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We present LQR-CBF-RRT*, an incremental sampling-based algorithm for offlinemotion planning. Our framework leverages the strength of Control BarrierFunctions (CBFs) and Linear Quadratic Regulators (LQR) to generatesafety-critical and optimal trajectories for a robot with dynamics described byan affine control system. CBFs are used for safety guarantees, while LQRs areemployed for optimal control synthesis during edge extensions. PopularCBF-based formulations for safety critical control require solving QuadraticPrograms (QPs), which can be computationally expensive. Moreover, LQR-basedcontrollers require repetitive applications of first-order Taylorapproximations for nonlinear systems, which can also create an additionalcomputational burden. To improve the motion planning efficiency, we verify thesatisfaction of the CBF constraints directly in edge extension to avoid theburden of solving the QPs. We store computed optimal LQR gain matrices in ahash table to avoid re-computation during the local linearization of therewiring procedure. Lastly, we utilize the Cross-Entropy Method for importancesampling to improve sampling efficiency. Our results show that the proposedplanner surpasses its counterparts in computational efficiency and performswell in an experimental setup.

LQR-CBF-RRT*: Safe and Optimal Motion Planning