Related papers: Explicit Time-Optimal Speed Profiles for Planar Pa…
We propose a novel method for motion planning and illustrate its implementation on several canonical examples. The core novel idea underlying the method is to define a metric for which a path of minimal length is an admissible path, that is…
Continuous optimization based motion planners require specifying a maneuver class before calculating the optimal trajectory for that class. In traffic, the intentions of other participants are often unclear, presenting multiple maneuver…
Continuous formulations of trajectory planning problems have two main benefits. First, constraints are guaranteed to be satisfied at all times. Secondly, dynamic obstacles can be naturally considered with time. This paper introduces a novel…
The basic module for the solution of the minimum time optimal control of a car-like vehicle is herein presented. The vehicle is subject to the effect of laminar (linear) and aerodynamic (quadratic) drag, taking into account the asymmetric…
We present a fast algorithm for the design of smooth paths (or trajectories) that are constrained to lie in a collection of axis-aligned boxes. We consider the case where the number of these safe boxes is large, and basic preprocessing of…
Ground robots navigating in complex, dynamic environments must compute collision-free trajectories to avoid obstacles safely and efficiently. Nonconvex optimization is a popular method to compute a trajectory in real-time. However, these…
We analyze the convergence rate of various momentum-based optimization algorithms from a dynamical systems point of view. Our analysis exploits fundamental topological properties, such as the continuous dependence of iterates on their…
We present the concept of speed maps: speed limits for mobile robots in human environments. Static speed maps allow for faster navigation on corridors while limiting the speed around corners and in rooms. Dynamic speed maps put limits on…
We study statistical properties of a family of maps acting in the space of integer valued sequences, which model dynamics of simple deterministic traffic flows. We obtain asymptotic (as time goes to infinity) properties of trajectories of…
By variational methods, we prove existence of planar closed curves with prescribed curvature for some classes of curvature functions. The main difficulty is to obtain bounded Palais-Smale sequences. This is achieved by adding a parameter in…
In this paper, we present a fast, on-line mapping and planning solution for operation in unknown, off-road, environments. We combine obstacle detection along with a terrain gradient map to make simple and adaptable cost map. This map can be…
We propose an online planning approach for racing that generates the time-optimal trajectory for the upcoming track section. The resulting trajectory takes the current vehicle state, effects caused by \acl{3D} track geometries, and speed…
Ensuring safety and driving consistency is a significant challenge for autonomous vehicles operating in partially observed environments. This work introduces a consistent parallel trajectory optimization (CPTO) approach to enable safe and…
We consider an asynchronous system with transitions corresponding to the instructions of a computer system. For each instruction, a runtime is given. We propose a mathematical model, allowing us to construct an algorithm for finding the…
Time-optimal trajectories drive quadrotors to their dynamic limits, but computing such trajectories involves solving non-convex problems via iterative nonlinear optimization, making them prohibitively costly for real-time applications. In…
In this paper, motion planning for a vehicle moving on a unit sphere with unit speed is considered, wherein the desired terminal location is fixed, but the terminal orientation is free. The motion of the vehicle is modeled to be constrained…
In this paper, we propose a new modeling approach and a fast algorithm for 3D motion planning, applicable for fixed-wing unmanned aerial vehicles. The goal is to construct the shortest path connecting given initial and final configurations…
Agile quadrotor flight pushes the limits of control, actuation, and onboard perception. While time-optimal trajectory planning has been extensively studied, existing approaches typically neglect the tight coupling between vehicle dynamics,…
We study the problem of path planning with soft homology constraints on a surface topologically equivalent to a disk with punctures. Specifically, we propose an algorithm, named $\Hstar$, for the efficient computation of a path homologous…
Both humans and the sensors on an autonomous vehicle have limited sensing capabilities. When these limitations coincide with scenarios involving vulnerable road users, it becomes important to account for these limitations in the motion…