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This paper presents an algorithm to solve non-convex optimal control problems, where non-convexity can arise from nonlinear dynamics, and non-convex state and control constraints. This paper assumes that the state and control constraints…
We provide theoretical analysis of the statistical and computational properties of penalized $M$-estimators that can be formulated as the solution to a possibly nonconvex optimization problem. Many important estimators fall in this…
This paper describes continuous-space methodologies to estimate the collision probability, Euclidean distance and gradient between an ellipsoidal robot model and an environment surface modeled as a set of Gaussian distributions.…
This paper studies a variant of the minimum-cost flow problem in a graph with convex cost function where the demands at the vertices are functions depending on a one-dimensional parameter $\lambda$. We devise two algorithmic approaches for…
We study several polygonal curve problems under the Fr\'{e}chet distance via algebraic geometric methods. Let $\mathbb{X}_m^d$ and $\mathbb{X}_k^d$ be the spaces of all polygonal curves of $m$ and $k$ vertices in $\mathbb{R}^d$,…
We consider the motion planning problem for a point constrained to move along a smooth closed convex path of bounded curvature. The workspace of the moving point is bounded by a convex polygon with m vertices, containing an obstacle in a…
This work considers a Motion Planning Problem with Dynamic Obstacles (MPDO) in 2D that requires finding a minimum-arrival-time collision-free trajectory for a point robot between its start and goal locations amid dynamic obstacles moving…
Sparse learning is a very important tool for mining useful information and patterns from high dimensional data. Non-convex non-smooth regularized learning problems play essential roles in sparse learning, and have drawn extensive attentions…
Consider the problem of minimizing the sum of two convex functions, one being smooth and the other non-smooth. In this paper, we introduce a general class of approximate proximal splitting (APS) methods for solving such minimization…
A new exact projective penalty method is proposed for the equivalent reduction of constrained optimization problems to nonsmooth unconstrained ones. In the method, the original objective function is extended to infeasible points by summing…
This paper addresses the problem of planning a safe (i.e., collision-free) trajectory from an initial state to a goal region when the obstacle space is a-priori unknown and is incrementally revealed online, e.g., through line-of-sight…
We consider geometric collision-detection problems for modular reconfigurable robots. Assuming the nodes (modules) are connected squares on a grid, we investigate the complexity of deciding whether collisions may occur, or can be avoided,…
In this paper, we consider the problem of planning a path for a robot to monitor a known set of features of interest in an environment. We represent the environment as a graph with vertex weights and edge lengths. The vertices represent…
This paper proposes a fast and accurate trajectory planning algorithm for autonomous parking. Nominally, an optimal control problem should be formulated to describe this scheme, but the dimensionality of the optimal control problem is…
This work presents a motion planning framework for robotic manipulators that computes collision-free paths directly in image space. The generated paths can then be tracked using vision-based control, eliminating the need for an explicit…
Navigating a collision-free and optimal trajectory for a robot is a challenging task, particularly in environments with moving obstacles such as humans. We formulate this problem as a stochastic optimal control problem. Since solving the…
Autonomous agents such as self-driving cars or parcel robots need to recognize and avoid possible collisions with obstacles in order to move successfully in their environment. Humans, however, have learned to predict movements intuitively…
Navigating safely in urban environments remains a challenging problem for autonomous vehicles. Occlusion and limited sensor range can pose significant challenges to safely navigate among pedestrians and other vehicles in the environment.…
This article considers two variants of a shortest path problem for a car-like robot visiting a set of waypoints. The sequence of waypoints to be visited is specified in the first variant while the robot is allowed to visit the waypoints in…
The geometric intersection number of a curve on a surface is the minimal number of self-intersections of any homotopic curve, i.e. of any curve obtained by continuous deformation. Given a curve $c$ represented by a closed walk of length at…