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Direct optimal control methods first discretize a continuous-time Optimal Control Problem (OCP) and then solve the resulting Nonlinear Program (NLP). Sequential Quadratic Programming (SQP) is a popular family of algorithms to solve this finite dimensional optimization problem. In the specific case of a least squares cost, the Generalized Gauss-Newton (GGN) method is a popular approach which works very well under some assumptions. This paper proposes a Sequential Convex Quadratic Programming (SCQP) scheme which exploits additional convexities in the NLP in order to generalize the GGN algorithm, possibly extend its applicability and improve its local convergence. These properties are studied in detail for the proposed SCQP algorithm, which will be compared to the classical GGN method using a numerical case study of the optimal control of an inverted pendulum.

This paper discusses path-following control for robotics, moving a manipulator along a path in Cartesian space, making a trade-off between tracking accuracy and the speed at which the path is followed. We present and validate a nonlinear model predictive control (NMPC) approach suitable for this nonlinear control task. This approach entails a method to model the position of the robot end-effector with respect to the path and, in addition, a reformulation of the robot prediction model in terms of an independent path parameter instead of time. This way, we obtain a convenient parameterization of path properties in the optimal control formulation and many geometric constraints, such as tracking tolerance, transform into simple linear or vector-norm constraints. Numerical simulations illustrate the benefits of this novel NMPC approach in an implementation that employs a direct multiple shooting discretization strategy and the real-time iteration scheme for fast computation of the control law. We show results of closed-loop simulations for a 6-DOF industrial robot executing a writing task, with computation times close to enabling real-time implementation. *Niels van Duijkeren en Robin Verschueren are fellows of the TEMPO Initial Training Network. The work leading to these results has been carried out within the framework of FP7-ITN-TEMPO (607 957). This work also benefits from project G0C4515N of the Research Foundation-Flanders (FWO-Flanders), KU Leuven-BOF PFV/10/002 Centre of Excellence: Optimization in Engineering (OPTEC) and the Belgian Programme on Interuniversity Attraction Poles, initiated by the Belgian Federal Science Policy Office (DYSCO).

Time-optimal motion planning for robotic manipulators consists of moving the robot along a path in Cartesian space as fast as possible. In contrast to time-optimal path following, small deviations from a predefined path are acceptable and can be exploited to further reduce the overall motion time. In this paper, we present a new method to compute timeoptimal motions around a path. By employing an appropriate change of variables for the robot dynamics to path coordinates, geometric constraints enter the optimal control formulation in a convenient way. The reformulation of the robot dynamics and the path constraints is shown with numerical examples.