Kinematic Modeling and Control of a Soft Robotic Arm with Non-constant Curvature Deformation

The passive compliance of soft robotic arms renders the development of accurate kinematic models and model-based controllers challenging. The most widely used model in soft robotic kinematics assumes Piecewise Constant Curvature (PCC). However, PCC introduces errors when the robot is subject to external forces or even gravity. In this paper, we establish a three-dimensional (3D) kinematic representation of a soft robotic arm with pseudo universal and prismatic joints that are capable of capturing non-constant curvature deformations of the soft segments. We theoretically demonstrate that this constitutes a more general methodology than PCC. Simulations and experiments on the real robot attest to the superior modeling accuracy of our approach in 3D motions with unknown loads. The maximum position/rotation error of the proposed model is verified 6.7×/4.6× lower than the PCC model considering gravity and external forces. Furthermore, we devise an inverse kinematic controller that is capable of positioning the tip, tracking trajectories, as well as performing interactive tasks in the 3D space.