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Autonomous vehicles face the problem of optimizing the expected performance of subsequent maneuvers while bounding the risk of collision with surrounding dynamic obstacles. These obstacles, such as agent vehicles, often exhibit stochastic…
We provide a control-theoretic perspective on optimal tensor algorithms for minimizing a convex function in a finite-dimensional Euclidean space. Given a function $\Phi: \mathbb{R}^d \rightarrow \mathbb{R}$ that is convex and twice…
An efficient approach to compute near time-optimal trajectories for linear kinematic systems with oscillatory internal dynamics is presented. Thereby, kinematic constraints with respect to velocity, acceleration and jerk are taken into…
This paper proposes a novel approach to formulate time-optimal point-to-point motion planning and control under uncertainty. The approach defines a robustified two-stage Optimal Control Problem (OCP), in which stage 1, with a fixed time…
Optimization based motion planning provides a useful modeling framework through various costs and constraints. Using Graph of Convex Sets (GCS) for trajectory optimization gives guarantees of feasibility and optimality by representing…
This paper presents a convex approach to the optimization of a cooperative rendezvous, that is, the problem of two distant spacecraft that simultaneously operate to get closer. Convex programming guarantees convergence towards the optimal…
Path planning for multiple robots is well studied in the AI and robotics communities. For a given discretized environment, robots need to find collision-free paths to a set of specified goal locations. Robots can be fully anonymous,…
In this paper, a novel real-time acceleration-continuous path-constrained trajectory planning algorithm is proposed with an appealing built-in tradability mechanism between cruise motion and time-optimal motion. Different from existing…
We consider the speed planning problem for a vehicle moving along an assigned trajectory, under maximum speed, tangential and lateral acceleration, and jerk constraints. The problem is a nonconvex one, where nonconvexity is due to jerk…
In this paper we propose a unified two-phase scheme for convex optimization to accelerate: (1) the adaptive cubic regularization methods with exact/inexact Hessian matrices, and (2) the adaptive gradient method, without any knowledge of the…
We develop polynomial-size LP-relaxations for {\em orienteering} and the {\em regret-bounded vehicle routing problem} (\rvrp) and devise suitable LP-rounding algorithms that lead to various new insights and approximation results for these…
An effective method for optimizing path planning for a specific model of a 6-degree-of-freedom (6-DOF) robot manipulator is presented as part of the motion planning of the manipulator using computer algebra. We assume that we are given a…
Multi-robot motion planning (MRMP) is the problem of finding collision-free paths for a set of robots in a continuous state space. The difficulty of MRMP increases with the number of robots and is exacerbated in environments with narrow…
In drone racing, the time-minimum trajectory is affected by the drone's capabilities, the layout of the race track, and the configurations of the gates (e.g., their shapes and sizes). However, previous studies neglect the configuration of…
This paper presents an algorithm that finds a centroidal motion and footstep plan for a Spring-Loaded Inverted Pendulum (SLIP)-like bipedal robot model substantially faster than real-time. This is achieved with a novel representation of the…
Two-stage methods addressing continuous shortest path problems start local minimization from discrete shortest paths in a spatial graph. The convergence of such hybrid methods to global minimizers hinges on the discretization error induced…
We consider the rooted orienteering problem in Euclidean space: Given $n$ points $P$ in $\mathbb R^d$, a root point $s\in P$ and a budget $\mathcal B>0$, find a path that starts from $s$, has total length at most $\mathcal B$, and visits as…
Vehicle trajectory optimization is essential to ensure vehicles travel efficiently and safely. This paper presents an infrastructure assisted constrained connected automated vehicles (CAVs) trajectory optimization method on curved roads.…
Let $B$ be a point robot moving in the plane, whose path is constrained to forward motions with curvature at most one, and let $P$ be a convex polygon with $n$ vertices. Given a starting configuration (a location and a direction of travel)…
Motion planning under differential constraints is a classic problem in robotics. To date, the state of the art is represented by sampling-based techniques, with the Rapidly-exploring Random Tree algorithm as a leading example. Yet, the…