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Robust optimal or min-max model predictive control (MPC) approaches aim to guarantee constraint satisfaction over a known, bounded uncertainty set while minimizing a worst-case performance bound. Traditionally, these methods compute a…

We propose an interior point method (IPM) for solving semidefinite programming problems (SDPs). The standard interior point algorithms used to solve SDPs work in the space of positive semidefinite matrices. Contrary to that the proposed…

Effective close-proximity human-robot interaction (CP-HRI) requires robots to be able to both efficiently perform tasks as well as adapt to human behavior and preferences. However, this ability is mediated by many, sometimes competing,…

We study the problem of Trajectory Optimization (TO) for a general class of stiff and constrained dynamic systems. We establish a set of mild assumptions, under which we show that TO converges numerically stably to a locally optimal and…

Trajectory following is one of the complicated control problems when its dynamics are nonlinear, stochastic and include a large number of parameters. The problem has significant difficulties including a large number of trials required for…

Efficient and safe trajectory planning plays a critical role in the application of quadrotor unmanned aerial vehicles. Currently, the inherent trade-off between constraint compliance and computational efficiency enhancement in UAV…

Quadrotors are agile flying robots that are challenging to control. Considering the full dynamics of quadrotors during motion planning is crucial to achieving good solution quality and small tracking errors during flight. Optimization-based…

We consider the problem of learning control policies that optimize a reward function while satisfying constraints due to considerations of safety, fairness, or other costs. We propose a new algorithm, Projection-Based Constrained Policy…

This paper presents a computationally efficient optimization algorithm for solving nonconvex optimal control problems that involve discrete logic constraints. Traditional solution methods for these constraints require binary variables and…

Trajectory planning is a critical component in ensuring the safety, stability, and efficiency of autonomous vehicles. While existing trajectory planning methods have achieved progress, they often suffer from high computational costs,…

A typical manipulation task consists of a manipulator equipped with a gripper to grasp and move an object with constraints on the motion of the hand-held object, which may be due to the nature of the task itself or from object-environment…

Point sets matching problems can be handled by optimal transport. The mechanism behind it is that optimal transport recovers the point-to-point correspondence associated with the least curl deformation. Optimal transport is a special form…

We propose an approach to trajectory optimization for piecewise polynomial systems based on the recently proposed graphs of convex sets framework. We instantiate the framework with a convex relaxation of optimal control based on occupation…

Humanoid robots often face significant balance issues due to the motion of their heavy limbs. These challenges are particularly pronounced when attempting dynamic motion or operating in environments with irregular terrain. To address this…

We present an evaluation of several representative sampling-based and optimization-based motion planners, and then introduce an integrated motion planning system which incorporates recent advances in trajectory optimization into a sparse…

In recent years, numerous vision and learning tasks have been (re)formulated as nonconvex and nonsmooth programmings(NNPs). Although some algorithms have been proposed for particular problems, designing fast and flexible optimization…

In this paper, we study optimal experimental design problems with a broad class of smooth convex optimality criteria, including the classical A-, D- and p th mean criterion. In particular, we propose an interior point (IP) method for them…

Several algorithms are available in the literature for finding the entire set of Pareto-optimal solutions in MultiObjective Linear Programming (MOLP). However, it has not been proposed so far an interior point algorithm that finds all…

We propose a primal-dual interior-point (PDIP) method for solving quadratic programming problems with linear inequality constraints that typically arise form MPC applications. We show that the solver converges (locally) quadratically to a…

Real-time optimal control remains a fundamental challenge in robotics, especially for nonlinear systems with stringent performance requirements. As one of the representative trajectory optimization algorithms, the iterative Linear Quadratic…