David Auckly, Lev Kapitanski
In this paper we will discuss problems and techniques related to underactuated systems. We give a mathematical formulation of several problems arising from applications, review some standard and new techniques, and pose some interesting and challenging open questions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
In this paper we introduce a new method to design control laws for non-linear underactuated systems. Our method produces an infinite dimensional family of control laws, whereas most control techniques only produce a finite dimensional family. These control laws each come with a natural Lyapunov function. The inverted pendulum cart is used as an example. In addition, we construct an abstract system which is open loop unstable and cannot be stabilized using any linear control law, and demonstrate that our method produces a stabilizing control law.
This note describes two problems related to the digital implementation of control laws in the infinite dimensional family of matching control laws, namely state estimation and sampled data induced error. The entire family of control laws is written for an inverted pendulum cart. Numerical simulations which include sampled data and a state estimator are presented for one of the control laws in this family.
In this paper, we present a global state feedback tracking controller for underactuated surface marine vessels. This controller is based on saturated control inputs and, under an assumption on the reference trajectory, the closed-loop system is globally asymptotically stable (GAS). It has been designed using a 3 Degree of Freedom benchmark vessel model used in marine engineering. The main feature of our controller is the boundedness of the control inputs, which is an essential consideration in real life. In absence of velocity measurements, the controller works and remains stable with observer…
In this paper, the control problem for underactuated systems in the presence of external disturbances and model uncertainties is considered. An adaptive fuzzy sliding mode controller (AFSMC) is proposed to solve the problem, satisfying the robustness properties against uncertainties and disturbances. The designed controller can be applied to a wide class of underactuated systems and have fewer restrictions, compared with many pervious works. To evaluate the performance of proposed algorithm, it is applied to an underactuated inverted pendulum and a Translational Oscillator/Rotational Actuator …
We consider tracking control for multibody systems which are modelled using holonomic and nonholonomic constraints. Furthermore, the systems may be underactuated and contain kinematic loops and are thus described by a set of differential-algebraic equations that cannot be reformulated as ordinary differential equations in general. We propose a control strategy which combines a feedforward controller based on the servo-constraints approach with a feedback controller based on a recent funnel control design. As an important tool for both approaches we present a new procedure to derive the interna…
This paper solves the rendezvous problem for a network of underactuated rigid bodies such as quadrotor helicopters. A control strategy is presented that makes the centres of mass of the vehicles converge to an arbitrarily small neighborhood of one another. The convergence is global, and each vehicle can compute its own control input using only an on-board camera and a three-axis rate gyroscope. No global positioning system is required, nor any information about the vehicles' attitudes.
This paper derives nonlinear feedback control synthesis for general control affine systems using second-order actions---the needle variations of optimal control---as the basis for choosing each control response to the current state. A second result of the paper is that the method provably exploits the nonlinear controllability of a system by virtue of an explicit dependence of the second-order needle variation on the Lie bracket between vector fields. As a result, each control decision necessarily decreases the objective when the system is nonlinearly controllable using first-order Lie bracket…
This paper derives nonlinear feedback control synthesis for general control affine systems using second-order actions---the second-order needle variations of optimal control---as the basis for choosing each control response to the current state. A second result of the paper is that the method provably exploits the nonlinear controllability of a system by virtue of an explicit dependence of the second-order needle variation on the Lie bracket between vector fields. As a result, each control decision necessarily decreases the objective when the system is nonlinearly controllable using first-orde…
This work concerns the internal stabilization of underactuated linear systems of $m$ heat equations in cascade, where the control is placed internally in the first equation only and the diffusion coefficients are distinct. Combining the modal decomposition method with a recently introduced state-transformation approach for observation problems, a proportional-type stabilizing control is given explicitly. It is based on a transformation for the ODE system corresponding to the comparatively unstable modes into a target one, where calculation of the stabilization law is independent of the arbitra…
Stabilization of underactuated linear coupled reaction-diffusion PDEs via distributed or boundary actuation
本文提出一种基于模态分解和广义Sylvester方程的构造性镇定算法，解决具有不同扩散系数的级联线性反应-扩散PDE系统的欠驱动镇定问题，适用于分布式和边界控制。
Privacy-Preserving Formation Control for Networked Underactuated USVs: A Passivity-Based Approach
本文研究了在严格隐私要求下多无人水面舰艇的协同轨迹规划与跟踪控制，采用估计的舰队质心作为唯一共享变量，实现编队协调与隐私保护。基于此机制，为舰队生成编队轨迹，利用端口哈密顿系统建模集体动力学，并为每个USV设计基于被动性的跟踪控制器，通过实验验证了系统稳定性和有效编队跟踪。
Constructive Safety-Critical Control for a Class of Underactuated Systems: A Hierarchical Approach
针对类四旋翼欠驱动系统的安全关键控制设计难题，提出构造性分层控制框架，明确其自然分层架构的适用条件，设计了分层控制障碍函数合成流程并给出成功条件。
Motion planning and control are key problems in a collection of robotic applications including the design of autonomous agile vehicles and of minimalist manipulators. These problems can be accurately formalized within the language of affine connections and of geometric control theory. In this paper we overview recent results on kinematic controllability and on oscillatory controls. Furthermore, we discuss theoretical and practical open problems as well as we suggest control theoretical approaches to them.
