TY - GEN
T1 - Single Leg Dynamic Motion Planning with Mixed-Integer Convex Optimization
AU - Ding, Yanran
AU - Li, Chuanzheng
AU - Park, Hae Won
N1 - Funding Information:
This project is supported by NAVER LABS Corp. under grant 087387, and Air Force Office of Scientific Research under grant FA2386-17-1-4665.
Publisher Copyright:
© 2018 IEEE.
PY - 2018/12/27
Y1 - 2018/12/27
N2 - This paper proposes a mixed-integer convex programming formulation for dynamic motion planning. Many dynamic constraints such as the actuator torque constraint are nonlinear and non-convex due to the trigonometrical terms from the Jacobian matrix. This often causes the optimization problem to converge to local optima or even infeasible set. In this paper, we convexify the torque constraint by formulating a mixed-integer quadratically-constrained program (MIQCP). More specifically, the workspace is discretized into a union of disjoint polytopes and torque constraint is enforced upon a convex outer approximation of the torque ellipsoid, obtained by solving a semidefinite program (SDP). Bilinear terms are approximated by McCormick envelope convex relaxation. The proposed MIQCP framework could be solved efficiently to global optimum and the generated trajectories could exploit the rich features of the rough terrain without any initial guess from the designer. The demonstrated experiment results prove that this approach is currently capable of planning consecutive jumps that navigates a single-legged robot through challenging terrains.
AB - This paper proposes a mixed-integer convex programming formulation for dynamic motion planning. Many dynamic constraints such as the actuator torque constraint are nonlinear and non-convex due to the trigonometrical terms from the Jacobian matrix. This often causes the optimization problem to converge to local optima or even infeasible set. In this paper, we convexify the torque constraint by formulating a mixed-integer quadratically-constrained program (MIQCP). More specifically, the workspace is discretized into a union of disjoint polytopes and torque constraint is enforced upon a convex outer approximation of the torque ellipsoid, obtained by solving a semidefinite program (SDP). Bilinear terms are approximated by McCormick envelope convex relaxation. The proposed MIQCP framework could be solved efficiently to global optimum and the generated trajectories could exploit the rich features of the rough terrain without any initial guess from the designer. The demonstrated experiment results prove that this approach is currently capable of planning consecutive jumps that navigates a single-legged robot through challenging terrains.
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U2 - 10.1109/IROS.2018.8594161
DO - 10.1109/IROS.2018.8594161
M3 - Conference contribution
AN - SCOPUS:85062965471
T3 - IEEE International Conference on Intelligent Robots and Systems
SP - 7391
EP - 7396
BT - 2018 IEEE/RSJ International Conference on Intelligent Robots and Systems, IROS 2018
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2018 IEEE/RSJ International Conference on Intelligent Robots and Systems, IROS 2018
Y2 - 1 October 2018 through 5 October 2018
ER -