Related papers: Optimal Trajectory Tracking of Nonholonomic Mechan…

A geometric method is described to characterize the different kinds of extremals in optimal control theory. This comes from the use of a presymplectic constraint algorithm starting from the necessary conditions given by Pontryagin's Maximum…

Learning to control unknown nonlinear dynamical systems is a fundamental problem in reinforcement learning and control theory. A commonly applied approach is to first explore the environment (exploration), learn an accurate model of it…

A geometric approach to kinematics in control theory is illustrated. A non-linear control system is derived for the problem and the Pontryagin maximum principle is used to find the time-optimal trajectories of the Parallel navigation. The…

Nonlinear control-affine systems with time-varying vector fields are considered in the paper. We propose a unified control design scheme with oscillating inputs for solving the trajectory tracking and stabilization problems. This…

A control optimization approach is presented for a chaser spacecraft tasked with maintaining proximity to a target space object while avoiding collisions. The target object trajectory is provided numerically to account for both passive…

Real-world environments are inherently uncertain, and to operate safely in these environments robots must be able to plan around this uncertainty. In the context of motion planning, we desire systems that can maintain an acceptable level of…

We study a trajectory-planning problem whose solution path evolves by means of a Lie group action and passes near a designated set of target positions at particular times. This is a higher-order variational problem in optimal control,…

This paper proposes a nonlinear guidance algorithm for fuel-optimal impulsive trajectories for rendezvous operations close to a reference orbit. The approach involves overparameterized monomial coordinates and a high-order approximation of…

This paper presents a control method and trajectory planner for vehicles with first-order nonholonomic constraints that guarantee asymptotic convergence to a time-indexed trajectory. To overcome the nonholonomic constraint, a fixed point in…

This paper addresses the nonovershooting control problem for strict-feedback nonlinear systems with unknown control direction. We propose a method that integrates extremum seeking with Lie bracket-based design to achieve approximately…

Trajectory optimization is a fundamental stochastic optimal control problem. This paper deals with a trajectory optimization approach for dynamical systems subject to measurement noise that can be fitted into linear time-varying stochastic…

In this paper, we develop the extremum-seeking approach to generate admissible trajectories in a neighborhood of a given reference curve in the state space. The cost function of the problem represents the distance between the current system…

This paper presents, using dynamical system theory, a framework for investigating the turnpike property in nonlinear optimal control. First, it is shown that a turnpike-like property appears in general dynamical systems with hyperbolic…

We propose an approach to trajectory optimization for piecewise polynomial systems based on the recently proposed graphs of convex sets framework. We instantiate the framework with a convex relaxation of optimal control based on occupation…

We address the risk bounded trajectory optimization problem of stochastic nonlinear robotic systems. More precisely, we consider the motion planning problem in which the robot has stochastic nonlinear dynamics and uncertain initial…

In this paper we study the problem of designing periodic orbits for a special class of hybrid systems, namely mechanical systems with underactuated continuous dynamics and impulse events. We approach the problem by means of optimal control.…

Motion trajectory planning is one crucial aspect for automated vehicles, as it governs the own future behavior in a dynamically changing environment. A good utilization of a vehicle's characteristics requires the consideration of the…

In this paper, we compare the performance of different numerical schemes in approximating Pontryagin's Maximum Principle's necessary conditions for the optimal control of nonholonomic systems. Retraction maps are used as a seed to construct…

The paper presents necessary and sufficient conditions for the order reduction of optimal control systems. Exploring the corresponding Hamiltonian system allows to solve the order reduction problem in terms of dynamical systems,…

Iterative trajectory optimization techniques for non-linear dynamical systems are among the most powerful and sample-efficient methods of model-based reinforcement learning and approximate optimal control. By leveraging time-variant local…