Joris Naudet

Forward Dynamics of Open-Loop Multibody Mechanisms Using an Efficient Recursive Algorithm Based on Canonical Momenta

A new method for establishing the equations of motion of multibodymechanisms based on canonical momenta is introduced in this paper.In absence of constraints, the proposed forward dynamicsformulation results in a Hamiltonian set of 2n first order ODEsin the generalized coordinates q and the canonical momenta p.These Hamiltonian equations are derived from a recursiveNewton–Euler formulation. As an example, it is shown how, in thecase of a serial structure with rotational joints, an O(n)formulation is obtained. The amount of arithmetical operations isconsiderably less than acceleration based O(n) formulations.

General Formulation of an Efficient Recursive Algorithm Based on Canonical Momenta for Forward Dynamics of Closed-Loop Multibody Systems

In previous work, a method for establishing the equations of motion of open-loop multibody mechanisms was introduced. T he proposed forward dynamics formulation resulted in a Hamilt onian set of 2n first order ODE’s in the generalized coordinates q and the canonical momenta p. These Hamiltonian equations were derived from a recursive Newton-Euler formulation. It was shown how an O(n) formulation could be obtained in the case of a serial structure with general joints. The amount of requ ired arithmetical operations was considerably less than compar able acceleration based formulations. In this paper, a further s tep is taken: the method is extended to constrained multibody syst ems. Using the principle of virtual power, it is possible to obtai n a recursive Hamiltonian formulation for closed-loop mechanis ms as well, enabling the combination of the low amount of arithmet ical operations and a better evolution of the constraints vio lation errors, when compared with acceleration based methods.

Control Architecture of LUCY, a Biped with Pneumatic Artificial Muscles

This paper describes the biped Lucy and it’s control architecture that will be used. Lucy is actuated by Pleated Pneumatic Artificial Muscles, which have a very high power to weight ratio and an inherent adaptable compliance. These characteristics will be used to let Lucy walk in a dynamically stable manner while exploiting the adaptable passive behaviour of these muscles. A quasi-static global control has been implemented while using adapted PID techniques for the local feedback joint control. These initial control techniques resulted in the first movements of Lucy. This paper will discuss a future control architecture of Lucy to induce faster and smoother motion. The proposed control scheme is a combination of a global trajectory planner and a local low-level joint controller. The trajectory planner generates motion patterns based on two specific concepts, being the use of objective locomotion parameters, and exploiting the natural upper body dynamics by manipulating the angular momentum equation. The low-level controller can be divided in four parts: a computed torque module, an inverse delta-p unit, a local PI controller and a bang-bang controller. In order to evaluate the proposed control structure a hybrid simulator was created. Both the pneumatics and mechanics are put together in this hybrid dynamic simulation.

CONSTRAINT GRADIENT PROJECTIVE METHOD FOR STABILIZED DYNAMIC SIMULATION OF CONSTRAINED MULTIBODY SYSTEMS

Constraint gradient projective method for stabilization of constraint violation during integration of constrained multibody systems is in the focus of the paper. Different mathematical models for constrained MBS dynamic simulation on manifolds are surveyed and violation of kinematical constraints is discussed. As an extension of the previous work focused on the integration procedures of the holonomic systems, the constraint gradient projective method for generally constrained mechanical systems is discussed. By adopting differentialgeometric point of view, the geometric and stabilization issues of the method are addressed. It is shown that the method can be applied for stabilization of holonomic and non-holonomic constraints in Pfaffian and general form.Copyright

Discrete Mechanical Systems: Projective Constraint Violation Stabilization Method for Numerical Forward Dynamics on Manifolds

During numerical forward dynamics of discrete mechanical systems with constraints, a numerical violation of system kinematical constraints is the basic source of time-integration errors and frequent difficulty that analyst has to cope with. The stabilized time-integration procedure, whose stabilization step is based on projection of the integration results to the underlying constraint manifold via post-integration correction of the selected coordinates, is proposed in the paper. After discussing optimization of the partitioning algorithm, the geometric and stabilization issues of the method are addressed and it is shown that the projective stabilization algorithm can be applied for numerical stabilization of holonomic and non-holonomic constraints in Pfaffian and general form. As a continuation of the previous work, a further elaboration of the projective stabilization method applied on non-holonomic discrete mechanical systems is reported in the paper and numerical example is provided.Copyright

Recursive Algorithm Based on Canonical Momenta for Forward Dynamics of Multibody Systems: Numerical Results

In this paper, a recursive O(n) method to obtain a set of Hamiltonian equations for open-loop and constrained multi body system is briefly discussed. The method is then used to perfor m a numerical comparison of acceleration based and canonical momenta based equations of motion. A relatively simple exam ple consisting of a biped during double support phase is used for that purpose. While no significant difference in efficiency is found when using a fixed step numerical integration method, t he Hamiltonian equations perform considerably better when us ing an adaptive method. This is at least the case when the error control is applied straightforwardly. Both methods can be m ade equally efficient by removing the error control on the veloci ties for the acceleration based equations.