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Page 16 of 19 Peng et al. Soft Sci. 2025, 5, 38 https://dx.doi.org/10.20517/ss.2025.31

As shown in Figure 10A, the continuum robot can automatically measure the weight of objects. By solving
the forward kinematics of the proposed model, the loaded shapes can be estimated according to the tensions
and weight at the tip. As shown in Figure 10B and C, the continuum robot can achieve accurate position
tracking results for a “circle” trajectory with a 10 g weight and for a “square” trajectory with a 20 g weight.
More details can be found in Supplementary Videos 3-5. Although the robot can accurately measure loads
within 100 g, the maximum load for precise trajectory motion should be limited to below 20 g due to
constraints in SMA driving force and structural rigidity; it can measure dynamic load weights, but load
variations cause changes in the end-effector operational space and SMA driving force, therefore subsequent
research will establish a relationship model between the load, operational space, and driving force to lay the
foundation for precise trajectory control under dynamic loads.

As shown in Figure 11A, the continuum robot can grasp a ball using a suction unit actuated by the pump
(connected with the tube), handle it while passing through a confined space, and drop it at the target
position. As shown in Figure 11B, two robots can handle an object based on collaborative operation for
complex task. More details can be found in Supplementary Videos 6 and 7. However, some disadvantages
need to be mentioned. First, the workspace of the continuum robot is limited due to the use of one single
segment design, and our future work will develop a multi-segment robot for a larger workspace and
complex tasks. Second, compared with motors and pumps, SMA actuators have the advantages of a high
power-to-weight ratio, small size and silence but suffer from slow response speed. Ongoing work will aim to
improve the actuation frequency by using SMA springs with thin diameters.

CONCLUSIONS
In this paper, we propose a method to simultaneously sense and control the 3D deformation of a continuum
robot actuated by three SMA springs. Compared with shape sensing methods using strain, vision, EMF and
FBG sensors based on CC assumptions, the proposed method can more accurately predict the bending
shape of a continuum robot even under an unknown external load. Furthermore, relative to robots actuated
by motors and pumps, the presented continuum robot possesses a simple and light structure and achieves
excellent compliance and elasticity through the use of two different types of SMA. SMA usually can achieve
a fatigue life of 10 cycles at strain levels below 4% without overload. However, high-frequency loading
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(> 1 Hz) may lead to temperature rise due to thermal hysteresis effects, accelerating fatigue damage,
reducing the maximum output force, displacement and response speed. The slow response speed of the
SMA actuator incurs limitations in practical applications. For example, SMA actuation mechanisms struggle
to meet real-time control requirements in fast interactive scenarios (such as dynamic grasping or obstacle
avoidance responses). A closed-loop controller based on the proposed model is presented, incorporating the
RBF algorithm to achieve fast and accurate tracking control.

To address the challenge of precise control over deformation in continuum robots caused by end-effector
loads, this system enables accurate perception and control of body deformation by measuring end-load
weight and applying Cosserat rod theory. This method provides reliable technical support for applications
such as foreign object retrieval within slender curved pipelines, narrow-space inspection in radiation-prone
nuclear power equipment (where SMA exhibits high radiation resistance), and deep-cavity surgeries in the
human body (e.g., tumor removal).