A unified derivative-free projection method model for large-scale nonlinear equations with convex constraints

<p style='text-indent:20px;'>Motivated by recent derivative-free projection methods proposed in the literature for solving nonlinear constrained equations, in this paper we propose a unified derivative-free projection method model for large-scale nonlinear equations with convex constraints. Under mild conditions, the global convergence and convergence rate of the proposed method are established. In order to verify the feasibility and effectiveness of the model, a practical algorithm is devised and the corresponding numerical experiments are reported, which show that the proposed practical method is efficient and can be applied to solve large-scale nonsmooth equations. Moreover, the proposed practical algorithm is also extended to solve the obstacle problem.</p>

Constrained Lipschitzian Error Bounds and Noncritical Solutions of Constrained Equations

For many years, local Lipschitzian error bounds for systems of equations have been successfully used for the design and analysis of Newton-type methods. There are characterizations of those error bounds by means of first-order derivatives like a recent result by Izmailov, Kurennoy, and Solodov on critical solutions of nonlinear equations. We aim at extending this result in two directions which shall enable, to some extent, to include additional constraints and to consider mappings with reduced smoothness requirements. This leads to new necessary as well as sufficient conditions for the existence of error bounds.

Optimal Feet-Forces’ and Torque Distributions of Six-Legged Robot Maneuvering on Various Terrains

SUMMARYAn analytical model with coupled dynamics for a realistic six-legged robotic system locomoting on various terrains has been developed, and its effectiveness has been proven through computer simulations and validated using virtual prototyping tools and real experiment. The approach is new and has not been attempted before. This study investigated the optimal feet-forces’ distributions under body force and foot–ground interaction considering compliant contact and friction force models for the feet undergoing slip. The kinematic model with 114 implicit constraints in 3D Cartesian space has been transformed in terms of generalized coordinates with a reduced explicit set of 24 constrained equations using kinematic transformations. The nonlinear constrained inverse dynamics model of the system has been formulated as a coupled dynamical problem using Newton–Euler method with realistic environmental conditions (compliant foot–ground contact, impact, and friction) and computed using optimization techniques due to its indeterminate nature. One case study has been carried out to validate the analytical data with the simulated ones executed in MSC.ADAMS® (Automated Dynamic Analysis of Mechanical Systems), while the other case study has been conducted to validate the analytical and simulated data with the experimental ones. In both these cases, results are found to be in close agreement, which proves the efficacy of the model.