A Penalty Method Based Approach for Autonomous Navigation using Nonlinear Model Predictive Control

Abstract

This paper presents a novel model predictive control strategy for controlling autonomous motion systems moving through an environment with obstacles of general shape. In order to solve such a generic non-convex optimization problem and find a feasible trajectory that reaches the destination, the approach employs a quadratic penalty method to enforce the obstacle avoidance constraints, and several heuristics to bypass local minima behind an obstacle. The quadratic penalty method itself aids in avoiding such local minima by gradually finding a path around the obstacle as the penalty factors are successively increased. The inner optimization problems are solved in real time using the proximal averaged Newton-type method for optimal control (PANOC), a first-order method which exhibits low runtime and is suited for embedded applications. The method is validated by extensive numerical simulations and shown to outperform state-of-the-art solvers in runtime and robustness. ⋆ This work benefits from KU Leuven-BOF PFV/10/002 Centre of Excellence: Optimization in Engineering (OPTEC), from the project G0C4515N of the Research Foundation-Flanders (FWO-Flanders), from Flanders Make ICON project: Avoidance of collisions and obstacles in narrow lanes, and from the KU Leuven Research project C14/15/067: B-spline based certificates of positivity with applications in engineering, from KU Leuven internal funding: StG/15/043, from Fonds de la Recherche Scientifique -FNRS and the Fonds Wetenschappelijk Onderzoek -Vlaanderen under EOS Project no 30468160 (SeLMA) and from FWO projects G086318N, G086518N.

Non-linear MPC based Navigation for Micro Aerial Vehicles in Constrained Environments

“…As the acronym implies, it uses a Newton-type method and is designed to be used for optimal control problems, while its main advantages lie in being matrix-free, requiring only simple algebraic operations, that allows for a very fast convergence time and makes it an ideal framework for real-life implementations on MAVs. Optimization Engine also employs a Penalty Method [14] for the consideration of constraints.…”

Active Fault Diagnosis via Reachable Set Separation using Interval Methods

“…In order to enforce that Ψ δ (U, k max ) = 0, we employ the penalty method [19], [20] which boils down to the iterative procedure of Algorithm 1.…”

Context-aware robotic arm using fast embedded model predictive control

“…The authors of [22] combine the proximal averaged Newtontype method for optimal control (PANOC) [23] with the penalty method to compute collision-free paths using MPC. PANOC has also been used to enable the solution of fast embedded nonlinear MPC problems in real time on embedded systems and is gaining momentum in applications [24]- [27].…”