Nonlinear Rigid Body Dynamics Research Articles

Convex geometric motion planning of multi-body systems on lie groups via variational integrators and sparse moment relaxation

This paper reports a novel result: with proper robot models based on geometric mechanics, one can formulate the kinodynamic motion planning problems for rigid body systems as exact polynomial optimization problems. Due to the nonlinear rigid body dynamics, the motion planning problem for rigid body systems is nonconvex. Existing global optimization-based methods do not parameterize 3D rigid body motion efficiently; thus, they do not scale well to long-horizon planning problems. We use Lie groups as the configuration space and apply the variational integrator to formulate the forced rigid body dynamics as quadratic polynomials. Then, we leverage Lasserre’s hierarchy of moment relaxation to obtain the globally optimal solution via semidefinite programming. By leveraging the sparsity of the motion planning problem, the proposed algorithm has linear complexity with respect to the planning horizon. This paper demonstrates that the proposed method can provide globally optimal solutions or certificates of infeasibility at the second-order relaxation for 3D drone landing using full dynamics and inverse kinematics for serial manipulators. Moreover, we extend the algorithms to multi-body systems via the constrained variational integrators. The testing cases on cart-pole and drone with cable-suspended load suggest that the proposed algorithms can provide rank-one optimal solutions or nontrivial initial guesses. Finally, we propose strategies to speed up the computation, including an alternative formulation using quaternion, which provides empirically tight relaxations for the drone landing problem at the first-order relaxation.

Dual-User Haptic Teleoperation of Complementary Motions of a Redundant Wheeled Mobile Manipulator Considering Task Priority

With the increasing applications of wheeled mobile manipulators (WMMs), consisting of a mobile platform (MP) and a manipulator, in diverse fields, new challenges have arisen in achieving multiple tasks such as obstacle avoidance in a constrained environment during the end-effector (EE) operation. A WMM is usually redundant due to the combination of the MP and the manipulator, making multitask control possible via employing its null space. Dual-user/two-handed teleoperation of a WMM is desirable for tasks where it is important to simultaneously control the poses of both the MP and the EE. The existing teleoperation approaches for WMMs are mostly executed at the kinematic level, without considering the nonlinear rigid-body dynamics of the WMMs. In this article, a task-priority-based dual-user teleoperation framework for a WMM is implemented to perform tasks in a constrained environment. It can simultaneously manipulate the MP and the EE, the overground obstacles are avoided by telecontrolling the MP using the WMM’s null space. Any residual redundancy can be further employed for other tasks such as singularity avoidance. The stability of the entire teleoperation design is rigorously proved even with arbitrary time delays. Experiments with a dual-user teleoperation system, consisting of two local robots and an omnidirectional WMM, are conducted to verify the proposed approach’s feasibility and effectiveness.

A complete modeling for fish robots with actuators

PurposeFor precisely presenting the swimming behavior of fish robots underwater and the practical implementation purpose, this paper aims to investigate a well-formulated fish robot model which integrates the nonlinear rigid body dynamics, kinematics and models of actuators.Design/methodology/approachThis fish robot model is mainly built up by three basic parts: a balance mechanism, a four-links vibrator and a caudal fin. In the fish robot’s head, there is a balance mechanism used to control the rotations in pitch and roll directions of the fish robot by moving two movable masses. The four-links vibrator with three active joints actuated by DC motors is designed to vibrate the fish’s body. In the end of the fish robot body, a caudal fin which connects with the passive joint is developed to generate hydrodynamic thrust forces to propel the fish robot.FindingsFrom the real stability tests and control verification, it is obvious that this proposed model can precisely present the swimming behavior of fish robots and possesses the potential to develop a fish-like robotic prototype.Originality/valueA well-formulated model with dynamics of actuators is integrated for presenting the swimming behavior of carangiform locomotion type fish robots in this investigation. From the simulation results and the practical test of a real fish robot, the feasibility of this proposed model for building up real fish robots can be proven, and this proposed model is accurate enough to effectively present the swimming behavior of fish robots.

Seismic Load Capacity of Historical Masonry Mosques by Rigid Body Kinetics

ABSTRACTKinetic analysis methods based on linear and nonlinear rigid body dynamics are used to evaluate earthquake safety of masonry structures. In this study, the formulas used to calculate the in-plane and out-of-plane load capacities of masonry load-bearing walls were evaluated and a procedure based on rigid body mechanism was proposed to calculate the out-of-plane load capacities of the walls of Ottoman period masonry mosques. New aspects of the method with respect to existing formulations is the inclusion of dynamic axial load and definition of the collapse limit spectral acceleration on the overturning wall. The calculated capacities of the mosque and individual walls were compared with the results of nonlinear pushover analysis and time history analyses performed under 1.0 and 0.5 scaled forms of nine different 3-component ground motion records. It was displayed that the seismic load capacity estimated by the proposed method is very close to the values calculated by pushover and time history analyses. The method was developed on Lala Pasha Mosque, and the reliability and applicability of the proposed methodology is verified on a different historical masonry mosque in comparison to finite element analyses results.

