Predicting tip positions of a spring based continuum manipulator is highly challenging due to its nonlinear deformations. External loading on the tip further deteriorates the accuracy. Model-less control has shown great success in the tip positioning. However, the model less control strategies require a large data set and considerable amount of time for the training. Performance of these controllers also deteriorates with external loads. To address these problems, this paper presents a MAML(Model-Agnostic Meta-Learning) based closed loop controller for the continuum manipulators. This controller requires relatively small amount of data to achieve the state-of-art positioning accuracy. It can also adapt to the changes due to the external loads with less than 2.5 percent of the original data. Two algorithms for the offline adaptation of the known and unknown external loading are proposed. This technique is also helpful for automatic stiffness tuning of the spring based continuum manipulators. The experimental validations have been done on the simulation environment and on the real prototype. The continuum arm used for the experimentation is a tendon based non constant curvature spring-based manipulator. The average relative positioning error for the zero loading case was found to be 3.83% on the spring based prototype . The controller was successful in bringing down the relative tip positioning error of the manipulator from 5.42% to 2.7% in the simulation environment. It also showed success in bringing down the relative tip positioning error from 7.8% to 3.96% on the real prototype. Average relative tip positioning errors below 4.27% and 4.89% have been achieved in the trajectory following tasks for the known and unknown external loading cases respectively.

Non linear deformation of spring based continuum manipulators cause difficulty in predicting the position of the tip. When we put different tools on the tip for various purposes, the difficulty further increases. Model less control of the manipulator has shown great success in tip positioning of these types of manipulators. One of the major drawbacks of model less control is the requirement of a large data set and time. Hence, this paper studies the effect of the implementation of MAML(Model-Agnostic Meta-Learning) for fast adaptation of different offset conditions. The effects have been studied in the simulation environment and on the real prototype. The continuum arm used for the experimentation is a tendon based non constant curvature spring based manipulator. An average error of 0.03m has been achieved on the prototype. MAML was successful in bringing down the relative tip positioning error of the manipulator from 7.02\% to 1.55\% in the simulation environment. It also showed success in bringing down the relative tip positioning error from 11.06\% to 4.09\% on real prototype. We also studied the effectiveness of the same in trajectory following.

Purpose The purpose of this paper is to develop a tendon actuated variable stiffness double spring based continuously tapered multi-section flexible robot and study its capability to achieve the desired bending and compression for inspection in cluttered environments. Design/methodology/approach Spring-based continuum manipulators get compressed while actuated for bending. This property can be used for the advantage in cluttered environments if one is able to control both bending and compression. Here, this paper uses a mechanics based model to achieve the desired bending and compression. Moreover, this study tries to incorporate the tapered design to help in independent actuation of the distal sections with minimal effects on proximal sections. This study is also trying to incorporate the double spring based design to minimize the number of spacers in the robot body. Findings The model was able to produce desired curvature at the tip section with less than 4.62% error. The positioning error of the manipulator is nearly 3.5% which is at par with the state-of-the-art manipulators for search and rescue operations. It was also found that the use of double spring can effectively reduce the number of spacers required. It can be helpful in smooth robot to outer world interaction without any kink. From the experiments, it has been found that the error of the kinematic model decreases as one moves from high radius of curvature to low radius of curvature. Error is maximum when the radius of curvature is infinity. Practical implications The proposed manipulator can be used for search operations in cluttered environments such as collapsed buildings and maintenance of heavy machineries in industries. Originality/value The novelty of this paper lies in the design and the proposed kinematics inverse kinematics for a spring-based continuously tapered multi-section manipulator.