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Trajectory optimization has been used extensively in robotic systems. Inparticular, iterative Linear Quadratic Regulator (iLQR) has performed well asan off-line planner and online nonlinear model predictive control solver, witha lower computational cost. However, standard iLQR cannot handle anyconstraints or perform reasonable initialization of a state trajectory. In thispaper, we propose a hybrid constrained iLQR variant with a multiple-shootingframework to incorporate general inequality constraints and infeasible statesinitialization. The main technical contributions are twofold: 1) In addition toinheriting the simplicity of the initialization in multiple-shooting settings,a two-stage framework is developed to deal with state and/or controlconstraints robustly without loss of the linear feedback term of iLQR. Such ahybrid strategy offers fast convergence of constraint satisfaction. 2) Animproved globalization strategy is proposed to exploit the coupled effectsbetween line-searching and regularization, which is able to enhance thenumerical robustness of the constrained iLQR approaches. Our approach is testedon various constrained trajectory optimization problems and outperforms thecommonly-used collocation and shooting methods.

Inequality Constrained Trajectory Optimization with A Hybrid Multiple-shooting iLQR