Toward a real-time framework for solving the kinodynamic motion planning problem

Abstract

In this paper we propose a framework combining techniques from sampling-based motion planning, machine learning, and trajectory optimization to address the kinodynamic motion planning problem in real-time environments. This framework relies on a look-up table that stores precomputed optimal solutions to boundary value problems (assuming no obstacles), which form the directed edges of a precomputed motion planning roadmap. A sampling-based motion planning algorithm then leverages such a precomputed roadmap to compute online an obstacle-free trajectory. Machine learning techniques are employed to minimize the number of online solutions to boundary value problems required to compute the neighborhoods of the start state and goal regions. This approach is demonstrated to reduce online planning times up to six orders of magnitude. Simulation results are presented and discussed. Problem-specific framework modifications are then discussed that would allow further computation time reductions.

Topology-guided path integral approach for stochastic optimal control in cluttered environment

“…The time horizon considered in this procedure can be given by a user or set as the horizon of the minimum length trajectory among X. Suppose there are H number of stochastic dynamics (21) controlled by u (h) in = g (h) and let Q h , h = 1, 2, ..., H be corresponding probability measures. Equations ( 22) and ( 23) can be rewritten as…”

“…Especially, Karaman and Frazzoli have proposed the incremental sampling-based algorithm, namely the Rapidly-exploring Random Tree star (RRT*) [16], and more recently, Janson et al have proposed the Fast Marching Tree star (FMT*) algorithm [17] which utilizes batch process; both algorithms guarantee probabilistic completeness and asymptotic optimality. They have naturally extended to the planning problem with high-dimensional space and system dynamics [18,19,20,21]. Very few attempts, however, have been made at adopting sampling-based algorithm to topological motion planning problem whose configuration space is augmented by topological signature.…”

A Real-Time Framework for Kinodynamic Planning with Application to Quadrotor Obstacle Avoidance

“…There are no known analytical solutions to the minimum-time optimal control problem under the quadrotor's nonlinear dynamics (3). While numerical solutions are possible [18], they are computationally expensive. To minimize online computation times we apply an approximator-corrector structure to our framework.…”

“…To elaborate more, the framework (originally proposed in our earlier work [18]) splits computation into offline (Algorithm 1) and online (Algorithm 2) phases. During the offline phase the subroutine Sample quasi-randomly draws N s samples from the continuous state space, without any regard to obstacle locations, which are unknown until online initiation.…”

“…Our paper, arguably, provides the first demonstration of truly real-time kinodynamic planning and control of a quadrotor. Our approach and key intellectual contribution is to integrate three components of planning and control into one seamless architecture: the machine-learning-based, real-time, kinodynamic framework [18]; minimum snap trajectory generation [7]; and the nonlinear feedforward/feedback quadrotor controller [19].…”