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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…
This paper examines the question of finding feasible points to discrete-time optimal control problems. The optimization problem of finding a feasible trajectory is transcribed to an unconstrained optimal control problem. An efficient…
We consider the problem of designing policies for Markov decision processes (MDPs) with dynamic coherent risk objectives and constraints. We begin by formulating the problem in a Lagrangian framework. Under the assumption that the risk…
A common strategy today to generate efficient locomotion movements is to split the problem into two consecutive steps: the first one generates the contact sequence together with the centroidal trajectory, while the second one computes the…
Connections between Deep Neural Networks (DNNs) training and optimal control theory has attracted considerable attention as a principled tool of algorithmic design. Differential Dynamic Programming (DDP) neural optimizer is a recently…
There has been significant interest in generalizations of the Nesterov accelerated gradient descent algorithm due to its improved performance guarantee compared to the standard gradient descent algorithm, and its applicability to large…
Deep reinforcement learning (DRL) has attracted much attention as an approach to solve optimal control problems without mathematical models of systems. On the other hand, in general, constraints may be imposed on optimal control problems.…
This paper extends the Model Predictive Static Programming (MPSP) framework for nonlinear systems evolving on Euclidean spaces to simple mechanical systems evolving on Lie groups. Classical optimal control approaches based on Pontryagin's…
This paper introduces a novel Differential Dynamic Programming (DDP) algorithm for solving discrete-time finite-horizon optimal control problems with inequality constraints. Two variants, namely Feasible- and Infeasible-IPDDP algorithms,…
Dynamic maneuvers for legged robots present a difficult challenge due to the complex dynamics and contact constraints. This paper introduces a versatile trajectory optimization framework for continuous-time multi-phase problems. We…
This paper presents a Differential Dynamic Programming (DDP) framework for trajectory optimization (TO) of hybrid systems with state-based switching. The proposed Hybrid Systems DDP (HS-DDP) approach is considered for application to…
Interpretation of Deep Neural Networks (DNNs) training as an optimal control problem with nonlinear dynamical systems has received considerable attention recently, yet the algorithmic development remains relatively limited. In this work, we…
Motion planning for manipulators under task space constraints is difficult as it constrains the joint configurations to always lie on an implicitly defined manifold. It is possible to view task constrained motion planning as an optimization…
Motion planning and control are two core components of the robotic systems autonomy stack. The standard approach to combine these methodologies comprises an offline/open-loop stage, planning, that designs a feasible and safe trajectory to…
Differential equations (DE) constrained optimization plays a critical role in numerous scientific and engineering fields, including energy systems, aerospace engineering, ecology, and finance, where optimal configurations or control…
Embedding parameterized optimization problems as layers into machine learning architectures serves as a powerful inductive bias. Training such architectures with stochastic gradient descent requires care, as degenerate derivatives of the…
This paper presents a spatial-based trajectory planning method for automated vehicles under actuator, obstacle avoidance, and vehicle dimension constraints. Starting from a nonlinear kinematic bicycle model, vehicle dynamics are transformed…
In this paper, we propose two novel decentralized optimization frameworks for multi-agent nonlinear optimal control problems in robotics. The aim of this work is to suggest architectures that inherit the computational efficiency and…
In this paper, we study representation formulas for finite-horizon optimal control problems with or without state constraints, unifying two different viewpoints: the Lagrangian and dynamic programming (DP) frameworks. In a recent work [1],…
This paper generalizes a previously-conceived, continuation-based optimization technique for scalar objective functions on constraint manifolds to cases of periodic and quasiperiodic solutions of delay-differential equations. A Lagrange…