This article presents a modeling methodology and experimental validation for soft manipulators to obtain forward kinematic model (FKM) and inverse kinematic model (IKM) under quasi-static conditions (in the literature, these manipulators are usually classified as continuum robots. However, their main characteristic of interest in this article is that they create motion by deformation, as opposed to the classical use of articulations). It offers a way to obtain the kinematic characteristics of this type of soft robots that is suitable for offline path planning and position control. The modeling methodology presented relies on continuum mechanics, which does not provide analytic solutions in the general case. Our approach proposes a real-time numerical integration strategy based on finite element method with a numerical optimization based on Lagrange multipliers to obtain FKM and IKM. To reduce the dimension of the problem, at each step, a projection of the model to the constraint space (gathering actuators, sensors, and end-effector) is performed to obtain the smallest number possible of mathematical equations to be solved. This methodology is applied to obtain the kinematics of two different manipulators with complex structural geometry. An experimental comparison is also performed in one of the robots, between two other geometric approaches and the approach that is showcased in this article. A closed-loop controller based on a state estimator is proposed. The controller is experimentally validated and its robustness is evaluated using Lypunov stability method.
Research on continuum manipulators is increasingly developing in the context of bionic robotics because of their many advantages over conventional rigid manipulators. Due to their soft structure, they have inherent flexibility, which makes it a huge challenge to control them with high performances. Before elaborating a control strategy of such robots, it is essential to reconstruct first the behavior of the robot through development of an approximate behavioral model. This can be kinematic or dynamic depending on the conditions of operation of the robot itself. Kinematically, two types of modeling methods exist to describe the robot behavior; quantitative methods describe a model-based method, and qualitative methods describe a learning-based method. In kinematic modeling of continuum manipulator, the assumption of constant curvature is often considered to simplify the model formulation. In this work, a quantitative modeling method is proposed, based on the Pythagorean hodograph (PH) curves. The aim is to obtain a three-dimensional reconstruction of the shape of the continuum manipulator with variable curvature, allowing the calculation of its inverse kinematic model (IKM). It is noticed that the performances of the PH-based kinematic modeling of continuum manipulators are considerable regarding position accuracy, shape reconstruction, and time/cost of the model calculation, than other kinematic modeling methods, for two cases: free load manipulation and variable load manipulation. This modeling method is applied to the compact bionic handling assistant (CBHA) manipulator for validation. The results are compared with other IKMs developed in case of CBHA manipulator.
International audience—This paper deals with a methodology for a real-time solving of a complex kinematics of a class of continuum manipu-lators, namely the Compact Bionic Handling Assistant (CBHA). First, a quantitative approach is used to model kinematically the CBHA inspired from the modeling of parallel rigid manipulators. For this case, the CBHA is modeled as a series of vertebrae, where each vertebra is connected to the next one through a flexible link. The latter named an inter-vertebra is modeled by a 3UPS-1UP (Universal-Prismatic-Spherical) joints. The kinematic models of the CBHA are derived from the Inverse Kinematic Equations (IKE) of each inter-vertebra. A qualitative approach based on neural networks is used to provide approximated solutions of the IKE for real-time implementation. Thus, the combination of the advantages of quantitative and qualitative approaches allows proposing a hybrid methodology for accurate modeling and solving the kinematics of this class of continuum robots. A set of experiments are conducted using a CBHA in order evaluate the level of efficiency of the proposed hybrid approach
International audience—This paper deals with the forward kinematic calibration of a bionic arm inspired from the organic elephant trunk and called compact bionic handling assistant (CBHA). First, a forward kinematic model is developed based on the principle of the constant curvature continuum robot theory. Then, two experimental setups are proposed in order to carry out the model calibration and validation. The first one is based on the trilateration method, while the second one is based on the coupling of the CBHA with a rigid six-degree-of-freedom rigid manipulator. The aim of the calibration is to enhance the precision of the forward kinematic model
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