Related papers: Symmetry Reduction, Contact Geometry and Nonlinear…
This paper explores the role of symmetries and reduction in nonlinear control and optimal control systems. The focus of the paper is to give a geometric framework of symmetry reduction of optimal control systems as well as to show how to…
Control systems of interest are often invariant under Lie groups of transformations. For such control systems, a geometric framework based on Lie symmetry is formulated, and from this a sufficient condition for dynamic feedback…
We discuss smooth nonlinear control systems with symmetry. For a free and proper action of the symmetry group, the reduction of symmetry gives rise to a reduced smooth nonlinear control system. If the action of the symmetry group is only…
This paper demonstrates a refined approach to solving dynamic optimization problems for underactuated marine surface vessels. To this end the differential flatness of a mathematical model assuming full actuation is exploited to derive an…
Aircraft failures alter dynamics, diminishing manoeuvrability. Such manoeuvring flight envelope variations, governed by the aircraft's complex nonlinear dynamics, are unpredictable by pilots and existing flight management systems. To…
We develop an optimization-based framework for joint real-time trajectory planning and feedback control of feedback-linearizable systems. To achieve this goal, we define a target trajectory as the optimal solution of a time-varying…
The feedback linearization method is further developed for the controller design on general nonlinear systems. Through the Lyapunov stability theory, the intractable nonlinear implicit algebraic control equations are effectively solved, and…
Lie symmetry analysis is applied to study the nonlinear rotating shallow water equations. The 9-dimensional Lie algebra of point symmetries admitted by the model is found. It is shown that the rotating shallow water equations are related…
Robots must make and break contact with the environment to perform useful tasks, but planning and control through contact remains a formidable challenge. In this work, we achieve real-time contact-implicit model predictive control with a…
Very high dimensional nonlinear systems arise in many engineering problems due to semi-discretization of the governing partial differential equations, e.g. through finite element methods. The complexity of these systems present…
For a system of partial differential equations admitting point, contact, or higher symmetries, the framework of invariant reduction systematically computes how invariant geometric structures, such as conservation laws, presymplectic…
We introduce the concept of a control contraction metric, extending contraction analysis to constructive nonlinear control design. We derive sufficient conditions for exponential stabilizability of all trajectories of a nonlinear control…
We study the reduction by symmetry for optimality conditions in optimal control problems of left-invariant affine multi-agent control systems, with partial symmetry breaking cost functions for continuous-time and discrete-time systems. We…
Symmetries of nonlinear control systems in state representation are considered. To this end, a geometric approach to ordinary differential equations is advocated. Invariant feedback laws for systems with Lie symmetries, i.e. feedback laws…
Actions of Lie groups on presymplectic manifolds are analyzed, introducing the suitable comomentum and momentum maps. The subsequent theory of reduction of presymplectic dynamical systems with symmetry is studied. In this way, we give a…
To be feasible for computationally intensive applications such as parametric studies, optimization and control design, large-scale finite element analysis requires model order reduction. This is particularly true in nonlinear settings that…
We propose an output feedback control-based motion planning technique for agents to enable them to converge to a specified polynomial trajectory while imposing a set of safety constraints on our controller to avoid collisions within the…
Tracking controllers enable robotic systems to accurately follow planned reference trajectories. In particular, reinforcement learning (RL) has shown promise in the synthesis of controllers for systems with complex dynamics and modest…
We present a contact-implicit trajectory optimization framework that can plan contact-interaction trajectories for different robot architectures and tasks using a trivial initial guess and without requiring any parameter tuning. This is…
Trajectory tracking for the kinematic unicycle has been heavily studied for several decades. The unicycle admits a natural $\SE(2)$ symmetry, a key structure exploited in many of the most successful nonlinear controllers in the literature.…