The use of Coulomb’s friction law with the principles of classical rigid-body dynamics introduces mathematical inconsistencies. Specifically, the forward dynamics problem can have no solutions or multiple solutions. In these situations, compliant contact models, while increasing the dimensionality of the state vector, can resolve these problems. The simplicity and efficiency of rigid-body models, however, provide strong motivation for their use during those portions of a simulation when the rigid-body solution is unique and stable. In this paper, we use singular perturbation analysis in conjunction with linear complementarity theory to establish conditions under which the solution predicted by the rigid-body dynamic model is stable. We employ a general model of contact compliance to derive stability criteria for planar mechanical systems. In particular, we show that for cases with one sliding contact, there is always at most one stable solution. Our approach is not directly applicable to transitions between rolling and sliding where the Coulomb friction law is discontinuous. To overcome this difficulty, we introduce a smooth nonlinear friction law, which approximates Coulomb friction. Such a friction model can also increase the efficiency of both rigid-body and compliant contact simulation. Numerical simulations for the different models and comparison with experimental results are also presented.

SUMMARYIn this paper, we formulate a semi-implicit time-stepping model for multibody mechanical systems with frictional, distributed compliant contacts. Employing a polyhedral pyramid model for the friction law and a distributed, linear, viscoelastic model for the contact, we obtain mixed linear complementarity formulations for the discrete-time, compliant contact problem. We establish the existence and finite multiplicity of solutions, demonstrating that such solutions can be computed by Lemke's algorithm. In addition, we obtain limiting results of the model as the contact stiffness tends to infinity. The limit analysis elucidates the convergence of the dynamic models with compliance to the corresponding dynamic models with rigid contacts within the computational time-stepping framework. Finally, we report numerical simulation results with an example of a planar mechanical system with a frictional contact that is modelled using a distributed, linear viscoelastic model and Coulomb's frictional law, verifying empirically that the solution trajectories converge to those obtained by the more traditional rigid-body dynamic model.

We describe a framework for controlling and coordinating a group of nonholonomic mobile robots equipped with range sensors, with applications ranging from scouting and reconnaissance, to search and rescue and manipulation tasks. We derive control algorithms that allow the robots to control their position and orientation with respect to neighboring robots or obstacles in the environment. We then outline a coordination protocol that automatically switches between the control laws to maintain a specified formation. Two simple trajectory generators are derived from potential field theory. The first allows each robot to plan its reference trajectory based on the information available to it. The second scheme requires sharing of information and enables a rigid group formation. Numerical simulations illustrate the application of these ideas and demonstrate the scalability of the proposed framework for a large group of robots.

SummaryThere have been significant interests and efforts in the field of impedance control on robotic manipulation over last decades. Impedance control aims to achieve the desired mechanical interaction between the robotic equipment and its environment. This paper gives the overview and comparison of basic concepts and principles, implementation strategies, crucial techniques, and practical applications concerning the impedance control of robotic manipulation. This work attempts to serve as a tutorial to people outside the field and to promote discussion of a unified vision of impedance control within the field of robotic manipulation. The goal is to help readers quickly get into the problems of their interests related to impedance control of robotic manipulation and to provide guidance and insights in finding appropriate strategies and solutions.

Beginning with a proof of the existence of a discrete-time trajectory, this paper establishes the convergence of a time-stepping method for solving continuous-time, boundary-value problems for dynamic systems with frictional contacts characterized by local compliance in the normal and tangential directions. Our investigation complements the analysis of the initial-value rigid-body model with one frictional contact encountering inelastic impacts by Stewart [Arch. Ration. Mech. Anal., 145 (1998), pp. 215-260] and the recent analysis by Anitescu [Optimization-Based Simulation for Nonsmooth Rigid Multibody Dynamics, Argonne National Laboratory, Argonne, IL, 2004] using the framework of measure differential inclusions. In contrast to the measure-theoretic approach of these authors, we follow a differential variational approach and address a broader class of problems with multiple elastic or inelastic impacts. Applicable to both initial and affine boundary-value problems, our main convergence result pertains to the case where the compliance in the normal direction is decoupled from the compliance in the tangential directions and where the friction coefficients are sufficiently small. Disciplines Engineering | Mechanical Engineering Comments