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Linear complementarity, linear and nonlinear programming
01 Jan 1988-
About: The article was published on 1988-01-01 and is currently open access. It has received 1012 citations till now. The article focuses on the topics: Mixed complementarity problem & Complementarity theory.
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TL;DR: Alefeld, Chen and Potra as discussed by the authors used the Farkas lemma to check if the interval contains a negative certification which shows the nonexistence of solutions in the whole space R n.
8 citations
TL;DR: For establishing a uniform theory for stick-slip phenomena and impact events, a Lagrangian approach is used connecting the additional constraint equations and the equations of motion by Lagrange multipliers, which are proportional to the constraint forces.
Abstract: Couplings in machines and mechanisms always have play and friction. While under loading, stick–slip phenomena and impact events can take place. Such processes are modeled as multibody systems whose structure is time variant or unsteady. The time‐variant number of degrees of freedom is due to stick–slip contacts. The coupling characteristics become unsteady, for instance there exist jumps in the loads, if impacts occur. For establishing a uniform theory for such phenomena we use a Lagrangian approach connecting the additional constraint equations and the equations of motion by Lagrange multipliers, which are proportional to the constraint forces. Stick–slip and impact events are evaluated by indicator functions leading to special numerical algorithms for the search of switching points. Contact problems are formulated as a complementarity problem which can be solved by efficient algorithms. The theory is applied to rattling in gears, impact drilling machines, turbine blade dampers, and a woodpecker toy. In some of these applications, chaos as a result of bifurcations is possible, which results from variations in the parameters.
8 citations
TL;DR: Inverse dynamics algorithms that are derived only from first principles and use established phenomenological models like Coulomb friction are described, which gives an upper bound on the performance of such controllers in situ.
Abstract: Inverse dynamics is used extensively in robotics and biomechanics applications. In manipulator and legged robots, it can form the basis of an effective nonlinear control strategy by providing a robot with both accurate positional tracking and active compliance. In biomechanics applications, inverse dynamics control can approximately determine the net torques applied at anatomical joints that correspond to an observed motion. In the context of robot control, using inverse dynamics requires knowledge of all contact forces acting on the robot; accurately perceiving external forces applied to the robot requires filtering and thus significant time delay. An alternative approach has been suggested in recent literature: predicting contact and actuator forces simultaneously under the assumptions of rigid body dynamics, rigid contact, and friction. Existing such inverse dynamics approaches have used approximations to the contact models, which permits use of fast numerical linear algebra algorithms. In contrast, we describe inverse dynamics algorithms that are derived only from first principles and use established phenomenological models like Coulomb friction. We assess these inverse dynamics algorithms in a control context using two virtual robots: a locomoting quadrupedal robot and a fixed-based manipulator gripping a box while using perfectly accurate sensor data from simulation. The data collected from these experiments gives an upper bound on the performance of such controllers in situ. For points of comparison, we assess performance on the same tasks with both error feedback control and inverse dynamics control with virtual contact force sensing.
8 citations
Cites background or methods from "Linear complementarity, linear and ..."
...to this LCP obeys the relationship Qz+r= w; given z, xis determined via Equation 114, solving the MCLP. 26 C The Principle Pivoting Method for solving LCPs The Principal Pivot Method I (Cottle, 1968; Murty, 1988) (PPM), which solves LCPs with P-matrices (complex square matrices with fully non-negative principal minors (Murty, 1988) that includes positive semi-denite matrices as a proper subset). The resultin...
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...Such classes include positive definite matrices, positive semi-definite matrices, P -matrices, and Z-matrices, to name only a few; (Murty, 1988; Cottle et al., 1992) contain far more information on complementarity problems, including algorithms for solving them....
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TL;DR: In this article, a theory for the study of cracks having a given geometry by taking into account all types of actions of monotone type like unilateral contact and friction phenomena between the two crack sides is presented.
8 citations
TL;DR: In this paper, a unified approach to control a rather general class of robotic systems with closed loops under a set of linear equality and inequality constraints using the notion of projection operator is presented.
Abstract: The equality and inequality constraints on constraint force and/or the actuator force/ torque arise in several robotic applications, for which different controllers have been specifically developed. This paper presents a unified approach to control a rather general class of robotic systems with closed loops under a set of linear equality and inequality constraints using the notion of projection operator. The controller does not require the kinematic constraints to be independent, i.e., systems with time-varying topology can be dealt with, while demanding minimum-norm actuation force or torque in the case that the system becomes redundant. The orthogonal decomposition of the control input force yields the null-space component and its orthogonal complement. The null-space component is obtained using the projected inverse dynamics control law, while the orthogonal complement component is found through solving a quadratic programming problem, in which the equality and inequality constraints are derived to be equivalent to the originally specified ones. Finally, a case study is presented to demonstrate how the control technique can be applied to multi-arms manipulation of an object. DOI: 10.1115/1.4002689
8 citations