In this paper we use an affine connection formulation to study an optimal control problem for a class of nonholonomic, under-actuated mechanical systems. In particular, we aim at minimizing the norm-squared of the control input to move the system from an initial to a terminal state. We consider systems evolving on general manifolds. The class of nonholonomic systems we study in this paper includes, in particular, wheeled-type vehicles, which are important for many robotic locomotion systems. The two special aspects of this optimal control problem are the nonholonomic constraints and under-actu…
We deal with regular Lagrangian constrained systems which are invariant under the action of a symmetry group. Fixing a connection on the higher-order principal bundle where the Lagrangian and the (independent) constraints are defined, the higher-order Lagrange-Poincaré equations of classical mechanical systems with higher-order constraints are obtained from classical Lagrangian reduction. Higher-order Lagrange-Poincaré operator is introduced to characterize higher-order Lagrange-Poincaré equations. Interesting applications are derived as, for instance, the optimal control of an underactuated E…
Optimal control problems for underactuated mechanical systems can be seen as a higher-order variational problem subject to higher-order constraints (that is, when the Lagrangian function and the constraints depend on higher-order derivatives such as the acceleration, jerk or jounces). In this paper we discuss the variational formalism for the class of underactuated mechanical control systems when the configuration space is a trivial principal bundle and the construction of variational integrators for such mechanical control systems. An interesting family of geometric integrators can be defined…
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 efficient representation of a finite dimensional nonlinear programming problem, which in turn is constrained to apply to the underactuated case. It is illustrated how the properties of the flat output can be employed for the generation of an initial guess to be used in the optimization algorithm in the presence of static and dynamic obstacles. As an example en…
Passivity-based control of underactuated mechanical systems with Coulomb friction: Application to earthquake prevention
本文针对带库仑摩擦的非自治不连续欠驱动机械系统，基于类不变性原理扩展了无源性反馈连接理论，提出一种结构化无源性控制策略，通过恢复无源性、引入积分作用及考虑执行动力学实现系统稳定与跟踪，并应用于地震预防场景通过流体注入缓慢耗散地震能量。
Real-Time Control-Constrained DDP for Underactuated Balancing of Legged Robots
针对经典DDP处理控制约束的局限，提出ABC-DDP算法，结合可行性驱动多射击框架，实现欠驱动腿式机器人实时MPC，仿真验证其可完成静态双腿站立及多种动态运动。
Control of underactuated dynamical systems has been studied for decades in robotics, and is now emerging in other fields such as neuroscience. Most of the advances have been in model based control theory, which has limitations when the system under study is very complex and it is not possible to construct a model. This calls for data driven control methods like machine learning, which has spread to many fields in the recent years including control theory. However, the success of such algorithms has been dependent on availability of large datasets. Moreover, due to their black box nature, it is…
Stability Analysis of Geometric Control for a Canonical Class of Underactuated Aerial Vehicles with Spurious Forces
本文针对一类欠驱动空中飞行器，提出了一种考虑杂音力影响的几何控制稳定性分析方法，通过构建李雅普诺夫证明，实现了悬停平衡点的局部指数稳定性。
The goal of the present article is to study controllability properties of mixed systems of linear parabolic-transport equations, with possibly non-diagonalizable diffusion matrix, on the one-dimensional torus. The equations are coupled by zero or first order coupling terms, with constant coupling matrices, without any structure assumptions on them. The distributed control acts through a constant matrix operator on the system, so that there might be notably less controls than equations, encompassing the case of indirect and simultaneous controllability. More precisely, we prove that in small ti…
Dynamic attitude planning for trajectory tracking in underactuated VTOL UAVs
本文针对欠驱动VTOL无人机的轨迹跟踪控制问题，提出了一种以位置跟踪为主的目标，通过引入姿态规划器动态系统，确保满足主要目标，将姿态跟踪作为次要目标，只要期望轨迹满足特定可跟踪性条件即可实现。
The task of inducing, via continuous static state-feedback control, an asymptotically stable heteroclinic orbit in a nonlinear control system is considered in this paper. The main motivation comes from the problem of ensuring convergence to a so-called point-to-point maneuver in an underactuated mechanical system. Namely, to a smooth curve in its state--control space, which is consistent with the system dynamics and connects two (linearly) stabilizable equilibrium points. The proposed method uses a particular parameterization, together with a state projection onto the maneuver as to combine tw…
Stabilization of 1D Linear Hyperbolic Balance Laws by Integral Difference Control and Application to Networks Stabilization
研究一阶线性双曲型平衡律在一般驱动下的指数镇定，提出统一方法，整合多种欠驱动配置，应用于含环网络，基于反步变换和积分差分方程设计控制律，增益由降秩程序和插值方程解构建，通过数值模拟验证对特定循环网络的有效性。
A path-following collision-avoidance model predictive control (MPC) method is proposed which approximates obstacle shapes as convex polygons. Collision-avoidance is ensured by means of the signed distance function which is calculated efficiently as part of the MPC problem by making use of a dual formulation. The overall MPC problem can be solved by standard nonlinear programming (NLP) solvers. The dual signed distance formulation yields, besides the (dual) collision-avoidance constraints, norm, and consistency constraints. A novel approach is presented that combines the arising norm equality w…
Distributed end-effector formation control for mixed fully- and under-actuated manipulators with flexible joints
本文针对具有柔性关节的混合全驱动与欠驱动机械臂，提出基于虚拟弹簧的分布式控制律实现末端执行器编队保持，并刻画了可达编队形状集合，通过数值仿真验证了方法的有效性。
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。