Branch-and-lift algorithm for deterministic global optimization in nonlinear optimal control

This paper presents a branch-and-lift algorithm for solving optimal control problems with smooth nonlinear dynamics and potentially nonconvex objective and constraint functionals to guaranteed global optimality. This algorithm features a direct sequential method and builds upon a generic, spatial branch-and-bound algorithm. A new operation, called lifting, is introduced, which refines the control parameterization via a Gram-Schmidt orthogonalization process, while simultaneously eliminating control subregions that are either infeasible or that provably cannot contain any global optima. Conditions are given under which the image of the control parameterization error in the state space contracts exponentially as the parameterization order is increased, thereby making the lifting operation efficient. A computational technique based on ellipsoidal calculus is also developed that satisfies these conditions. The practical applicability of branch-and-lift is illustrated in a numerical example. © 2013 Springer Science+Business Media New York

Optimal Control of Multibody Systems in Minimal Coordinates

onstrained optimization problems. Results for an industrial robot with six joints demonstrate that tailored optimization methods are very well suited for fast off-line optimization of robot trajectories. 1. Introduction In automotive industry, robotic manipulators play an important role for car production in automated assembly lines. The reduction of the cycle time of the production line is of great importance in order to reduce costs by improving efficiency. Here "optimal" robot trajectories and robust and efficient optimization methods for computing them are of great interest when planning production processes. 2. Modeling of the optimization problem Equations of Motion. Industrial robots have to act extremely fast. Therefore all dynamical effects have to be taken into account. The dynamical behavior of most industrial robots can be described in minimal coordinates by a system of second order differential equations (multibody system with tre

The role of motion dynamics in the design, control and stability of bipedal and quadrupedal robots

Fundamental principles and recent methods for investigating the nonlinear dynamics of legged robot motions with respect to control, stability and design are discussed. One of them is the still challenging problem of producing dynamically stable gaits. The generation of fast walking or running motions require methods and algorithms adept at handling the nonlinear dynamical effects and stability issues which arise. Reduced, recursive multibody algorithms, a numerical optimal control package, and new stability and energy performance indices are presented which are well-suited for this purpose. Difficulties and open problems are discussed along with numerical investigations into the proposed gait generation scheme. Our analysis considers both biped and quadrupedal gaits with particular reference to the problems arising in soccer-playing tasks encountered at the RoboCup where our team, the Darmstadt Dribbling Dackels, participates as part of the German Team in the Sony Legged Robot League