Valentin Sonneville

A nonlinear finite element formalism for modelling flexible and soft manipulators

This paper presents a nonlinear finite element formalism for modelling the dynamics of flexible manipulators using the special Euclidean group SE(3) framework. The method is based on a local description of the motion variables, and results in a singularity — free formulation which exhibits important advantages regarding numerical implementation. The motivation behind this work is the development of a new class of model — based control systems which may predict and thus avoid the deformations of a real flexible mechanism. Finite element methods based on the geometrically exact beam theory have been proven to be the most accurate to account for flexibility: in this paper we highlight the key aspects of this formulation deriving the equations of motion of a flexible constrained manipulator and we illustrate its potential in robotics through a simple case study, the dynamic analysis of a two-link manipulator, simulating different model assumptions in order to emphasize its real physical behavior as flexible mechanism.

Discrete adjoint method for the sensitivity analysis of flexible multibody systems

The gradient-based design optimization of mechanical systems requires robust and efficient sensitivity analysis tools. The adjoint method is regarded as the most efficient semi-analytical method to evaluate sensitivity derivatives for problems involving numerous design parameters and relatively few objective functions. This paper presents a discrete version of the adjoint method based on the generalized-alpha time integration scheme, which is applied to the dynamic simulation of flexible multibody systems. Rather than using backward integration, the proposed approach leads to a straightforward algebraic procedure that provides design sensitivities evaluated to machine accuracy. The approach is based on an intrinsic representation of motion that does not require a parameterization of rotation. Design parameters associated with rigid bodies, kinematic joints, and beam sectional properties are considered. Rigid and flexible mechanical systems are investigated to validate the proposed approach and demonstrate its accuracy, efficiency, and robustness.

Solving the inverse dynamics of a flexible 3D robot for a trajectory tracking task

The end-effector trajectory tracking of robotic manipulators with flexible links requires advanced control concepts. In order to compute the feedforward component of the control scheme, the inverse dynamics of such flexible 3D multibody system is solved using an optimal control method. The robot is modeled using nonlinear finite elements formulated on the SE(3) group. Hence singularity and parameterization issues that can arise from 3D rotations are avoided. A numerical example of a 3D flexible arm is analyzed to demonstrate the capabilities of the method.