Visual Modeling System for Optimization-Based Real-Time Trajectory Planning for Autonomous Aerial Drones

In this paper, we present a visual modeling system to enable users to seamlessly describe the constraints of trajectory planning problems for autonomous aerial drones. The proposed modeling system comes with an intuitive GUI-based interface that enables the user to specify trajectory objectives, add and remove motion constraints, and update the constraint parameters in real-time. The interface algorithm acts as a high-level parser to convert graphically specified constraints into a standard form of the underlying optimal control problem. Then a sequence of convex optimization problems, convex subproblems, are generated whose solutions will converge to a solution of the trajectory planning problem. This convex optimization based method is referred to as successive convexification (SCvx) [1]. Beneath the interface, there is another low-level layer of problem parsing, which aims to model each convex subproblem as a Second Order Cone Programming (SOCP) problem in a standard form. Once each SOCP is formulated in this standard form, it can be passed to our in-house developed primal-dual interior point method (IPM) SOCP solver [2], [3] to obtain a solution for each convex subproblem within SCvx. This paper is aimed to describe the functional architecture of the visual modeling system and its core algorithms, and also presents some illustrative flight experiments.

1. Introduction

Optimization-based trajectory planning has become a crucial part of many autonomous aerospace vehicles [4]–[7]. Research and tools for optimization-based trajectory planning utilizing successive solutions to convex optimization subproblems in order to refine trajectories have found widespread use for aerospace applications [8]–[18]. Specifically, the framework of successive convexification (SCvx) has been developed as a real-time methodology that has efficient convergence properties [19], [20]. This framework has proven to be effective in trajectory planning with applications to rocket landing and quadrotor trajectory planning. However, there is much room for improvement in the realm of user transparency. Historically, implementing SCvx requires an extensive amount of analytical work to be done a priori in order to formulate a nonlinear optimal control problem, which is subsequently reformulated as a sequence of convex subproblems. Before implementation, a discretization scheme must be determined and applied to set up the convex subproblems. This analytical process takes time, and requires an expert level of knowledge of the theory behind these methods. Figure 1:

A user of the visual modeling system specifies relevant constraints on a physics-first problem, shown in (a). These specifications are translated into meaningful constraints on the optimization problem that generates dynamically feasible trajectories for the vehicle pictured in (b). The vehicle's trajectory can be updated mid-flight as mission specifications change, enabling real-time decision-making for highly dynamic scenarios. (c) Our lab setup allows for rapid prototyping and evaluation of control and planning algorithms, and has proven to be indispensable for system identification and tuning the parameters associated with the optimizers.