A Kinetostatic Model for Concentric Push-Pull Robots

Concentric push-pull robots (CPPR) operate through the mechanical interactions of concentrically nested, laser-cut tubes with offset stiffness centers. The distal tips of the tubes are attached to each other, and relative displacement of the tube bases generates bending in the CPPR. Previous CPPR kinematic models assumed two tubes, planar shapes, no torsion, and no external loads. In this paper, we develop a new, more general CPPR model accounting for any number of tubes, describing their variable-curvature 3D shape when actuated, including the effects of torsion and external loads. To accomplish this, we employ a modified Kirchhoff rod model for each tube (with offset stiffness center) and embed the constraints of concentricity. We use an energy method to determine robot shape as a function of actuation and external loading. We experimentally validate this kinetostatic model on prototype CPPRs with two tubes and three tubes and non-constant laser-cut patterns that create variable curvature and stiffness. Experimental results agree with the model, paving the way for use of this model in design optimization, planning, and control of CPPRs.

Energy-shaping control of a muscular octopus arm moving in three dimensions

Flexible octopus arms exhibit an exceptional ability to coordinate large numbers of degrees of freedom and perform complex manipulation tasks. As a consequence, these systems continue to attract the attention of biologists and roboticists alike. In this article, we develop a three-dimensional model of a soft octopus arm, equipped with biomechanically realistic muscle actuation. Internal forces and couples exerted by all major muscle groups are considered. An energy-shaping control method is described to coordinate muscle activity so as to grasp and reach in three-dimensional space. Key contributions of this article are as follows: (i) modelling of major muscle groups to elicit three-dimensional movements; (ii) a mathematical formulation for muscle activations based on a stored energy function; and (iii) a computationally efficient procedure to design task-specific equilibrium configurations, obtained by solving an optimization problem in the Special Euclidean group SE ( 3 ) . Muscle controls are then iteratively computed based on the co-state variable arising from the solution of the optimization problem. The approach is numerically demonstrated in the physically accurate software environment Elastica . Results of numerical experiments mimicking observed octopus behaviours are reported.

Micrometer Positioning Accuracy With a Planar Parallel Continuum Robot

Parallel Continuum Robots (PCR) have several advantages over classical articulated robots, notably a large workspace, miniaturization capabilities and safe human-robot interactions. However, their low accuracy is still a serious drawback. Indeed, several conditions have to be met for PCR to reach a high accuracy, namely: a repeatable mechanical structure, a correct kinematic model, and a proper estimation of the model’s parameters. In this article, we propose a methodology that allows reaching a micrometer accuracy with a PCR. This approach emphasizes the importance of using a repeatable continuum mechanism, identifying the most influential parameters of an accurate kinematic model of the robot and precisely measuring them. The experimental results show that the proposed approach allows to reach an accuracy of 3.3 µm in position and 0.5 mrad in orientation over a 10 mm long circular path. These results push the current limits of PCR accuracy and make them good potential candidates for high accuracy automatic positioning tasks.

Closed-loop control of soft continuum manipulators under tip follower actuation

Continuum manipulators, inspired by nature, have drawn significant interest within the robotics community. They can facilitate motion within complex environments where traditional rigid robots may be ineffective, while maintaining a reasonable degree of precision. Soft continuum manipulators have emerged as a growing subfield of continuum robotics, with promise for applications requiring high compliance, including certain medical procedures. This has driven demand for new control schemes designed to precisely control these highly flexible manipulators, whose kinematics may be sensitive to external loads, such as gravity. This article presents one such approach, utilizing a rapidly computed kinematic model based on Cosserat rod theory, coupled with sensor feedback to facilitate closed-loop control, for a soft continuum manipulator under tip follower actuation and external loading. This approach is suited to soft manipulators undergoing quasi-static deployment, where actuators apply a follower wrench (i.e., one that is in a constant body frame direction regardless of robot configuration) anywhere along the continuum structure, as can be done in water-jet propulsion. In this article we apply the framework specifically to a tip actuated soft continuum manipulator. The proposed control scheme employs both actuator feedback and pose feedback. The actuator feedback is utilized to both regulate the follower load and to compensate for non-linearities of the actuation system that can introduce kinematic model error. Pose feedback is required to maintain accurate path following. Experimental results demonstrate successful path following with the closed-loop control scheme, with significant performance improvements gained through the use of sensor feedback when compared with the open-loop case.

TMTDyn: A Matlab package for modeling and control of hybrid rigid–continuum robots based on discretized lumped systems and reduced-order models

A reliable, accurate, and yet simple dynamic model is important to analyzing, designing, and controlling hybrid rigid–continuum robots. Such models should be fast, as simple as possible, and user-friendly to be widely accepted by the ever-growing robotics research community. In this study, we introduce two new modeling methods for continuum manipulators: a general reduced-order model (ROM) and a discretized model with absolute states and Euler–Bernoulli beam segments (EBA). In addition, a new formulation is presented for a recently introduced discretized model based on Euler–Bernoulli beam segments and relative states (EBR). We implement these models in a Matlab software package, named TMTDyn, to develop a modeling tool for hybrid rigid–continuum systems. The package features a new high-level language (HLL) text-based interface, a CAD-file import module, automatic formation of the system equation of motion (EOM) for different modeling and control tasks, implementing Matlab C-mex functionality for improved performance, and modules for static and linear modal analysis of a hybrid system. The underlying theory and software package are validated for modeling experimental results for (i) dynamics of a continuum appendage, and (ii) general deformation of a fabric sleeve worn by a rigid link pendulum. A comparison shows higher simulation accuracy (8–14% normalized error) and numerical robustness of the ROM model for a system with a small number of states, and computational efficiency of the EBA model with near real-time performances that makes it suitable for large systems. The challenges and necessary modules to further automate the design and analysis of hybrid systems with a large number of states are briefly discussed.

Real-time dynamics of soft and continuum robots based on Cosserat rod models

The dynamic equations of many continuum and soft robot designs can be succinctly formulated as a set of partial differential equations (PDEs) based on classical Cosserat rod theory, which includes bending, torsion, shear, and extension. In this work we present a numerical approach for forward dynamics simulation of Cosserat-based robot models in real time. The approach implicitly discretizes the time derivatives in the PDEs and then solves the resulting ordinary differential equation (ODE) boundary value problem (BVP) in arc length at each timestep. We show that this strategy can encompass a wide variety of robot models and numerical schemes in both time and space, with minimal symbolic manipulation required. Computational efficiency is gained owing to the stability of implicit methods at large timesteps, and implementation is relatively simple, which we demonstrate by providing a short MATLAB-coded example. We investigate and quantify the tradeoffs associated with several numerical subroutines, and we validate accuracy compared with dynamic rod data gathered with a high-speed camera system. To demonstrate the method’s application to continuum and soft robots, we derive several Cosserat-based dynamic models for robots using various actuation schemes (extensible rods, tendons, and fluidic chambers) and apply our approach to achieve real-time simulation in each case, with additional experimental validation on a tendon robot. Results show that these models capture several important phenomena, such as stability transitions and the effect of a compressible working fluid.