skip to main content


The NSF Public Access Repository (NSF-PAR) system and access will be unavailable from 10:00 PM ET on Friday, December 8 until 2:00 AM ET on Saturday, December 9 due to maintenance. We apologize for the inconvenience.

Title: On the Mathematical Modeling of Slender Biomedical Continuum Robots
The passive, mechanical adaptation of slender, deformable robots to their environment, whether the robot be made of hard materials or soft ones, makes them desirable as tools for medical procedures. Their reduced physical compliance can provide a form of embodied intelligence that allows the natural dynamics of interaction between the robot and its environment to guide the evolution of the combined robot-environment system. To design these systems, the problems of analysis, design optimization, control, and motion planning remain of great importance because, in general, the advantages afforded by increased mechanical compliance must be balanced against penalties such as slower dynamics, increased difficulty in the design of control systems, and greater kinematic uncertainty. The models that form the basis of these problems should be reasonably accurate yet not prohibitively expensive to formulate and solve. In this article, the state-of-the-art modeling techniques for continuum robots are reviewed and cast in a common language. Classical theories of mechanics are used to outline formal guidelines for the selection of appropriate degrees of freedom in models of continuum robots, both in terms of number and of quality, for geometrically nonlinear models built from the general family of one-dimensional rod models of continuum mechanics. Consideration is also given to the variety of actuators found in existing designs, the types of interaction that occur between continuum robots and their biomedical environments, the imposition of constraints on degrees of freedom, and to the numerical solution of the family of models under study. Finally, some open problems of modeling are discussed and future challenges are identified.  more » « less
Award ID(s):
Author(s) / Creator(s):
Date Published:
Journal Name:
Frontiers in Robotics and AI
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. Underactuation is a core challenge associated with controlling soft and continuum robots, which possess theoretically infinite degrees of freedom, but few actuators. However, m actuators may still be used to control a dynamic soft robot in an m-dimensional output task space. In this paper we develop a task-space control approach for planar continuum robots that is robust to modeling error and requires very little sensor information. The controller is based on a highly underactuated discrete rod mechanics model in maximal coordinates and does not require conversion to a classical robot dynamics model form. This promotes straightforward control design, implementation and efficiency. We perform input-output feedback linearization on this model, apply sliding mode control to increase robustness, and formulate an observer to estimate the full state from sparse output measurements. Simulation results show exact task-space reference tracking behavior can be achieved even in the presence of significant modeling error, inaccurate initial conditions, and output-only sensing. 
    more » « less
  2. Soft Continuum arms, such as trunk and tentacle robots, can be considered as the “dual” of traditional rigid-bodied robots in terms of manipulability, degrees of freedom, and compliance. Introduced two decades ago, continuum arms have not yet realized their full potential, and largely remain as laboratory curiosities. The reasons for this lag rest upon their inherent physical features such as high compliance which contribute to their complex control problems that no research has yet managed to surmount. Recently, reservoir computing has been suggested as a way to employ the body dynamics as a computational resource toward implementing compliant body control. In this paper, as a first step, we investigate the information processing capability of soft continuum arms. We apply input signals of varying amplitude and bandwidth to a soft continuum arm and generate the dynamic response for a large number of trials. These data is aggregated and used to train the readout weights to implement a reservoir computing scheme. Results demonstrate that the information processing capability varies across input signal bandwidth and amplitude. These preliminary results demonstrate that soft continuum arms have optimal bandwidth and amplitude where one can implement reservoir computing. 
    more » « less
  3. null (Ed.)
    Continuum robots have strong potential for application in Space environments. However, their modeling is challenging in comparison with traditional rigid-link robots. The Kinematic-Model-Free (KMF) robot control method has been shown to be extremely effective in permitting a rigid-link robot to learn approximations of local kinematics and dynamics (“kinodynamics”) at various points in the robot’s task space. These approximations enable the robot to follow various trajectories and even adapt to changes in the robot’s kinematic structure. In this paper, we present the adaptation of the KMF method to a three-section, nine degrees-of-freedom continuum manipulator for both planar and spatial task spaces. Using only an external 3D camera, we show that the KMF method allows the continuum robot to converge to various desired set points in the robot’s task space, avoiding the complexities inherent in solving this problem using traditional inverse kinematics. The success of the method shows that a continuum robot can “learn” enough information from an external camera to reach and track desired points and trajectories, without needing knowledge of exact shape or position of the robot. We similarly apply the method in a simulated example of a continuum robot performing an inspection task on board the ISS. 
    more » « less
  4. The control and motion planning of bioinspired swimming robots is complicated by the fluid–robot interaction, which is governed by a very high (infinite)-dimensional nonlinear system. Many high dimensional nonlinear systems, often have low-dimensional attractors. From the perspective of swimming robots, such low-dimensional attractors simplify the analysis of the mechanics of swimming and prove to be useful to design controllers. This paper describes such a low-dimensional model for the swimming of a class of robots that are propelled by the motion of an internal reaction wheel. The model of swimming on a low-dimensional attractor is itself motivated by recent work on the dissipative Chaplygin sleigh, a well-known nonholonomic system, that exhibits limit cycle dynamics. We show that the governing equations of the Chaplygin sleigh are a very useful surrogate model for the swimming robot. The Chaplygin sleigh model is used to demonstrate certain maneuvers by the robot through computations. Experiments with such a robot provide evidence of limit cycle dynamics. Computational models based on discrete point vortex–body interaction confirm this behavior. Our work also suggests that there is a close phenomenological and mathematical similarity between the dynamics of swimming robots and those of ground based nonholonomic robots, which could motivate the development of very low-dimensional mathematical models for the motion of other fish-like swimming robots. 
    more » « less
  5. This paper presents a class of four-wheel drive autonomous robots designed to collaboratively traverse terrains with a deformable upper layer, where soil properties result in limited traction and have the potential to cause immobilization. The robots are designed to have front and rear axle yaw degrees of freedom, and front and rear axle roll degrees of freedom providing ground compliance and maneuverability on friable terrain. These degrees of freedom, along with four individually driven wheels and an actuated translational degree of freedom inside a mid-frame joint, enable poses and modes of mobility that differ significantly from a rigid vehicle. A primary goal of this work is to assess the capacity to use this vehicular form as a testbed that leverages these vehicle dynamics to assess mobility. Using a custom ROS-Gazebo simulation environment, a heterogenous driving surface is created and used to evaluate this capability. We show that the vehicle can sense imbalanced terrain resistances proprioceptively. Additionally, we show that rigidity of the vehicle can be controlled through a simple feedback control loop governing the robot’s unconstrained axles to maintain a proper heading angle and still can provide an avenue to monitor the dynamics related to full-vehicle immobilization. 
    more » « less