 18.78)	8.82 ∗∗∗ (5.50, 12.15)	7.80 ∗∗∗ (4.86, 10.74)	7.88 ∗∗∗ (4.9, 10.86)
Baseline	17.65 (14.17, 34.78)	11.55 (5.28, 21.15)	10.21 (4.66, 18.69)	15.75 (13.18, 19.13)	8.88 (5.52, 12.23)	7.84 (4.87, 10.81)

TABLE IV: Total trajectory RMSE for strain sensor placements from Table III , grouped by actuation input type

$\mathcal{J}(\mbf{W}_{\mathrm{o}})$	$p_{1}=1$	$p_{2}=3$
$\lambda_{\min}(\mbf{W}_{\mathrm{o}})$	N.A.	$\{1,7,8\}$
${\mathrm{tr}}(\mbf{W}_{\mathrm{o}})$	$\{5\}$	$\{1,2,3\}$
$\log(\det(\mbf{W}_{\mathrm{o}}))$	$\{5\}$	$\{1,2,7\}$
Baseline	$\{4\}$	$\{1,5,9\}$

TABLE V: Resulting placement for

p_{1}

position sensors and

p_{2}

strain sensors, using different

\mathcal{J}(\mbf{W}_{\mathrm{o}})

$\mathcal{J}(\mbf{W}_{\mathrm{o}})$	Step Input	Sinusoidal Input
${\mathrm{tr}}(\mbf{W}_{\mathrm{o}})$	6.81 ∗∗∗ (3.55, 12.47)	5.16 ∗∗∗ (3.25, 7.19)
$\log(\det(\mbf{W}_{\mathrm{o}}))$	7.49 ∗∗∗ (3.94, 13.72)	5.67 ∗∗∗ (3.56, 7.9)
Baseline	8.7 (3.84, 16.06)	6.78 (4.21, 9.18)

TABLE VI: Total trajectory RMSE for combined sensor placement from Table V , grouped by actuation input type.

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