TY - GEN
T1 - Trajectory generation on SE(3) with applications to a class of underactuated vehicles
AU - Dhullipalla, Mani H.
AU - Hamrah, Reza
AU - Sanyal, Amit K.
N1 - Publisher Copyright:
© 2017 IEEE.
PY - 2017/6/28
Y1 - 2017/6/28
N2 - This paper addresses the problem of generating a continuous and differentiable trajectory on the Lie group of rigid body motions, se(3), for a class of underactuated vehicles modeled as rigid bodies. The three rotational degrees of freedom (DOF) are independently actuated, while only one translational DOF is actuated by a body-fixed thrust vector. This model is applicable to a large set of unmanned vehicles, including fixed-wing and rotorcraft unmanned aerial vehicles (UAVs). The formulation utilizes exponential coordinates to express the underactuation constraint as an intrinsic part of the problem. It provides steps to generate a rest-to-rest trajectory after obtaining conditions that guarantee controllability. An attitude trajectory is selected to satisfy the given initial and final attitude state. The position trajectory generation is subsequently posed as an optimal control problem expressed as a linear quadratic regulator (LQR) in the exponential coordinates corresponding to position. As a result, an optimal position trajectory is obtained which ensures that the trajectory generated is feasible with realistic velocities and with given initial pose and final pose, while satisfying the underactuation constraint. Numerical simulation results are obtained that validate this trajectory generation scheme.
AB - This paper addresses the problem of generating a continuous and differentiable trajectory on the Lie group of rigid body motions, se(3), for a class of underactuated vehicles modeled as rigid bodies. The three rotational degrees of freedom (DOF) are independently actuated, while only one translational DOF is actuated by a body-fixed thrust vector. This model is applicable to a large set of unmanned vehicles, including fixed-wing and rotorcraft unmanned aerial vehicles (UAVs). The formulation utilizes exponential coordinates to express the underactuation constraint as an intrinsic part of the problem. It provides steps to generate a rest-to-rest trajectory after obtaining conditions that guarantee controllability. An attitude trajectory is selected to satisfy the given initial and final attitude state. The position trajectory generation is subsequently posed as an optimal control problem expressed as a linear quadratic regulator (LQR) in the exponential coordinates corresponding to position. As a result, an optimal position trajectory is obtained which ensures that the trajectory generated is feasible with realistic velocities and with given initial pose and final pose, while satisfying the underactuation constraint. Numerical simulation results are obtained that validate this trajectory generation scheme.
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U2 - 10.1109/CDC.2017.8264029
DO - 10.1109/CDC.2017.8264029
M3 - Conference contribution
AN - SCOPUS:85046119982
T3 - 2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017
SP - 2557
EP - 2562
BT - 2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 56th IEEE Annual Conference on Decision and Control, CDC 2017
Y2 - 12 December 2017 through 15 December 2017
ER -