arXiv subjects

Venanzio Cichella

Publications and source records attributed to Venanzio Cichella.

22 records · Page 2Linked to original sources

arXiv2020

Bernstein polynomial-based transcription method for solving optimal trajectory generation problems

This paper presents a method and an open-source implementation, Bernstein/Bézier Optimal Trajectories (BeBOT), for the generation of trajectories for autonomous system operations. The proposed method is based on infinite dimensional optimal control formulations of trajectory generation problems. By approximating the trajectories using Bernstein polynomials, these problems can be transcribed as nonlinear programming problems, which can then be solved using off-the-shelf solvers. Bernstein polynomials possess favorable geometric properties that enable the trajectory planner to efficiently evaluate and enforce constraints along the vehicles' trajectories, including maximum speed and angular rates, minimum distance between trajectories and between the vehicles and obstacles. By virtue of these properties, feasibility and safety constraints typically imposed in autonomous vehicle operations can be enforced and guaranteed independently on the order of the polynomials. Thus, the trajectory generation algorithm can efficiently generate feasible and collision-free trajectories, and can be deployed for real-time safety critical applications in complex environments and for multiple vehicle missions.

cs.RO↗

arXiv2019

Proximity Queries for Absolutely Continuous Parametric Curves

In motion planning problems for autonomous robots, such as self-driving cars, the robot must ensure that its planned path is not in close proximity to obstacles in the environment. However, the problem of evaluating the proximity is generally non-convex and serves as a significant computational bottleneck for motion planning algorithms. In this paper, we present methods for a general class of absolutely continuous parametric curves to compute: (i) the minimum separating distance, (ii) tolerance verification, and (iii) collision detection. Our methods efficiently compute bounds on obstacle proximity by bounding the curve in a convex region. This bound is based on an upper bound on the curve arc length that can be expressed in closed form for a useful class of parametric curves including curves with trigonometric or polynomial bases. We demonstrate the computational efficiency and accuracy of our approach through numerical simulations of several proximity problems.

cs.RO↗

arXiv2019

L1 Adaptive Output Feedback for Non-square Systems with Arbitrary Relative Degree

This paper considers the problem of output feedback control for non-square multi-input multi-output systems with arbitrary relative degree. The proposed controller, based on the L1 adaptive control architecture, is designed using the right interactor matrix and a suitably defined projection matrix. A state-output predictor, a low-pass filter, and adaptive laws are introduced that achieve output tracking of a desired reference signal. It is shown that the proposed control strategy guarantees closed-loop stability with arbitrarily small steady-state errors. The transient performance in the presence of non-zero initialization errors is quantified in terms of decreasing functions. Rigorous mathematical analysis and illustrative examples are provided to validate the theoretical claims.

math.OC↗

arXiv2018

Bernstein approximation of optimal control problems

Bernstein polynomial approximation to a continuous function has a slower rate of convergence as compared to other approximation methods. "The fact seems to have precluded any numerical application of Bernstein polynomials from having been made. Perhaps they will find application when the properties of the approximant in the large are of more importance than the closeness of the approximation." -- has remarked P.J. Davis in his 1963 book Interpolation and Approximation. This paper presents a direct approximation method for nonlinear optimal control problems with mixed input and state constraints based on Bernstein polynomial approximation. We provide a rigorous analysis showing that the proposed method yields consistent approximations of time continuous optimal control problems. Furthermore, we demonstrate that the proposed method can also be used for costate estimation of the optimal control problems. This latter result leads to the formulation of the Covector Mapping Theorem for Bernstein polynomial approximation. Finally, we explore the numerical and geometric properties of Bernstein polynomials, and illustrate the advantages of the proposed approximation method through several numerical examples.

math.OC↗