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Variational integrators are momentum-preserving and symplectic numerical methods used to propagate the evolution of Hamiltonian systems. In this paper, we introduce a new class of variational integrators that achieve fourth-order…
This paper develops numerical methods for optimal control of mechanical systems in the Lagrangian setting. It extends the theory of discrete mechanics to enable the solutions of optimal control problems through the discretization of…
Robot design optimization, imitation learning and system identification share a common problem which requires optimization over robot or task parameters at the same time as optimizing the robot motion. To solve these problems, we can use…
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…
Trajectory optimization is an efficient approach for solving optimal control problems for complex robotic systems. It relies on two key components: first the transcription into a sparse nonlinear program, and second the corresponding solver…
Numerical methods that preserves geometric invariants of the system such as energy, momentum and symplectic form, are called geometric integrators. These include variational integrators as an important subclass of geometric integrators. The…
Trajectory optimization considers the problem of deciding how to control a dynamical system to move along a trajectory which minimizes some cost function. Differential Dynamic Programming (DDP) is an optimal control method which utilizes a…
Distributed optimization algorithms are used in a wide variety of problems involving complex network systems where the goal is for a set of agents in the network to solve a network-wide optimization problem via distributed update rules. In…
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…
Mixed-integer optimization is at the core of many online decision-making systems that demand frequent updates of decisions in real time. However, due to their combinatorial nature, mixed-integer linear programs (MILPs) can be difficult to…
We reconsider the variational integration of optimal control problems for mechanical systems based on a direct discretization of the Lagrange-d'Alembert principle. This approach yields discrete dynamical constraints which by construction…
Optimal actuator and control design is studied as a multi-level optimisation problem, where the actuator design is evaluated based on the performance of the associated optimal closed loop. The evaluation of the optimal closed loop for a…
In recent years, much effort in designing numerical methods for the simulation and optimization of mechanical systems has been put into schemes which are structure preserving. One particular class are variational integrators which are…
A geometric derivation of numerical integrators for optimal control problems is proposed. It is based in the classical technique of generating functions adapted to the special features of optimal control problems.
Variational quantum algorithms are a class of techniques intended to be used on near-term quantum computers. The goal of these algorithms is to perform large quantum computations by breaking the problem down into a large number of shallow…
Driven by increased complexity of dynamical systems, the solution of system of differential equations through numerical simulation in optimization problems has become computationally expensive. This paper provides a smart data driven…
A multi-agent system designed to achieve distance-based shape control with flocking behavior can be seen as a mechanical system described by a Lagrangian function and subject to additional external forces. Forced variational integrators are…
Differential Dynamic Programming (DDP) is an efficient trajectory optimization algorithm relying on second-order approximations of a system's dynamics and cost function, and has recently been applied to optimize systems with time-invariant…
Surrogate model-based optimization has been increasingly used in the field of engineering design. It involves creating a surrogate model with objective functions or constraints based on the data obtained from simulations or real-world…
The numerical analysis of variational integrators relies on variational error analysis, which relates the order of accuracy of a variational integrator with the order of approximation of the exact discrete Lagrangian by a computable…