Dynamic Modeling of a Spatial Cable-Driven Continuum Robot Using Euler-Lagrange Method

Continuum robots are kinematically redundant and their dynamic models are highly nonlinear. This study aims to overcome this difficulty by presenting a more practical dynamic model of a certain class of continuum robots called cable-driven continuum robot (CDCR). Firstly, the structural design of a CDCR with two rotational degrees of freedom (DOF) is introduced. Then, the kinematic models are derived according to the constant curvature assumption. Considering the complexity of the kinetic energy expression, it has been approximated by the well-known Taylor expansions.  This case corresponds to weak bending angles within the specified bending angle range of the robot. On the other hand, due to the low weight of the CDCR components, the gravitational energy effects can be neglected compared to those stemmed from the elastic energy. Thereafter, the corresponding dynamic model is established using Euler-Lagrange method. Static and dynamic models have been illustrated by examples. This analysis and dynamic model development have been compared with the existing scientific literature. The obtained results shown that the consistency and the efficiency of accuracy for real-time have been carried out. However, the dynamic modeling of CDCR with more than 2-DOF leads to a more complex mathematical expression, and cannot be simplified by adopting the similar assumptions and methodology used in the case of 2-DOF

Dynamic modelling and visco-elastic parameter identification of a fibre-reinforced soft fluidic elastomer manipulator

A dynamic model of a soft fibre-reinforced fluidic elastomer is presented and experimentally verified, which can be used for model-based controller design. Due to the inherent visco-(hyper)elastic characteristics and nonlinear timedependent behaviour of soft fluidic elastomer robots, analytic dynamic modelling is challenging. The fibre reinforced noninflatable soft fluidic elastomer robot used in this paper can produce both planar and spatial movements. Dynamic equations are developed for both cases. Parameters, related to the viscoelastic behaviour of the robot during elongation and bending motion, are identified experimentally and incorporated into our model. The modified dynamic model is then validated in experiments comparing the time responses of the physical robot with the corresponding outputs of the simulation model. The results validate the accuracy of the proposed dynamic model

Model Reference Predictive Adaptive Control for Large Scale Soft Robots

Past work has shown Model Predictive Control (MPC) to be an effective strategy for controlling continuum joint soft robots using rudimentary models, however the in-accuracies of these models often mean that an integration scheme must be combined with MPC. Presented in this work is a novel dynamic model formulation for continuum joint soft robots which is more accurate than the authors’ previous models yet remains fast enough for MPC. This model is based on the Piecewise Constant Curvature (PCC) assumption and a relatively new configuration representation and allows for computationally efficient simulation. Due to the difficulty in determining model parameters (damping and spring effects) as well as effects common in continuum joint soft robots (hysteresis, complex pressure dynamics, etc.), we submit that most model-based controllers of continuum joint soft robots would benefit from some form of model adaptation. In this work a novel form of adaptive MPC is presented based on Model Reference Adaptive Control (MRAC). We call our novel adaptive MPC approach MRPAC. We show that like MRAC, MRPAC is able to compensate for ”known unknowns” such as unknown inertias and spring and damper coefficients. Our experiments also show that like MPC, MRPAC is also robust to ”unknown unknowns” such as unmodeled external forces and any forces not represented in the form of the adaptive model. Experiments in simulation and hardware show that MRPAC outperforms MPC and MRAC in every case except for that in which MPC uses a perfect model in simulation

Control Space Reduction and Real-Time Accurate Modeling of Continuum Manipulators Using Ritz and Ritz-Galerkin Methods

To address the challenges with real-time accurate modeling of multi-segment continuum manipulators in the presence of significant external and body loads, we introduce a novel series solution for variable-curvature Cosserat rod static and Lagrangian dynamic method. By combining a modified Lagrange polynomial series solution, based on experimental observations, with Ritz and Ritz-Galerkin methods, the infinite modeling state space of a continuum manipulator is minimized to geometrical position of a handful of physical points (in our case two). As a result, a unified easy to implement vector formalism is proposed for the nonlinear impedance and configuration control. We showed that by considering the mechanical effects of highly elastic axial deformation, the model accuracy is increased up to 6%. The proposed model predicts experimental results with 6-8% (4-6 [mm]) mean error for the Ritz-Galerkin method in static cases and 16-20% (12-14 [mm]) mean error for the Ritz method in dynamic cases, in planar and general 3D motions. Comparing to five different models in the literature, our approximate solution is shown to be more accurate with the smallest possible number of modeling states and suitable for real-time modeling, observation and control applications

Static kinematics for an antagonistically actuated robot based on a beam-mechanics-based model

Soft robotic structures might play a major role in the 4th industrial revolution. Researchers have successfully demonstrated advantages of soft robotics over traditional robots made of rigid links and joints in several application areas including manufacturing, healthcare and surgical interventions. However, soft robots have limited ability to exert higher forces when it comes to interaction with the environment, hence, change their stiffness on demand over a wide range. One stiffness mechanism embodies tendon-driven and pneumatic air actuation in an antagonistic way achieving variable stiffness values. In this paper, we apply a beammechanics-based model to this type of soft stiffness controllable robot. This mathematical model takes into account the various stiffness levels of the soft robotic manipulator as well as interaction forces with the environment at the tip of the manipulator. The analytical model is implemented into a robotic actuation system made of motorised linear rails with load cells (obtaining applied forces to the tendons) and a pressure regulator. Here, we present and analyse the performance and limitations of our model

Control Space Reduction and Real-Time Accurate Modeling of Continuum Manipulators Using Ritz and Ritz-Galerkin Methods

To address the challenges with real-time accurate modeling of multisegment continuum manipulators in the presence of significant external and body loads, we introduce a novel series solution for variable-curvature Cosserat rod static and Lagrangian dynamic methods. By combining a modified Lagrange polynomial series solution, based on experimental observations, with Ritz and Ritz-Galerkin methods, the infinite modeling state space of a continuum manipulator is minimized to geometrical position of a handful of physical points (in our case two). As a result, a unified easy to implement vector formalism is proposed for the nonlinear impedance and configuration control. We showed that by considering the mechanical effects of highly elastic axial deformation, the model accuracy is increased up to 6%. The proposed model predicts experimental results with 6%-8% (4-6 mm) mean error for the Ritz-Galerkin method in static cases and 16%-20% (12-14 mm) mean error for the Ritz method in dynamic cases, in planar and general three-dimensional motions. Comparing to five different models in the literature, our approximate solution is shown to be more accurate with the smallest possible number of modeling states and suitable for real-time modeling, observation, and control applications

Computing Pressure-Deformation Maps for Braided Continuum Robots

This paper presents a method for computing sensorimotor maps of braided continuum robots driven by pneumatic actuators. The method automatically creates a lattice-like representation of the sensorimotor map that preserves the topology of the input space by arranging its nodes into clusters of related data. Deformation trajectories can be simply represented with adjacent nodes whose values smoothly change along the lattice curve; this facilitates the computation of controls and the prediction of deformations in systems with unknown mechanical properties. The proposed model has an adaptive structure that can recalibrate to cope with changes in the mechanism or actuators. An experimental study with a robotic prototype is conducted to validate the proposed method