TY - JOUR
T1 - Solving Trajectory Optimization Problems in the Presence of Probabilistic Constraints
AU - Chai, Runqi
AU - Savvaris, Al
AU - Tsourdos, Antonios
AU - Chai, Senchun
AU - Xia, Yuanqing
AU - Wang, Shuo
N1 - Publisher Copyright:
© 2013 IEEE.
PY - 2020/10
Y1 - 2020/10
N2 - The objective of this paper is to present an approximation-based strategy for solving the problem of nonlinear trajectory optimization with the consideration of probabilistic constraints. The proposed method defines a smooth and differentiable function to replace probabilistic constraints by the deterministic ones, thereby converting the chance-constrained trajectory optimization model into a parametric nonlinear programming model. In addition, it is proved that the approximation function and the corresponding approximation set will converge to that of the original problem. Furthermore, the optimal solution of the approximated model is ensured to converge to the optimal solution of the original problem. Numerical results, obtained from a new chance-constrained space vehicle trajectory optimization model and a 3-D unmanned vehicle trajectory smoothing problem, verify the feasibility and effectiveness of the proposed approach. Comparative studies were also carried out to show the proposed design can yield good performance and outperform other typical chance-constrained optimization techniques investigated in this paper.
AB - The objective of this paper is to present an approximation-based strategy for solving the problem of nonlinear trajectory optimization with the consideration of probabilistic constraints. The proposed method defines a smooth and differentiable function to replace probabilistic constraints by the deterministic ones, thereby converting the chance-constrained trajectory optimization model into a parametric nonlinear programming model. In addition, it is proved that the approximation function and the corresponding approximation set will converge to that of the original problem. Furthermore, the optimal solution of the approximated model is ensured to converge to the optimal solution of the original problem. Numerical results, obtained from a new chance-constrained space vehicle trajectory optimization model and a 3-D unmanned vehicle trajectory smoothing problem, verify the feasibility and effectiveness of the proposed approach. Comparative studies were also carried out to show the proposed design can yield good performance and outperform other typical chance-constrained optimization techniques investigated in this paper.
KW - Approximation function
KW - chance-constrained
KW - nonlinear programming
KW - probabilistic constraints
KW - trajectory optimization
UR - http://www.scopus.com/inward/record.url?scp=85091547133&partnerID=8YFLogxK
U2 - 10.1109/TCYB.2019.2895305
DO - 10.1109/TCYB.2019.2895305
M3 - Article
C2 - 30763253
AN - SCOPUS:85091547133
SN - 2168-2267
VL - 50
SP - 4332
EP - 4345
JO - IEEE Transactions on Cybernetics
JF - IEEE Transactions on Cybernetics
IS - 10
M1 - 8637163
ER -