An Iterative Method Based on the Marginalized Particle Filter for Nonlinear B-Spline Data Approximation and Trajectory Optimization

The B-spline function representation is commonly used for data approximation and trajectory definition, but filter-based methods for nonlinear weighted least squares (NWLS) approximation are restricted to a bounded definition range. We present an algorithm termed nonlinear recursive B-spline approximation (NRBA) for an iterative NWLS approximation of an unbounded set of data points by a B-spline function. NRBA is based on a marginalized particle filter (MPF), in which a Kalman filter (KF) solves the linear subproblem optimally while a particle filter (PF) deals with nonlinear approximation goals. NRBA can adjust the bounded definition range of the approximating B-spline function during run-time such that, regardless of the initially chosen definition range, all data points can be processed. In numerical experiments, NRBA achieves approximation results close to those of the Levenberg–Marquardt algorithm. An NWLS approximation problem is a nonlinear optimization problem. The direct trajectory optimization approach also leads to a nonlinear problem. The computational effort of most solution methods grows exponentially with the trajectory length. We demonstrate how NRBA can be applied for a multiobjective trajectory optimization for a battery electric vehicle in order to determine an energy-efficient velocity trajectory. With NRBA, the effort increases only linearly with the processed data points and the trajectory length

Trajectory Planning and Tracking Control of a Differential-Drive Mobile Robot in a Picture Drawing Application

This paper proposes a method for trajectory planning and control of a mobile robot for application in picture drawing from images. The robot is an accurate differential drive mobile robot platform controlled by a field-programmable-gate-array (FPGA) controller. By not locating the tip of the pen at the middle between two wheels, we are able to construct an omnidirectional mobile platform, thus implementing a simple and effective trajectory control method. The reference trajectories are generated based on line simplification and B-spline approximation of digitized input curves obtained from Canny’s edge-detection algorithm on a gray image. Experimental results for image picture drawing show the advantage of this proposed method