Recently, continuum flexible robots have been designed for the use in diverse applications; including the exploration of confined static and dynamic environments. One of the challenging tasks for those robots is planning optimal trajectories due to, not only the redundant Degrees of Freedom (DOF) they own but also their compliant behaviour. In this paper, an Imitation-based Pose Planning (IbPP) approach is proposed to teach a two-section continuum robot the motion primitives that will facilitate achieving and generalizing for spatial point-to-point motion which involves both position and orientation goals encoded in a dual quaternion form. Two novel approaches are proposed in this research to intuitively generate the motion demonstrations that will be used in the proposed IbPP. Namely, a flexible input interface, acting as a twin robot, is designed to allow a human to demonstrate different motions for the robot end-effector. Alternatively, as a second approach, the Microsoft Kinect sensor is used to provide motion demonstrations faster via human arm movements. Based on the kinematic model of the two-section continuum robot, a Model Reference Adaptive Control (MRAC) algorithm is developed to achieve tracking the generated trajectory from the IbPP and to guarantee the robustness against the model uncertainties and external disturbances. Moreover, controller stability analysis is developed based on Lyapunov criteria. Finally, simulations are conducted for the two-section continuum robot to prove the ability of the proposed IbPP with the two proposed inputs to learn and generalize for spatial motions, which in future could be easily accommodated for robots with multiple sections. In addition, the proposed MRAC shows a significant performance towards following the required trajectory and rejecting the external disturbance.

Recently, there has been an increased interest in the deployment of continuum robots in unstructured and challenging environments. However, the application of the state-of-the-art motion planning strategies, that have been developed for rigid robots, could be challenging in continuum robots. This, in fact, is due to the compliance that continuum robots possess besides their increased number of degrees of freedom. In this paper, a Demonstration Guided Pose Planning (DGPP) technique is proposed to learn and subsequently plan for spatial point-to-point motions for multi-section continuum robots. Motion demonstrations, including position and orientation, are collected from a human via a flexible input interface that is developed to command the continuum robot intuitively via teleoperation. A dynamic model based on Euler-Lagrange formalism is derived for a two-section continuum robot to be considered while planning for the robot motions. Meanwhile, a Proportional-Derivative (PD) computed torque controller with a Model Reference Adaptive Kinematic Control (MRAKC) scheme are developed to ensure the tracking performance against system uncertainties and disturbances. Also, the system stability analysis based on Lyapunov quadratic equation is proven. Simulation results prove that the proposed DGPP approach, along with the developed control scheme, have the ability to learn, generalize and reproduce spatial motions for a two-section continuum robot while avoiding both static and dynamic obstacles that could exist in the environments.

Continuum robots have been recently used in the inspection of tight and confined spaces. State-of-the-art motion planning algorithms that are developed for rigid robots could be inadequate when applied to redundant and complainant continuum robots. In this research, a Demonstration-Guided Motion Planning (DGMP) framework is proposed to let continuum robots imitate a set of given demonstrations to plan and execute point-to-point spatial motions. A flexible interface is incorporated to allow humans to intuitively demonstrate motions for the robot via teleoperation. The Dynamic Movement Primitives (DMP) framework is adopted to learn, reproduce and generalize the given demonstrations while avoiding static or moving obstacles existing in the environment. Meanwhile, a Model Reference Adaptive Controller (MRAC) is proposed to ensure the robot robustness against perturbation while tracking the generated motions from the DGMP. The developed approach is evaluated over a simulated model of a two-section continuum robot. The obtained results show evidence that the proposed DGMP is effective in generating and tracking spatial motions for continuum robots. This could encourage a further investigation towards planning complex motions in the future for redundant continuum robots.