Mobility of bodies in contact. II. How forces are generated bycurvature effects

For part I, see ibid., p.696-708. The paper considers how forces are produced by compliance and surface curvature effects in systems where an object a is kinematically immobilized to second-order by finger bodies Al,...,Ak. A class of configuration-space based elastic deformation models is introduced. Using these elastic deformation models, it is shown that any object which is kinematically immobilized to first or second-order is also dynamically locally asymptotically stable with respect to perturbations. Moreover, it is shown that for preloaded grasps kinematic immobility implies that the stiffness matrix of the grasp is positive definite. The stability result provides physical justification for using second-order effects for purposes of immobilization in practical applications. Simulations illustrate the concepts

Energy-based trajectory tracking and vibration control for multilink highly flexible manipulators

In this paper, a discrete model is adopted, as proposed by Hencky for elastica based on rigid bars and lumped rotational springs, to design the control of a lightweight planar manipulator with multiple highly flexible links. This model is particularly suited to deal with nonlinear equations of motion as those associated with multilink robot arms, because it does not include any simplification due to linearization, as in the assumed modes method. The aim of the control is to track a trajectory of the end effector of the robot arm, without the onset of vibrations. To this end, an energy-based method is proposed. Numerical simulations show the effectiveness of the presented approach

Compliant contact force models in multibody dynamics : evolution of the Hertz contact theory

Over the last decades, several compliant contact force models have been proposed. However, no complete and systematic comparison has been done on these models, which provides information on their range of application and accuracy for use in different contact scenarios. Thus, the selection of an appropriate model for a given contact problem is still an important and challenging issue to be addressed. The Hertzian contact theory remains the foundation for almost all of the available force models, but by itself, it is not appropriate for most impacts in practice, due to the amount of energy dissipated during the impact. A good number of contact force models have been offered that augment the Hertzian law with a damping term to accommodate the energy loss during the impact process for small or moderate impact velocities. In this work, the main issues associated with the most common compliant contact force models of this type are analyzed. Results in terms of the dynamic simulations of multibody systems are presented, which allow for the comparison of the similarities and differences among the models considered.Fundação para a Ciência e a Tecnologia (FCT) - DACHOR - Multibody Dynamics and Control of Hybrid Active Orthoses (MIT-Pt/BSHHMS/0042/2008), BIOJOINTS - Development of advanced biological joint models for human locomotion biomechanics (PTDC/EMEPME/ 099764/2008), SFRH/BD/40164/2007, SFRH/BD/64477/200

Swarm robot social potential fields with internal agent dynamics

Swarm robotics is a new and promising approach to the design and control of multiagent robotic systems. In this paper we use a model for a second order non-linear system of self-propelled agents interacting via pair-wise attractive and repulsive potentials. We propose a new potential field method using dynamic agent internal states to successfully solve a reactive path-planning problem. The path planning problem cannot be solved using static potential fields due to local minima formation, but can be solved by allowing the agent internal states to manipulate the potential field. Simulation results demonstrate the ability of a single agent to perform reactive problem solving effectively, as well as the ability of a swarm of agents to perform problem solving using the collective behaviour of the entire swarm

Geometric control of particle manipulation in a two-dimensional fluid

Manipulation of particles suspended in fluids is crucial for many applications, such as precision machining, chemical processes, bio-engineering, and self-feeding of microorganisms. In this paper, we study the problem of particle manipulation by cyclic fluid boundary excitations from a geometric-control viewpoint. We focus on the simplified problem of manipulating a single particle by generating controlled cyclic motion of a circular rigid body in a two-dimensional perfect fluid. We show that the drift in the particle location after one cyclic motion of the body can be interpreted as the geometric phase of a connection induced by the system's hydrodynamics. We then formulate the problem as a control system, and derive a geometric criterion for its nonlinear controllability. Moreover, by exploiting the geometric structure of the system, we explicitly construct a feedback-based gait that results in attraction of the particle towards the rigid body. We argue that our gait is robust and model-independent, and demonstrate it in both perfect fluid and Stokes fluid

Numerical study of the hydraulic excavator overturning stability during performing lifting operations

This article presents a numerical study of the stability of a hydraulic excavator during performing lifting operations. A planar dynamic model is developed with six degrees of freedom, which considers the base body elastic connection with the terrain, the front digging manipulator links, and the presence of the freely suspended payload. Differential equations describing the excavator dynamic behavior are obtained by using the Lagrange formalism. Numerical experiments are carried out to study the excavator dynamic stability under different operating conditions during the motion along a vertical straight-line trajectory. It is shown that the arising inertial loads during the movement of the links along the vertical trajectory, combined with the payload swinging and the motion of the base body, decreases the excavator stability. It was found that the excavator stability during following vertical straight-line trajectory decreases considerably in the lower part of the vertical trajectory. If the stability coefficient is close to 1, the payload swinging can cause the separation of a support from the terrain; nevertheless, the excavator stability can be restored. A method for tire stiffness and damping coefficients estimation is presented. The validation of the dynamical model is performed by the use of a small-scale elastically mounted manipulator.DFG, 414044773, Open Access Publizieren 2019 - 2020 / Technische Universität Berli