Three-dimensional modeling of the wave dynamics of tensegrity lattices

This paper develops effective numerical models to study the wave dynamics of highly nonlinear tensegrity metamaterials. Recent studies have highlighted the geometrically nonlinear response of structural lattices based on tensegrity prisms, which may gradually change their elastic response from stiffening to softening through the modification of mechanical, geometrical, and prestress variables. We here study the nonlinear dynamics of columns of tensegrity prisms subject to impulsive compressive loading. An effective nonlinear rigid body dynamics is employed to simulate the dynamic response of such metamaterials. We illustrate how to pass from the matrix to the vector form of the equations of motions, on accounting for a rigid response of the compressive members (bars). Numerical simulations show that the wave dynamics of the examined metamaterials supports compression solitary pulses with profile dependent on the elastic properties of the tensile members (strings), the given impact velocity, and the applied prestress. We conclude that tensegrity columns can be effectively used as tunable acoustic lenses, which are able to generate acoustic solitary waves with adjustable profile in a host medium.

μ-Synthesis Based Adaptive Robust Control of Linear-Motor-Driven Stages with High-Frequency Flexible Modes

Linear motors have good potential to achieve high speed and high accuracy by eliminating gear related mechanical problems. By using the effective model compensation of nonlinear rigid-body dynamics, the close-loop bandwidth limitation due to the appearance of neglected high-frequency flexible modes has to be the main issue to maximize the achievable performance. In this paper, the modeling and identifications are carried out to verify the existing rigid-body and high-frequency dynamics. The μ-synthesis based adaptive robust control strategy is developed. The adaptive feedforward loop is used to keep good online parameter estimation and nonlinear model compensation, and also transfers the trajectory tracking problem into the traditional regulation problem which μ-synthesis control can more easily deal with. Since considering the fundamental flexible mode as a part of the nominal plant model, the μ-synthesis feedback loop can achieve higher close-loop bandwidth with the appearance of various model uncertainties. Comparative experiments have been done and the results show the excellent tracking performance of the propose algorithm.

Parallel finite element simulation of mooring forces on floating objects

AbstractThe coupling between the equations governing the free‐surface flows, the six degrees of freedom non‐linear rigid body dynamics, the linear elasticity equations for mesh‐moving and the cables has resulted in a fluid‐structure interaction technology capable of simulating mooring forces on floating objects. The finite element solution strategy is based on a combination approach derived from fixed‐mesh and moving‐mesh techniques. Here, the free‐surface flow simulations are based on the Navier–Stokes equations written for two incompressible fluids where the impact of one fluid on the other one is extremely small. An interface function with two distinct values is used to locate the position of the free‐surface. The stabilized finite element formulations are written and integrated in an arbitrary Lagrangian–Eulerian domain. This allows us to handle the motion of the time dependent geometries. Forces and momentums exerted on the floating object by both water and hawsers are calculated and used to update the position of the floating object in time. In the mesh moving scheme, we assume that the computational domain is made of elastic materials. The linear elasticity equations are solved to obtain the displacements for each computational node. The non‐linear rigid body dynamics equations are coupled with the governing equations of fluid flow and are solved simultaneously to update the position of the floating object. The numerical examples includes a 3D simulation of water waves impacting on a moored floating box and a model boat and simulation of floating object under water constrained with a cable. Copyright © 2003 John Wiley & Sons, Ltd.

Flexible multibody dynamics based fixture-workpiece analysis model for fixturing stability

The machining force and torque exerted on a workpiece vary as the cutter moves along the tool path, therefore a dynamic approach is essential for fixturing stability analysis. This paper presents a technique to dynamically model and analyze the fixture-workpiece system subjected to time-varying machining loads. Combining the advantages of FEA (Finite Element Analysis) and nonlinear rigid body dynamics, a flexible multibody dynamic model is formulated to incorporate the overall interaction (clamping forces, machining loads, and contact friction) between flexible workpiece and compliant fixture elements. Three major parameters affecting the fixturing stability, namely the magnitude, application sequence, and placement of fixturing clamps, are analyzed. Additionally, the time dependent deformation of a flexible workpiece under clamping and machining loads is estimated. A scaled engine block with the 3–2–1 fixturing scheme subjected to face milling operation is given as an example. Comparison between the simulation result and experimental data shows a reasonable agreement.

Stability guaranteed teleoperation: an adaptive motion/force control approach

An adaptive motion/force controller is developed for unilateral or bilateral teleoperation systems. The method can be applied in both position and rate control modes, with arbitrary motion or force scaling. No acceleration measurements are required. Nonlinear rigid-body dynamics of the master and the slave robots are considered. A model of the flexible or rigid environment is incorporated into the dynamics of the slave, while a model of the human operator is incorporated into the dynamics of the master. The master and the slave are subject to independent adaptive motion/force controllers that assume parameter uncertainty bounds. Each parameter is independently updated within its known lower and upper bounds. The states of the master (slave) are sent to the slave (master) as motion/force tracking commands instead of control actions (efforts and/or flows). Under the modeling assumptions for the human operator and the environment, the proposed teleoperation control scheme is L/sub 2/ and L/sub /spl infin// stable in both free motion and flexible or rigid contact motion and is robust against time delays. The controlled master-slave system behaves essentially as a linearly damped free-floating mass. If the parameter estimates converge, the environment impedance and the impedance transmitted to the master differ only by a control-parameter dependent mass/damper term. Asymptotic motion (velocity/position) tracking and force tracking with zero steady-state error are achieved. Experimental results are presented in support of the analysis.