相关论文: ALGAMES: A Fast Augmented Lagrangian Solver for Co…
By exploiting double-penalty terms for the primal subproblem, we develop a novel relaxed augmented Lagrangian method for solving a family of convex optimization problems subject to equality or inequality constraints. The method is then…
This paper is devoted to the theoretical and numerical investigation of an augmented Lagrangian method for the solution of optimization problems with geometric constraints. Specifically, we study situations where parts of the constraints…
We consider the problem of interaction-aware motion planning for automated vehicles in general traffic situations. We model the interaction between the controlled vehicle and surrounding road users using a generalized potential game, in…
We address a multi-class traffic model, for which we computationally assess the ability of mean-field games (MFGs) to yield approximate Nash equilibria for traffic flow games of intractable large finite-players. We introduce ad hoc…
This paper develops a Distributed Differentiable Dynamic Game (D3G) framework, which can efficiently solve the forward and inverse problems in multi-robot coordination. We formulate multi-robot coordination as a dynamic game, where the…
The multi-contact nonlinear complementarity problem (NCP) is a naturally arising challenge in robotic simulations. Achieving high performance in terms of both accuracy and efficiency remains a significant challenge, particularly in…
Autonomous driving has been the subject of increased interest in recent years both in industry and in academia. Serious efforts are being pursued to address legal, technical and logistical problems and make autonomous cars a viable option…
In cooperative stochastic games multiple agents work towards learning joint optimal actions in an unknown environment to achieve a common goal. In many real-world applications, however, constraints are often imposed on the actions that can…
The mathematical framework of hybrid system is a recent and general tool to treat control systems involving control action of heterogeneous nature. In this paper, we construct and test a semi-Lagrangian numerical scheme for solving the…
We construct a semi-Lagrangian scheme for first-order, time-dependent, and non-local Mean Field Games. The convergence of the scheme to a weak solution of the system is analyzed by exploiting a key monotonicity property. To solve the…
Safe, agile, and socially compliant multi-robot navigation in cluttered and constrained environments remains a critical challenge. This is especially difficult with self-interested agents with unique, unknown priorities in decentralized…
We present a numerical method for the minimization of constrained optimization problems where the objective is augmented with large quadratic penalties of inconsistent equality constraints. Such objectives arise from quadratic integral…
Generating motions for robots interacting with objects of various shapes is a complex challenge, further complicated by the robot geometry and multiple desired behaviors. While current robot programming tools (such as inverse kinematics,…
Recent work on decision making and planning for autonomous driving has made use of game theoretic methods to model interaction between agents. We demonstrate that methods based on the Stackelberg game formulation of this problem are…
Although significant progress has been made in decision-making for automated driving, challenges remain for deployment in the real world. One challenge lies in addressing interaction-awareness. Most existing approaches oversimplify…
Decision-making for autonomous driving is challenging, considering the complex interactions among multiple traffic agents (e.g., autonomous vehicles (AVs), human drivers, and pedestrians) and the computational load needed to evaluate these…
Motivated by robotic trajectory optimization problems we consider the Augmented Lagrangian approach to constrained optimization. We first propose an alternative augmentation of the Lagrangian to handle the inequality case (not based on…
The augmented Lagrangian method (ALM) is a classical optimization tool that solves a given "difficult" (constrained) problem via finding solutions of a sequence of "easier"(often unconstrained) sub-problems with respect to the original…
Differential Dynamic Programming (DDP) has become a well established method for unconstrained trajectory optimization. Despite its several applications in robotics and controls however, a widely successful constrained version of the…
This work considers the problem of approximating initial condition and time-dependent optimal control and trajectory surfaces using multivariable Fourier series. A modified Augmented Lagrangian algorithm for translating the optimal control…