Journal
IEEE TRANSACTIONS ON ROBOTICS
Volume 23, Issue 6, Pages 1277-1285Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TRO.2007.909805
Keywords
3-DOF; energy-based control; swing-up control; the Lyapunov stability theory; underactuated robots
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This paper concerns a swing-up control problem for a three-link gymnastic planar robot in a vertical plane with its first joint being passive (unactuated) and the rest being active (actuated). The objectives of this paper are to: 1) design a controller under which the robot can be brought into any arbitrarily small neighborhood of the upright equilibrium point, where all three links of the robot remain in their upright positions; and 2) attain a global analysis of the motion of the robot under the controller. To tailor the energy-based control approach to achieve the aforementioned objectives, first, this paper considers the links 2 and 3 as a virtually composite link, and proposes a coordinate transformation of the angles of active joints. Second, this paper constructs a novel Lyapunov function based on the transformation, and devises an energy-based swing-up controller. Third, this paper carries out a global analysis of the motion of the robot under the controller, and establishes some conditions on control parameters for achieving the swing-up control objective. To validate the theoretical results obtained, this paper provides simulation results for a three-link robot with its mechanical parameters being obtained from a human gymnast.
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