3 research outputs found
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.Comment: Proceedings of Robotics: Science and System
Optimal Motion Planning for Differentially Flat Systems with Guaranteed Constraint Satisfaction
© 2015 American Automatic Control Council. This research deals with the computation of optimal trajectories considering state and input constraints for linear and nonlinear systems that admit a polynomial representation through differential flatness. Based on a polynomial spline parameterization of the flat output an optimization problem in terms of the B-spline coefficients is derived that guarantees constraint satisfaction over the entire time horizon whereas classical approaches in the literature only impose the constraints on a finite time grid. As the proposed constraints are only sufficient conditions, a novel method is presented that effectively reduces their conservatism. Two numerical examples, a linear benchmark tracking problem and an optimal quadrotor maneuver, illustrate the efficiency and practicality of the presented method.status: publishe