Thomas A. Wettergren

James P. Wilson, Zongyuan Shen, Shalabh Gupta et al.

In this paper, we develop a new algorithm, called T$^{\star}$-Lite, that enables fast time-risk optimal motion planning for variable-speed autonomous vehicles. The T$^{\star}$-Lite algorithm is a significantly faster version of the previously developed T$^{\star}$ algorithm. T$^{\star}$-Lite uses the novel time-risk cost function of T$^{\star}$; however, instead of a grid-based approach, it uses an asymptotically optimal sampling-based motion planner. Furthermore, it utilizes the recently developed Generalized Multi-speed Dubins Motion-model (GMDM) for sample-to-sample kinodynamic motion planning. The sample-based approach and GMDM significantly reduce the computational burden of T$^{\star}$ while providing reasonable solution quality. The sample points are drawn from a four-dimensional configuration space consisting of two position coordinates plus vehicle heading and speed. Specifically, T$^{\star}$-Lite enables the motion planner to select the vehicle speed and direction based on its proximity to the obstacle to generate faster and safer paths. In this paper, T$^{\star}$-Lite is developed using the RRT$^{\star}$ motion planner, but adaptation to other motion planners is straightforward and depends on the needs of the planner

Khushboo Mittal, Junnan Song, Shalabh Gupta et al.

This paper presents a rapid (real time) solution to the minimum-time path planning problem for Dubins vehicles under environmental currents (wind or ocean currents). Real-time solutions are essential in time-critical situations (such as replanning under dynamically changing environments or tracking fast moving targets). Typically, Dubins problem requires to solve for six path types; however, due to the presence of currents, four of these path types require to solve the root-finding problem involving transcendental functions. Thus, the existing methods result in high computation times and their applicability for real-time applications is limited. In this regard, in order to obtain a real-time solution, this paper proposes a novel approach where only a subset of two Dubins path types (LSL and RSR) are used which have direct analytical solutions in the presence of currents. However, these two path types do not provide full reachability. We show that by extending the feasible range of circular arcs in the LSL and RSR path types from $2π$ to $4π$: 1) full reachability of any goal pose is guaranteed, and 2) paths with lower time costs as compared to the corresponding $2π$-arc paths can be produced. Theoretical properties are rigorously established, supported by several examples, and evaluated in comparison to the Dubins solutions by extensive Monte-Carlo simulations.