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Time-jerk optimal trajectory planning is crucial in advancing robotic arms' performance in dynamic tasks. Traditional methods rely on solving complex nonlinear programming problems, bringing significant delays in generating optimized…
This manuscript develops a new framework to analyze and design iterative optimization algorithms built on the notion of Integral Quadratic Constraints (IQC) from robust control theory. IQCs provide sufficient conditions for the stability of…
We propose controller synthesis for state regulation problems in which a human operator shares control with an autonomy system, running in parallel. The autonomy system continuously improves over human action, with minimal intervention, and…
This paper presents an algorithm to solve the infinite horizon constrained linear quadratic regulator (CLQR) problem using operator splitting methods. First, the CLQR problem is reformulated as a (finite-time) model predictive control (MPC)…
Designing controllers to generate various trajectories has been studied for years, while recently, recovering an optimal controller from trajectories receives increasing attention. In this paper, we reveal that the inherent linear quadratic…
Motion planning under uncertainty is of significant importance for safety-critical systems such as autonomous vehicles. Such systems have to satisfy necessary constraints (e.g., collision avoidance) with potential uncertainties coming from…
Current research suggests the use of a liner quadratic performance index for optimal control of regulators in various applications. Some examples include correcting the trajectory of rocket and air vehicles, vibration suppression of…
This paper investigates the performance of Newton's method, iterative Linear Quadratic Regulator (iLQR), and Differential Dynamic Programming (DDP) in solving discrete-time optimal control problems. We offer a unified perspective on these…
Although the classical LQR design method has been very successful in real world engineering designs, in some cases, the classical design method needs modifications because of the saturation in actuators. This modified problem is sometimes…
This paper presents a new framework for controller robustness verification with respect to F-16 aircraft's closed-loop performance in longitudinal flight. We compare the state regulation performance of a linear quadratic regulator (LQR) and…
This paper presents a novel trajectory planning pipeline for complex driving scenarios like autonomous lane changing, by integrating risk-aware planning with guaranteed collision avoidance into a unified optimization framework. We first…
Being able to solve a task in diverse ways makes agents more robust to task variations and less prone to local optima. In this context, constrained diversity optimization has become a useful reinforcement learning (RL) framework for…
This paper studies data-driven approaches to the continuous-time linear quadratic regulator (LQR) problem based on two existing parameterizations, namely a closed-loop (CL) parameterization from behavioral system theory and an integral…
In this work, we develop a scalable, local trajectory optimization algorithm that enables robots to interact with other robots. It has been shown that agents' interactions can be successfully captured in game-theoretic formulations, where…
This paper introduces an extension of the LQR-tree algorithm, which is a feedback-motion-planning algorithm for stabilizing a system of ordinary differential equations from a bounded set of initial conditions to a goal. The constructed…
This paper focuses on adaptive control of the discrete-time linear quadratic regulator (adaptive LQR). Recent literature has made significant contributions in proving non-asymptotic convergence rates, but existing approaches have a few…
We present LQR-CBF-RRT*, an incremental sampling-based algorithm for offline motion planning. Our framework leverages the strength of Control Barrier Functions (CBFs) and Linear Quadratic Regulators (LQR) to generate safety-critical and…
Autonomous drifting is a complex challenge due to the highly nonlinear dynamics and the need for precise real-time control, especially in uncertain environments. To address these limitations, this paper presents a hierarchical control…
In numerous reinforcement learning (RL) problems involving safety-critical systems, a key challenge lies in balancing multiple objectives while simultaneously meeting all stringent safety constraints. To tackle this issue, we propose a…
Models involving hybrid systems are versatile in their application but difficult to optimize efficiently due to their combinatorial nature. This work presents a method to cope with hybrid optimal control problems which, in contrast to…