Related papers: Real-Time QP Solvers: A Concise Review and Practic…

In a wide range of applications, we are required to rapidly solve a sequence of convex multiparametric quadratic programs (mp-QPs) on resource-limited hardwares. This is a nontrivial task and has been an active topic for decades in control…

Model predictive control (MPC) has become a hot cake technology for various applications due to its ability to handle multi-input multi-output systems with physical constraints. The optimization solvers require considerable time, limiting…

When Model Predictive Control (MPC) is used in real-time to control linear systems, quadratic programs (QPs) need to be solved within a limited time frame. Recently, several parametric methods have been proposed that certify the number of…

Solving linear systems and quadratic programming (QP) problems are both ubiquitous tasks in the engineering and computing fields. Direct methods for solving systems, such as Cholesky, LU, and QR factorizations, exhibit data-independent time…

Online optimal control of quadruped robots would enable them to adapt to varying inputs and changing conditions in real time. A common way of achieving this is linear model predictive control (LMPC), where a quadratic programming (QP)…

Symmetry is the essential element of lifted inference that has recently demon- strated the possibility to perform very efficient inference in highly-connected, but symmetric probabilistic models models. This raises the question, whether…

We present ReLU-QP, a GPU-accelerated solver for quadratic programs (QPs) that is capable of solving high-dimensional control problems at real-time rates. ReLU-QP is derived by exactly reformulating the Alternating Direction Method of…

A hierarchical control architecture is presented for energy-efficient control of legged robots subject to variety of linear/nonlinear inequality constraints such as Coulomb friction cones, switching unilateral contacts, actuator saturation…

This paper presents a unified framework that connects sequential quadratic programming (SQP) and the iterative linear-parameter-varying model predictive control (LPV-MPC) technique. Using the differential formulation of the LPV-MPC, we…

In this paper, we present efficient solutions for the nonlinear program (NLP) associated with nonlinear model predictive control (NMPC) by leveraging the linear parameter-varying (LPV) embedding of nonlinear models and sequential quadratic…

This paper aims to develop a hierarchical nonlinear control algorithm, based on model predictive control (MPC), quadratic programming (QP), and virtual constraints, to generate and stabilize locomotion patterns in a real-time manner for…

First-order methods for quadratic optimization such as OSQP are widely used for large-scale machine learning and embedded optimal control, where many related problems must be rapidly solved. These methods face two persistent challenges:…

Robotic manipulators are often designed with more actuated degrees-of-freedom than required to fully control an end effector's position and orientation. These "redundant" manipulators can allow infinite joint configurations that satisfy a…

This paper presents a novel learning-based trajectory planning framework for quadrotors that combines model-based optimization techniques with deep learning. Specifically, we formulate the trajectory optimization problem as a quadratic…

We present experimental results using a passive whole-body control approach for quadruped robots that achieves dynamic locomotion while compliantly balancing the robot's trunk. We formulate the motion tracking as a Quadratic Program (QP)…

Convex Quadratic Programs (QPs) have come to play a central role in the computation of control action for constrained dynamical systems. In this paper, we present a novel Homogeneous QP (HQP) formulation which is obtained by embedding the…

Optimal control is a successful approach to generate motions for complex robots, in particular for legged locomotion. However, these techniques are often too slow to run in real time for model predictive control or one needs to drastically…

This paper introduces the quadratically-constrained quadratic programming (QCQP) framework recently added in HPIPM alongside the original quadratic-programming (QP) framework. The aim of the new framework is unchanged, namely providing the…

Thanks to recent advancements in accelerating non-linear model predictive control (NMPC), it is now feasible to deploy whole-body NMPC at real-time rates for humanoid robots. However, enforcing inequality constraints in real time for such…

Quadratic programming (QP) forms a crucial foundation in optimization, encompassing a broad spectrum of domains and serving as the basis for more advanced algorithms. Consequently, as the scale and complexity of modern applications continue…