Search results for: IPOPT

Authors: El Hassene Osmani, Mounir Haddou, Naceurdine Bensalem

Abstract:

In this paper, we investigate optimal control problems governed by semilinear elliptic variational inequalities involving constraints on the state, and more precisely, the obstacle problem. We present a relaxed formulation for the problem using smoothing functions. Since we adopt a numerical point of view, we first relax the feasible domain of the problem, then using both mathematical programming methods and penalization methods, we get optimality conditions with smooth Lagrange multipliers. Some numerical experiments using IPOPT algorithm (Interior Point Optimizer) are presented to verify the efficiency of our approach.

Keywords: complementarity problem, IPOPT, Lagrange multipliers, mathematical programming, optimal control, smoothing methods, variationally inequalities

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Authors: A. Ramalho, L. Romeiro, R. Ventura, A. Suleman

Abstract:

A real-time path planning framework for Unmanned Air Vehicles, and in particular multi-rotors is proposed. The framework is designed to provide feasible trajectories from the current UAV position to a goal state, taking into account constraints such as obstacle avoidance, problem kinematics, and vehicle limitations such as maximum speed and maximum acceleration. The framework computes feasible paths online, allowing to avoid new, unknown, dynamic obstacles without fully re-computing the trajectory. These features are achieved using an iterative process in which the robot computes and optimizes the trajectory while performing the mission objectives. A first trajectory is computed using a modified Rapidly-Exploring Random Tree (RRT) algorithm, that provides trajectories that respect a maximum curvature constraint. The trajectory optimization is accomplished using the Interior Point Optimizer (IPOPT) as a solver. The framework has proven to be able to compute a trajectory and optimize to a locally optimal with computational efficiency making it feasible for real-time operations.

Keywords: interior point optimization, multi-rotors, online path planning, rapidly exploring random trees, trajectory optimization

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