Continuum robots suffer large deflections due to internal and external forces. Accurate modeling of their passive compliance is necessary for accurate environmental interaction, especially in scenarios where direct force sensing is not practical. This paper focuses on deriving analytic formulations for the compliance of continuum robots that can be modeled as Kirchhoff rods. Compared to prior works, the approach presented herein is not subject to the constant-curvature assumptions to derive the configuration space compliance, and we do not rely on computationally-expensive finite difference approximations to obtain the task space compliance. Using modal approximations over curvature space and Lie group integration, we obtain closed-form expressions for the task and configuration space compliance matrices of continuum robots, thereby bridging the gap between constant-curvature analytic formulations of configuration space compliance and variable curvature task space compliance. We first present an analytic expression for the compliance of aingle Kirchhoff rod.We then extend this formulation for computing both the task space and configuration space compliance of a tendon-actuated continuum robot. We then use our formulation to study the tradeoffs between computation cost and modeling accuracy as well as the loss in accuracy from neglecting the Jacobian derivative term in the compliance model. Finally, we experimentally validate the model on a tendon-actuated continuum segment, demonstrating the model’s ability to predict passive deflections with error below 11.5% percent of total arc length.
more »
« less
Kinematics and Stiffness Modeling of Soft Robot With a Concentric Backbone
Abstract Soft robots can undergo large elastic deformations and adapt to complex shapes. However, they lack the structural strength to withstand external loads due to the intrinsic compliance of fabrication materials (silicone or rubber). In this paper, we present a novel stiffness modulation approach that controls the robot’s stiffness on-demand without permanently affecting the intrinsic compliance of the elastomeric body. Inspired by concentric tube robots, this approach uses a Nitinol tube as the backbone, which can be slid in and out of the soft robot body to achieve robot pose or stiffness modulation. To validate the proposed idea, we fabricated a tendon-driven concentric tube (TDCT) soft robot and developed the model based on Cosserat rod theory. The model is validated in different scenarios by varying the joint-space tendon input and task-space external contact force. Experimental results indicate that the model is capable of estimating the shape of the TDCT soft robot with an average root-mean-square error (RMSE) of 0.90 (0.56% of total length) mm and average tip error of 1.49 (0.93% of total length) mm. Simulation studies demonstrate that the Nitinol backbone insertion can enhance the kinematic workspace and reduce the compliance of the TDCT soft robot by 57.7%. Two case studies (object manipulation and soft laparoscopic photodynamic therapy) are presented to demonstrate the potential application of the proposed design.
more »
« less
- Award ID(s):
- 1718755
- PAR ID:
- 10388875
- Date Published:
- Journal Name:
- Journal of Mechanisms and Robotics
- Volume:
- 15
- Issue:
- 5
- ISSN:
- 1942-4302
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Prior models of continuously flexible robots typically assume uniform stiffness, and in this paper we relax this assumption. Geometrically varying stiffness profiles provide additional design freedom to influence the motions and workspaces of continuum robots. These results are timely, because with recent rapid advancements in multimaterial additive manufacturing techniques, it is now straightforward to create more complex stiffness profiles in robots. The key insight of this paper is to project forces and moments applied to the robot onto its center of stiffness (i.e. the Young’s modulus-weighted center of each cross section). We show how the center of stiffness can be thought of as analogous to a “precurved backbone” in a robot with uniform stiffness. This analogy enables a large body of prior work in Cosserat Rod modeling of such robots to be applied directly to those with stiffness variations. We experimentally validate this approach using multimaterial, soft, tendon-actuated robots. Lastly, to illustrate how these results can be used in practice, we investigate how stiffness variation can improve performance in a neurosurgical task.more » « less
-
Tendon actuated multisection continuum arms have high potential for inspection applications in highly constrained spaces. They generate motion by axial and bending deformations. However, because of the high mechanical coupling between continuum sections, variable length-based kinematic models produce poor results. A new mechanics model for tendon actuated multisection continuum arms is proposed in this paper. The model combines the continuum arm curve parameter kinematics and concentric tube kinematics to correctly account for the large axial and bending deformations observed in the robot. Also, the model is computationally efficient and utilizes tendon tensions as the joint space variables thus eliminating the actuator length related problems such as slack and backlash. A recursive generalization of the model is also presented. Despite the high coupling between continuum sections, numerical results show that the model can be used for generating correct forward and inverse kinematic results. The model is then tested on a thin and long multisection continuum arm. The results show that the model can be used to successfully model the deformation.more » « less
-
Soft machines typically exhibit slow locomotion speed and low manipulation strength because of intrinsic limitations of soft materials. Here, we present a generic design principle that harnesses mechanical instability for a variety of spine-inspired fast and strong soft machines. Unlike most current soft robots that are designed as inherently and unimodally stable, our design leverages tunable snap-through bistability to fully explore the ability of soft robots to rapidly store and release energy within tens of milliseconds. We demonstrate this generic design principle with three high-performance soft machines: High-speed cheetah-like galloping crawlers with locomotion speeds of 2.68 body length/s, high-speed underwater swimmers (0.78 body length/s), and tunable low-to-high-force soft grippers with over 1 to 10 3 stiffness modulation (maximum load capacity is 11.4 kg). Our study establishes a new generic design paradigm of next-generation high-performance soft robots that are applicable for multifunctionality, different actuation methods, and materials at multiscales.more » « less
-
Summary A design and manufacturing method is described for creating a motor tendon–actuated soft foam robot. The method uses a castable, light, and easily compressible open-cell polyurethane foam, producing a structure capable of large (~70% strain) deformations while requiring low torques to operate ( < 0.2 N·m). The soft robot can change shape, by compressing and folding, allowing for complex locomotion with only two actuators. Achievable motions include forward locomotion at 13 mm/s (4.3% of body length per second), turning at 9◦/s, and end-over-end flipping. Hard components, such as motors, are loosely sutured into cavities after molding. This reduces unwanted stiffening of the soft body. This work is the first demonstration of a soft open-cell foam robot locomoting with motor tendon actuators. The manufacturing method is rapid (~30 min per mold), inexpensive (under $3 per robot for the structural foam), and flexible, and will allow a variety of soft foam robotic devices to be produced.more » « less