This paper presents biped walking control using a library of optimal trajectories. The biped walking control problem is formulated as an optimal control problem. We take advantage of a parametric trajectory optimization method to find the periodic steady-state trajectory in regular walking. Then we use Differential Dynamic Programming (DDP) to generate a library of optimal trajectories and loca...

Many algorithms for control, optimization and estimation in robotics depend on derivatives of the underlying system dynamics, e.g. to compute linearizations, sensitivities or gradient directions. However, we show that when dealing with Rigid Body Dynamics, these derivatives are difficult to derive analytically and to implement efficiently. To overcome this issue, we extend the modelling tool ‘R...

The leapfrog algorithm, so-called because of its geometric nature, for solving a class of optimal control problems is proposed. Initially a feasible trajectory is given and subdivided into smaller pieces. In each subdivision, with the assumption that local optimal controls can easily be calculated, a piecewise-optimal trajectory is obtained. Then the junctions of these smaller pieces of optimal...

Résumé en anglais This article introduces a continuous representation for controlled model and state jump hybrid systems. Such a representation is valuable in that it manages to cope with the difficulties related to discontinuities, by replacing the study of these systems by that of continuous ones, which is simple. The studied hybrid systems are first introduced, together with their associated...

This paper is concerned with the dynamic motion analysis and the planning of maximum payload path of flexible manipulators. The finite element method was employed for dynamic modelling of the system and the motion of the model was considered as a combination of the rigid displacement and the elastic deformation of each link. Each manipulator link was treated as a finite number of elements and t...

The task of trajectory design of autonomous vehicles is typically two-fold. First, it needs to take into account the intrinsic dynamics of the vehicle, which are sometimes termed local constraints. Second, on a higher level, the designed trajectories must allow the vehicle to achieve some application-specific task. The specification of the task results in the so-called global constraints. Both ...

This paper presents how a problem of optimal trajectory planning, that is an optimal control problem, can be transformed into a parametric optimization problem and in consequence be tackled using efficient deterministic or stochastic parametric optimization techniques. The transformation is done thanks to discretizing some or all continuous system’s variables and forming their time-histories by...

A Radau pseudospectral method is derived for solving state-inequality path constrained optimal control problems. The continuous-time state-inequality path constrained optimal control problem is modified by applying a set of tangency conditions at the entrance of the activity of the path constraint. It is shown that the first-order optimality condition of the nonlinear programming problem associ...

As a means of measuring progress towards fuel and emissions reduction targets, the United Kingdom Air Navigation Service Provider NATS developed the 3Di flight efficiency metric. In principle the 3Di score of a flight is calculated by comparing a flown trajectory to a theoretical fuel/CO2 optimum trajectory. In response to a Eurocontrol review of the metric, the 3Di score has been analysed usin...

As a consequence of physical constraints and of dynamical nonlinearities, optimal control problems involving mobile robots are generally difficult ones. Many algorithms have been developed to solve such problems, the more common being related to trajectory planning, minimum-time control or any specific performance index. Nevertheless optimal control problems associated to mobile robots have not...