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This paper offers a unified perspective on different approaches to the solution of optimal control problems through the lens of constrained sequential quadratic programming. In particular, it allows us to find the relationships between…
The recent works on quadrotor have focused on more and more challenging tasks on increasingly complex systems. Systems are often augmented with slung loads, inverted pendulums or arms, and accomplish complex tasks such as going through a…
This paper extends the RRT* algorithm, a recently developed but widely-used sampling-based optimal motion planner, in order to effectively handle nonlinear kinodynamic constraints. Nonlinearity in kinodynamic differential constraints often…
In this paper, we consider the problem of generating inspection paths for robots. These paths should allow an attached measurement device to perform high-quality measurements. We formally show that generating robot paths, while maximizing…
Trajectory replanning for quadrotors is essential to enable fully autonomous flight in unknown environments. Hierarchical motion planning frameworks, which combine path planning with path parameterization, are popular due to their time…
This study develops a graph search algorithm to find the optimal discrimination path for the binary classification problem. The objective function is defined as the difference of variations between the true positive (TP) and false positive…
In this study a new approach is proposed for the generation of aircraft trajectories. The relative guidance of an aircraft, which is aimed to join in minimum time the track of a leader aircraft, is particularly considered. In a first place,…
We present a semi-infinite program (SIP) solver for trajectory optimizations of general articulated robots. These problems are more challenging than standard Nonlinear Program (NLP) by involving an infinite number of non-convex, collision…
Column generation is often used to solve multi-commodity flow problems. A program for column generation always includes a module that solves a linear equation. In this paper, we address three major issues in solving linear problem during…
This paper considers the problem of quantum compilation from an optimization perspective by fixing a circuit structure of CNOTs and rotation gates then optimizing over the rotation angles. We solve the optimization problem classically and…
Trajectory optimization considers the problem of deciding how to control a dynamical system to move along a trajectory which minimizes some cost function. Differential Dynamic Programming (DDP) is an optimal control method which utilizes a…
Ordinary differential equations that model technical systems often contain states, that are considered dangerous for the system. A trajectory that reaches such a state usually indicates a flaw in the design. In this paper, we present and…
Path planning is critical for autonomous driving, generating smooth, collision-free, feasible paths based on perception and localization inputs. However, its computationally intensive nature poses significant challenges for…
We study the problem of optimal multi-robot path planning on graphs MPP over four distinct minimization objectives: the makespan (last arrival time), the maximum (single-robot traveled) distance, the total arrival time, and the total…
We propose a novel quantum algorithm for solving linear optimization problems by quantum-mechanical simulation of the central path. While interior point methods follow the central path with an iterative algorithm that works with successive…
We consider algorithmic approaches to the D-optimality problem for cases where the input design matrix is large and highly structured, in particular implicitly specified as a full quadratic or linear response-surface model in several levels…
Motion planning and control are two core components of the robotic systems autonomy stack. The standard approach to combine these methodologies comprises an offline/open-loop stage, planning, that designs a feasible and safe trajectory to…
This paper studies existing direct transcription methods for trajectory optimization applied to robot motion planning. There are diverse alternatives for the implementation of direct transcription. In this study we analyze the effects of…
We consider a class of nonsmooth fractional programming problems with fixed-point constraints, where the numerator is convex and the denominator is concave. To solve this problem, we propose splitting algorithms that compute subgradient…
We consider the problem of planning a collision-free path of a robot in the presence of risk zones. The robot is allowed to travel in these zones but is penalized in a super-linear fashion for consecutive accumulative time spent there. We…