Related papers: Computational Geometric Optimal Control of Rigid B…
This paper formulates an optimal control problem for a system of rigid bodies that are connected by ball joints and immersed in an irrotational and incompressible fluid. The rigid bodies can translate and rotate in three-dimensional space,…
A time optimal attitude control problem is studied for the dynamics of a rigid body. The objective is to minimize the time to rotate the rigid body to a desired attitude and angular velocity while subject to constraints on the control…
In this paper we study a discrete variational optimal control problem for the rigid body. The cost to be minimized is the external torque applied to move the rigid body from an initial condition to a pre-specified terminal condition.…
An efficient and accurate computational approach is proposed for optimal attitude control of a rigid body. The problem is formulated directly as a discrete time optimization problem using a Lie group variational integrator. Discrete…
Discrete control systems, as considered here, refer to the control theory of discrete-time Lagrangian or Hamiltonian systems. These discrete-time models are based on a discrete variational principle, and are part of the broader field of…
Optimal control problems are formulated and efficient computational procedures are proposed for combined orbital and rotational maneuvers of a rigid body in three dimensions. The rigid body is assumed to act under the influence of forces…
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…
We establish a variety of results extending the well-known Pontryagin maximum principle of optimal control to discrete-time optimal control problems posed on smooth manifolds. These results are organized around a new theorem on critical and…
Optimal control problems are formulated and efficient computational procedures are proposed for attitude dynamics of a rigid body with symmetry. The rigid body is assumed to act under a gravitational potential and under a structured control…
In this paper we study a discrete variational optimal control problem for the rigid body. The cost to be minimized is the external torque applied to move the rigid body from an initial condition to a pre-specified terminal condition.…
In this paper, we describe a constrained Lagrangian and Hamiltonian formalism for the optimal control of nonholonomic mechanical systems. In particular, we aim to minimize a cost functional, given initial and final conditions where the…
In this paper we present a general framework that allows one to study discretization of certain dynamical systems. This generalizes earlier work on discretization of Lagrangian and Hamiltonian systems on tangent bundles and cotangent…
Numerical methods that preserve geometric invariants of the system, such as energy, momentum or the symplectic form, are called geometric integrators. In this paper we present a method to construct symplectic-momentum integrators for…
Adaptive tracking control for rigid body dynamics is of critical importance in control and robotics, particularly for addressing uncertainties or variations in system model parameters. However, most existing adaptive control methods are…
The optimal control of a mechanical system is of crucial importance in many realms. Typical examples are the determination of a time-minimal path in vehicle dynamics, a minimal energy trajectory in space mission design, or optimal motion…
In this paper, we consider a geometric formalism for optimal control of underactuated mechanical systems. Our techniques are an adaptation of the classical Skinner and Rusk approach for the case of Lagrangian dynamics with higher-order…
In this paper we study, from a variational and geometrical point of view, second-order variational problems on Lie groupoids and the construction of variational integrators for optimal control problems. First, we develop variational…
Inspired by flight characteristics captured from live Monarch butterflies, an optimal control problem is presented while accounting the effects of low-frequency flapping and abdomen undulation. A flapping-wing aerial vehicle is modeled as…
We develop the equations of motion for full body models that describe the dynamics of rigid bodies, acting under their mutual gravity. The equations are derived using a variational approach where variations are defined on the Lie group of…
We geometrically describe optimal control problems in terms of Morse families in the Hamiltonian framework. These geometric structures allow us to recover the classical first order necessary conditions for optimality and the starting point…