3-D shape control of deformable linear objects for branch handling using an adaptive Lyapunov-based scheme

Despite its various applications, robotic manipulation of deformable objects in agriculture has experienced limited development so far. This is due to the specific challenges in this domain, i.e., the variety of objects in this field is wide, and the deformation properties of the objects cannot be easily recognized in advance. In addition, deformable objects generally have complex dynamics and high-dimensional configuration space. In this paper, the manipulation of deformable linear objects (DLOs) is addressed by considering these challenges. Concretely, anew indirect adaptive control method is proposed to manipulate DLOs by controlling their shape in 3-D space towards previously defined targets, with a specific focus on agricultural applications. The proposed method can follow a desired dynamic evolution of the shape with a smooth deformation that brings about a stable gripper motion. This property of the method can protect the object from possible damages, even under large deformations, which is crucial in agricultural scenarios. An adaptation law is leveraged for estimating the system parameters, and Lyapunov analysis is employed to study the validity of the proposed control scheme. The scheme can be applied to diverse objects that can be modeled as linear, including tree branches or other rod-like structures. The effectiveness of the scheme is demonstrated through various experiments where, using shape feedback obtained from a 3-D camera, a robotic arm controls the shape of a flexible foam rod and of branches of different plants.