Model Predictive Planning: Trajectory Planning in Obstruction-Dense Environments for Low-Agility Aircraft

TL;DR

This paper addresses obstacle avoidance for low-agility fixed-wing aircraft by distinguishing geometric paths from dynamic trajectories and introducing Model Predictive Planning (MPP). MPP combines a multi-path planner (based on a variant of RRT*-AR) with a raytracing step that converts each path into convex linear constraints, followed by a convex quadratic program that refines each path into a feasible trajectory when possible. By evaluating many candidate paths in parallel and enforcing obstacle avoidance through convex constraints, MPP mitigates the susceptibility of nonlinear trajectory optimization to poor initial guesses and local minima. Empirical results on a longitudinal aircraft model show substantial improvements in success rate as the number of candidate paths increases, illustrating the practical potential of a multi-path, convex-refinement framework for in-loop trajectory planning.

Abstract

We present Model Predictive Planning (MPP), a trajectory planner for low-agility vehicles such as a fixed-wing aircraft to navigate obstacle-laden environments. MPP consists of (1) a multi-path planning procedure that identifies candidate paths, (2) a raytracing procedure that generates linear constraints around these paths to enforce obstacle avoidance, and (3) a convex quadratic program that finds a feasible trajectory within these constraints if one exists. Low-agility aircraft cannot track arbitrary paths, so refining a given path into a trajectory that respects the vehicle's limited maneuverability and avoids obstacles often leads to an infeasible optimization problem. The critical feature of MPP is that it efficiently considers multiple candidate paths during the refinement process, thereby greatly increasing the chance of finding a feasible and trackable trajectory. We demonstrate the effectiveness of MPP on a longitudinal aircraft model.

Figures (8)

• Figure 1: A visualization of some challenges of trajectory optimization around obstacles. Left: the trajectory is caught in a flytrap; the vector pointing to the goal directly opposes the obstacle constraint vector. Middle: the constraint vector for the obstacle directly opposes the dynamic constraint. These two cases result in optimizers returning no solution. Right: optimizer chooses the long way around the obstacle and gets stuck in a local minimum.
• Figure 2: The system architecture, which consists of four components: the plant, sensor models, high-frequency (HF) controller, and model predictive planner (MPP). The HF controller regulates the system and also provides a high-frequency (100Hz) estimate of the airspeed and angles for trajectory optimization. MPP begins with planning a path from the occupancy grid, which is then used to determine constraints on an optimization problem through raytracing, and finally a convex quadratic program (QP) is solved to find the trajectory.
• Figure 3: Free body diagram of forces acting on the system.
• Figure 4: The MPP trajectory creation process. Top-left: Lidar sweep used to create an occupancy grid. Top-right: Feasible path generated from the occupancy grid and RRT*-AR. Bottom-left: Raytracing around the path. For clarity, only 1/100 of the collocation points are shown (in red); see \ref{['fig:searchFig']} for more details. Bottom-right: Trajectory produced from the raytracing by solving a convex QP.
• Figure 5: Visualization of raytracing (see bottom-left pane in \ref{['fig:TrajGen1']}). Left: Collocation points are placed along the path (equally spaced in time). Middle: Rays (in green) are drawn in different directions from a collocation point (in red) until they reach an obstacle or travel a given distance. Right: Each ray is the normal vector to a linear constraint and these constraints define a convex region. This process is repeated with all collocation points. Each point is allowed to move within its prescribed convex region subject to satisfying vehicle dynamics in order to produce an improved path.