State estimation for a hybrid rigid-continuum space manipulator system

Lorenzo Ticozzi; Patricio A. Vela; Panagiotis Tsiotras

cs.ROOct 27, 2026

State estimation for a hybrid rigid-continuum space manipulator system

Authors: Lorenzo Ticozzi, Patricio A. Vela, Panagiotis Tsiotras

Organizations: School of Aerospace Engineering, Georgia Institute of Technology · School of Electrical and Computer Engineering, Georgia Institute of Technology

Abstract

Spacecraft-mounted robotic manipulators can support long-term operability of orbiting assets by conducting tasks such as on-orbit assembly, repair, upgrade, and refueling. In this context, the integration of continuum/soft robotic mechanisms into space manipulator designs promises to reduce stowage volume and mass, as well as to improve operational safety through the inherent mechanical compliance of soft structures. This work presents a novel state reconstruction pipeline for a hybrid soft-rigid space manipulator, in which the distal link is a tendon-driven continuum robot. The estimation problem is formulated as a maximum a posteriori (MAP) inference problem over the hybrid manipulator's configuration, conditioned on discrete, noisy measurements from joint encoders and a vision-based sensing pipeline. The resulting soft-constrained optimization problem is transcribed as a factor graph, providing a compact representation for fusing heterogeneous measurements with the rigid-soft kinematic model. Furthermore, the adoption of the Geometric Variable Strain (GVS) approach yields a minimum-order parameterization of the configuration, a property expected to facilitate model-based feedback control design in future work. The proposed implementation is validated in simulation on a closed-loop trajectory where, for better realism, position measurements for the continuum link are obtained by means of a simulated visual pipeline leveraging synthetic photorealistic images. The state reconstruction accuracy and computational performance confirm the potential of the proposed framework for hybrid soft-rigid robotic applications in orbit.

Figures & tables

Figure 1: Diagram of a hybrid space manipulator system. The hybrid soft-rigid manipulator is attached to the satellite bus and features two rigid links, actuated by revolute joints, and a tendon-driven continuum link. Frame $\mathcal{I}$ can be interpreted, for instance, as the Hill frame centered on a client satellite.

Figure 2: Factor graph example. Variable nodes are represented as circles, while factor nodes are represented as squares.

Figure 3: Hybrid space manipulator factor graph. Variables are represented by circles (yellow for poses, green for scalars and vectors); factor nodes are represented by squares.

Figure 4: Upper face of the HSMS base with the left and right camera frames, denoted by $\mathcal{C}_{L}$ and $\mathcal{C}_{R}$ , respectively. The camera elevation angle and stereo baseline are denoted by $\alpha$ and $b$ , respectively, with $\alpha=41.6^{\circ}$ and $b=0.4$ m.

Panel of Figure 5 — Figure 5: HSMS configuration along the $60$ -s simulated maneuver, with the end-effector trajectory displayed in white.

Figure 6: Blender render of the left-camera view. The continuum link carries five colored bands at equally-spaced arclength coordinates, which are detected in both views and triangulated to obtain the position measurements $\tilde{\bm{p}}_{i}^{\mathcal{C}_{L}}$ in Eq. ( 25 ).

Figure 7: Color-based stereo matching across the left and right images.

Covariance	Value
$\bm{\Sigma}_{\mathcal{B}}$	$3\cdot\mathrm{blkdiag}(\sigma^{2}_{\mathcal{B},\mathrm{rot}}\bm{I}_{3},\,\sigma^{2}_{\mathcal{B},\mathrm{pos}}\bm{I}_{3})$
$\bm{\Sigma}_{p}$	$9\cdot 10^{6}\bm{I}_{8}$
$\bm{\Sigma}_{\mathcal{J}}^{R}$	$1\cdot 10^{-8}\bm{I}_{6}$
$\Sigma_{q}$	$3\cdot\sigma_{q}^{2}$
$\bm{\Sigma}_{\mathrm{off}}$	$1\cdot 10^{-8}\bm{I}_{6}$
$\bm{\Sigma}_{M}$	$1\cdot 10^{-10}\bm{I}_{6}$

Table 1: Covariance values for the HSMS factors.

