Related papers: Second-Order Convergent Collision-Constrained Opti…

This paper presents a novel method for reformulating non-differentiable collision avoidance constraints into smooth nonlinear constraints using strong duality of convex optimization. We focus on a controlled object whose goal is to avoid…

Uncertain dynamic obstacles, such as pedestrians or vehicles, pose a major challenge for optimal robot navigation with safety guarantees. Previous work on motion planning has followed two main strategies to provide a safe bound on an…

We introduce a refined immersed boundary (IB) methodology that is better-than-first-order accurate in practice, while preserving key properties of "continuous-forcing" IB approaches that retain a singular source term in the governing…

This paper proposes a new set of conditions for exactly representing collision avoidance constraints within optimization-based motion planning algorithms. The conditions are continuously differentiable and therefore suitable for use with…

The collision avoidance constraints are prominent as non-convex, non-differentiable, and challenging when defined in optimization-based motion planning problems. To overcome these issues, this paper presents a novel non-conservative…

The goal of this paper is to study approaches to bridge the gap between first-order and second-order type methods for composite convex programs. Our key observations are: i) Many well-known operator splitting methods, such as…

We develop a new method for equality constrained optimization problems based on a sequential cubic programming framework. Each iteration utilizes a step decomposition based on the Jacobian of the constraints into a normal and a tangential…

We present a novel method for designing higher-order Control Barrier Functions (CBFs) that guarantee convergence to a safe set within a user-specified finite. Traditional Higher Order CBFs (HOCBFs) ensure asymptotic safety but lack…

Control barrier functions (CBFs) have been widely applied to safety-critical robotic applications. However, the construction of control barrier functions for robotic systems remains a challenging task. Recently, collision detection using…

Mobile robots in dynamic environments require fast planning, especially when onboard computational resources are limited. While classic potential field based algorithms may suffice in simple scenarios, in most cases algorithms able to…

This research addresses the increasing demand for advanced navigation systems capable of operating within confined surroundings. A significant challenge in this field is developing an efficient planning framework that can generalize across…

This research focuses on trajectory planning problems for autonomous vehicles utilizing numerical optimal control techniques. The study reformulates the constrained optimization problem into a nonlinear programming problem, incorporating…

Ensuring the safety of dynamical systems is crucial, where collision avoidance is a primary concern. Recently, control barrier functions (CBFs) have emerged as an effective method to integrate safety constraints into control synthesis…

This study introduces two second-order methods designed to provably avoid saddle points in composite nonconvex optimization problems: (i) a nonsmooth trust-region method and (ii) a curvilinear linesearch method. These developments are…

Obstacle avoidance of polytopic obstacles by polytopic robots is a challenging problem in optimization-based control and trajectory planning. Many existing methods rely on smooth geometric approximations, such as hyperspheres or ellipsoids,…

Obstacle avoidance is central to safe navigation, especially for robots with arbitrary and nonconvex geometries operating in cluttered environments. Existing Control Barrier Function (CBF) approaches often rely on analytic clearance…

Real-world environments are inherently uncertain, and to operate safely in these environments robots must be able to plan around this uncertainty. In the context of motion planning, we desire systems that can maintain an acceptable level of…

This paper considers the problem of robot motion planning in a workspace with obstacles for systems with uncertain 2nd-order dynamics. In particular, we combine closed form potential-based feedback controllers with adaptive control…

Differentially private (stochastic) gradient descent is the workhorse of DP private machine learning in both the convex and non-convex settings. Without privacy constraints, second-order methods, like Newton's method, converge faster than…

As robots are being increasingly used in close proximity to humans and objects, it is imperative that robots operate safely and efficiently under real-world conditions. Yet, the environment is seldom known perfectly. Noisy sensors and…