Trajectory tracking for fully actuated mechanical systems

Bullo, Francesco; Murray, Richard M.

doi:10.23919/ecc.1997.7082530

Cited by 13 publications

(12 citation statements)

References 19 publications

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“…The form (2.9) was reported in [59] and later in [60,61], but was already derived before in [62]. Expression (2.13) was reported in [58].…”

Section: Motion Parameterization Via the Exponential Mapmentioning

confidence: 94%

“…The expression (2.14) was reported in [59][60][61], and (2.16) was used in [58]. In the form (2.15) and (2.16), the inverse can be numerically evaluated without difficulties.…”

Section: Motion Parameterization Via the Exponential Mapmentioning

confidence: 99%

“…Relations (2. 19), (2.20) and a slightly different form of (2.21), (2.22) were derived in [60] with help of computer algebra software.…”

Section: Motion Parameterization Via the Exponential Mapmentioning

confidence: 99%

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Review of the exponential and Cayley map on SE(3) as relevant for Lie group integration of the generalized Poisson equation and flexible multibody systems

Müller

2021

Proc. R. Soc. A.

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The exponential and Cayley maps on SE(3) are the prevailing coordinate maps used in Lie group integration schemes for rigid body and flexible body systems. Such geometric integrators are the Munthe–Kaas and generalized- α schemes, which involve the differential and its directional derivative of the respective coordinate map. Relevant closed form expressions, which were reported over the last two decades, are scattered in the literature, and some are reported without proof. This paper provides a reference summarizing all relevant closed-form relations along with the relevant proofs, including the right-trivialized differential of the exponential and Cayley map and their directional derivatives (resembling the Hessian). The latter gives rise to an implicit generalized- α scheme for rigid/flexible multibody systems in terms of the Cayley map with improved computational efficiency.

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“…The form (2.9) was reported in [59] and later in [60,61], but was already derived before in [62]. Expression (2.13) was reported in [58].…”

Section: Motion Parameterization Via the Exponential Mapmentioning

confidence: 94%

“…The expression (2.14) was reported in [59][60][61], and (2.16) was used in [58]. In the form (2.15) and (2.16), the inverse can be numerically evaluated without difficulties.…”

Section: Motion Parameterization Via the Exponential Mapmentioning

confidence: 99%

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Review of the exponential and Cayley map on SE(3) as relevant for Lie group integration of the generalized Poisson equation and flexible multibody systems

Müller

2021

Proc. R. Soc. A.

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“…Jen-Te Yu [21] system. The tracking on 𝑆𝑂(3) based on exponential coordinates has also been investigated in [22], proposed to design tracking controllers for mechanical systems defined on the group of rotations 𝑆𝑂(3).…”

Section: Introductionmentioning

confidence: 99%

Attitude Control of a Quadrotor with Fuzzy Logic Controller on SO(3)

Ginting¹,

Doo

Pollo

et al. 2022

Journal of Robotics and Control

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A quadrotor is an unmanned aerial vehicle (UAV) with two pairs of rotors rotating in opposite directions. Some of its unique abilities are hovering and vertical take-off and landing (VTOL). Most recent works carried out the UAVs' rotation parametrization using Euler angles and a quaternion. Those UAVs suffer from singularities and ambiguities. A geometric control is generally used to deal with those problems. Exponential coordinate in the geometric control maps R3 into SO(3). This paper presented a fuzzy logic controller on SO(3) to control the attitude of the quadrotor. The input of the fuzzy logic controller is the angular velocity (ω) and exponential coordinate error of rotation (ζ), while the output is torque (τ). The error function in this controller is a rotation matrix on SO(3). This proposed controller can control the attitude of the quadrotor based on the expected attitude for maneuvers both on one axis and all axis with a steady-state error of about 0.02 rad.

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“…This includes PD control on the Euclidean group [Bullo and Murray, 1999;Leonard and Krishnaprasad 1995], tracking problems [Han and Park, 2001;Han, 2004], and estimation [Lo and Eshleman, 1979]. The representation and estimation of spatial uncertainty has also received attention in the robotics and vision literature [Smith and Cheeseman, 1986;Su and Lee, 1992].…”

Section: Introductionmentioning

confidence: 99%

Advances in Robot Kinematics

2006

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Trajectory tracking for fully actuated mechanical systems

Cited by 13 publications

References 19 publications

Review of the exponential and Cayley map on SE(3) as relevant for Lie group integration of the generalized Poisson equation and flexible multibody systems

Review of the exponential and Cayley map on SE(3) as relevant for Lie group integration of the generalized Poisson equation and flexible multibody systems

Attitude Control of a Quadrotor with Fuzzy Logic Controller on SO(3)

Advances in Robot Kinematics

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