Abstract: This paper presents a nonlinear H∞ control law for underactuated mechanical systems with input coupling. Apart from the controlled degrees of freedom (DOF), the proposed controller considers the dynamics of the remaining DOF in the cost variable, which allows to stabilize them. The underactuated mechanical system is normalized to obtain a diagonal inertia matrix allowing to weigh with...

This paper studies control properties of the dynamics of underactuated vehicles (e.g. underactuated surface vessels, underwater vehicles, aeroplanes or spacecraft). The unactuated dynamics implies constraints on the accelerations. Both the necessary and suucient conditions for these constraints to be second-order nonholonomic, rst-order nonholonomic or holonomic are developed. It is shown that ...

We propose a constructive control design for stabilization of non-periodic trajectories of underactuated robots. An important example of such a system is an underactuated “dynamic walking” biped robot traversing rough or uneven terrain. The stabilization problem is inherently challenging due to the nonlinearity, open-loop instability, hybrid (impact) dynamics, and target motions which are not k...

This paper considers the task of stabilizing underactuated mechanical systems via high-amplitude, high-frequency actuation. Using higher order averaging techniques, we extend previous work to the case where symmetric products of order higher than one are necessary for controllability. We first introduce a second order averaged mechanical system model that incorporates higher order terms. Using ...

We propose a method to drive an underactuated manipulator among obstacles in its workspace. The method allows for collision-free trajectories to be generated from the dynamic equations of the manipulator. When the passive joints are locked, these trajectories lie on surfaces parallel to the axes of the active joints. When the passive joints are free, the trajectories lie on surfaces determined ...

This paper addresses the feedback control design for a class of nonholonomic systems which are subject to inequality stateconstraints defining a constrained (viability) set K. Based on concepts from viability theory, the necessary conditions forselecting viable controls for a nonholonomic system are given, so that system trajectories starting in K always remain inK. Furthermore, a c...

Lagrangian control systems that are diierentially at with at outputs that only depend on connguration variables are said to be connguration at. We provide a complete characterisation of connguration atness for systems with n degrees of freedom and n ?1 controls whose range of control forces only depends on connguration and whose Lagrangian has the form of kinetic energy minus potential. The met...

This paper examines joint coupling in underactuated robotic grippers for unstructured environments where object properties and location may not be well known. A simplified grasper consisting of a pair of two-link planar fingers with compliant revolute joints was simulated as it grasped a target object. The joint coupling configuration of the gripper was varied in order to maximize successful gr...

In this paper, the model-based robotic control problem with disturbance attenuation (or robotic H∞ control problem), presented in Chen et all (1994), is extended to underactuated manipulators. The dynamic coupling between the links is used to control all manipulator’s free joints. A global explicit solution is found solving a minimax Bellman-Isaacs equation, generated via differential game theo...

A new method for control of underactuated nonlinear systems is proposed, based on introducing artificial invariants and using speed-gradient algorithms. General statement concerning achievement of the control goal is formulated and proven. Application of the proposed approach is illustrated by an example: stabilization of cart-pendulum oscillations around the upper equilibrium. Copyright c ©200...