Control of mechanical systems with second-order nonholonomic constraints: underactuated manipulators

Oriolo, Giuseppe; Nakamura, Yoshihiko

doi:10.1109/cdc.1991.261620

Cited by 289 publications

(157 citation statements)

References 10 publications

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“…With reference to [16], the constraint in Eq. 7 is: 1) partially integrable if and only if: a) the gravitational torque G u is constant; b) the unactuated joint variables φ do not appear in the inertia matrix M(q).…”

Section: Integrability Of Constraintsmentioning

confidence: 99%

Trajectory planning and control of an underactuated dynamically stable single spherical wheeled mobile robot

Nagarajan

Kantor

Hollis

2009

2009 IEEE International Conference on Robotics and Automation

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Abstract-The ballbot is a dynamically stable mobile robot that moves on a single spherical wheel and is capable of omnidirectional movement. The ballbot is an underactuated system with nonholonomic dynamic constraints. The authors propose an offline trajectory planning algorithm that provides a class of parametric trajectories to the unactuated joint in order to reach desired static configurations of the system with regard to the dynamic constraint. The parameters of the trajectories are obtained using optimization techniques. A feedback controller is proposed that ensures accurate trajectory tracking. The trajectory planning algorithm and tracking controller are validated experimentally. The authors also extend the offline trajectory planning algorithm to a generalized case of motion between non-static configurations.

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Section: Integrability Of Constraintsmentioning

confidence: 99%

Trajectory planning and control of an underactuated dynamically stable single spherical wheeled mobile robot

Nagarajan

Kantor

Hollis

2009

2009 IEEE International Conference on Robotics and Automation

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“…As an interesting class of nonlinear systems the tangent linear approximation of which is not controllable, underactuated robots, like flexible or non-holonomic ones, have been soon targeted by researchers from the automatic control area. For example, [11,10,12] consider planar robots with joint elasticities; more generally, [13] studies robotics systems with 2nd order non-holonomic constraints. The capacity of controlling underactuated robots using their dynamical coupling characteristics is modelled in [7,8].…”

Section: A Brief Tour Of the Literaturementioning

confidence: 99%

Can an underactuated leg with a passive spring at the knee achieve a ballistic step?

Espiau

Guigues

Pissard-Gibollet

2000

Experimental Robotics VI

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Abstract:In this paper, we present the design and the results of a control scheme aimed at moving an underactuated double pendulum simulating a leg. The system is actuated at the hip and includes a spring at the knee. It interacts with the grou nd, which is in fact a treadmill, through a telescopic foot made of a linear spri ng and a damper. The control scheme is different in the 2 phases, swing and stance, and a repetitive step is achieved by switching between these two controls. The paper describes the used models, the control algorithms and their implementation. It pr esents also experimental results of the approach. Key-words:

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“…This theorem is applied to general form of underactuated manipulators [20] where the possibility of asymptotic stabilization to the equilibrium manifold is shown. General class of UNMS can be asymptotically stabilized using discontinuous [4], structural-variable [5] or time-variant [12] control feedback law.…”

Section: Introductionmentioning

confidence: 99%

“…General class of UNMS can be asymptotically stabilized using discontinuous [4], structural-variable [5] or time-variant [12] control feedback law. Conditions for partial and full integrability of underactuated robot manipulators are shown in [20], and for underactuated vehicles in [31].…”

Section: Introductionmentioning

confidence: 99%

Simultaneous stabilization and trajectory tracking of underactuated mechanical systems with included actuators dynamics

et al. 2012

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The paper deals with a novel control algorithm for simultaneous stabilization and trajectory tracking of underactuated nonlinear mechanical systems (UNMS) with included actuators dynamics. Simultaneous stabilization and trajectory tracking refer to arbitrary chosen actuated and unactuated degrees of freedom (DOF) of the system. The proposed control approach can be applied both to the second-order nonholonomic systems and the systems with input coupling, while a general model of actuators dynamics includes electrical, pneumatic, and hydraulic drives. Control law is based on linear combination of two control signals, where the first signal is designed to separately control only actuated DOF, and second to separately control only unactuated DOF. Simulation example of rotational inverted pendulum driven by electrical DC motor is presented, showing the effectiveness of the proposed approach.

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Control of mechanical systems with second-order nonholonomic constraints: underactuated manipulators

Cited by 289 publications

References 10 publications

Trajectory planning and control of an underactuated dynamically stable single spherical wheeled mobile robot

Trajectory planning and control of an underactuated dynamically stable single spherical wheeled mobile robot

Can an underactuated leg with a passive spring at the knee achieve a ballistic step?

Simultaneous stabilization and trajectory tracking of underactuated mechanical systems with included actuators dynamics

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