	Position [mm]						Orientation [deg]
Frame	mean	% $d$	max	emp	pred	ratio	mean	max	emp	pred	ratio
$\mathcal{B}$	16.13	0.41%	41.39	17.49	30.00	0.583	1.60	4.92	1.73	3.01	0.577
$\mathcal{R}_{1}$	37.03	0.95%	133.48	41.14	70.95	0.580	1.60	4.92	1.73	3.01	0.576
$\mathcal{R}_{2}$	66.52	1.70%	261.70	74.43	128.62	0.579	1.60	4.92	1.73	3.01	0.577
$\mathcal{F}$	80.39	2.06%	307.83	90.22	156.13	0.578	1.60	4.92	1.73	3.01	0.577
$\mathcal{M}$	87.04	2.23%	323.17	97.66	169.20	0.577	1.76	6.13	1.92	3.64	0.527

Table 2: Error statistics of the estimated frame poses with respect to ground truth, expressed in the world frame. The columns mean and max report the trajectory mean and maximum of the error magnitude

\|\bm{e}(t_{k})\|

, with the mean position error additionally expressed as a percentage of the characteristic length of the system,

d=3.905

m, taken as the Cartesian distance between the base frame

\mathcal{B}

and the tip frame

\mathcal{E}

in the home configuration. The columns emp and pred report the empirical and estimator-predicted standard deviations, RMS-combined across axes as

\sqrt{\mathrm{tr}\,\bm{\Sigma}}

; ratio is their quotient.

Panel of Figure 8 — Figure 8: Ground-truth versus estimated pose of frames $\mathcal{F}$ , $\mathcal{M}$ , and $\mathcal{E}$ w.r.t. the global frame $\mathcal{I}$ , with estimator-predicted $\pm 3\sigma$ intervals.

Figure 9: Ground-truth versus estimated pose of the end-effector frame $\mathcal{E}$ w.r.t. the base frame $\mathcal{B}$ .

Timesteps	1,801
Avg solve time	1.230 ms/timestep
Avg LM iterations	7.271
Max solve time	4.462 ms
Max LM iterations	24
Total solve time	2.216 s

Table 3: Computational performance data.

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Reconstructing the shape of continuum manipulators from sparse, noisy sensor data is a challenging task, owing to the infinite-dimensional nature of such systems. Existing approaches broadly trade off between parametric methods that yield compact state representations but lack probabilistic structure, and Cosserat rod inference on factor graphs, which provides principled uncertainty quantification at the cost of a state dimension that grows with the spatial discretization. This letter combines the strengths of both these approaches by estimating the coefficients of a compact Geometric Variable Strain (GVS) parameterization within a factor graph framework. A novel kinematic factor, derived from the Magnus expansion of the strain field, encodes the closed-form rod geometry as a prior constraint linking the GVS strain coefficients to the backbone pose variables. The resulting formulation yields a compact state vector, is directly amenable to model-based control, and it retains the modularity, probabilistic treatment, and computational efficiency of factor graph inference. The proposed method is evaluated on both simulated and experimental data and compared against a Gaussian Process (GP) regression baseline, demonstrating increased accuracy in partial and sparse measurement scenarios while preserving computational efficiency.

Lorenzo Ticozzi, Sabyasachi Dash, Yangkun Liu +2

School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA, USA · School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA, USA

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Precise control of soft manipulators remains challenging due to the difficulty of developing accurate yet computationally tractable models for model-based estimation and control. Reduced Cosserat-rod models provide a physics-based and control-oriented description of soft-robot dynamics, offering an explicit alternative to purely data-driven input-output representations. In this paper, we propose a moving-horizon estimation (MHE) and nonlinear model predictive control (NMPC) framework for cable-driven soft manipulators based on reduced Cosserat dynamics. A smooth cable-length-driven modeling formulation is developed by approximating the complementarity relationship between cable tension and cable slackness, enabling cable-length control without direct tension sensing. Based on this formulation, an MHE method is introduced to estimate the reduced state and reconstruct the manipulator configuration from end-effector pose measurements and cable-length information. An NMPC controller is then formulated to achieve task-space control under cable-length and cable-rate constraints. The proposed framework is validated through numerical simulations and experiments. Simulation results demonstrate the effectiveness of the estimator and controller for pose and strain-related regulation on a multi-cable soft manipulator. Experimental results on a four-cable prototype further show that the proposed MHE-NMPC scheme can be implemented in real time and enables accurate end-effector position tracking through cable-length control.

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