Stochastic Extended LQR for Optimization-Based Motion Planning Under Uncertainty


We have a tendency to introduce a novel optimization-based mostly motion planner, the stochastic extended linear quadratic regulator (SELQR), which computes a trajectory and associated linear control policy with the objective of minimizing the expected value of a user-outlined cost function. SELQR applies to robotic systems that have stochastic nonlinear dynamics with motion uncertainty modeled by Gaussian distributions which will be state- and management-dependent. In every iteration, SELQR uses a combination of forward and backward price iteration to estimate the price-to-come and the price-to-select every state along a trajectory. SELQR then regionally optimizes each state along the trajectory at each iteration to attenuate the expected total value, which results in smoothed states that are used for dynamics linearization and cost perform quadratization. SELQR progressively improves the approximation of the expected total cost, ensuing in higher quality plans. For applications with imperfect sensing, we tend to extend SELQR to arrange within the robot’s belief space. We tend to show that our iterative approach achieves fast and reliable convergence to high-quality plans in multiple simulated scenarios involving a car-like robot, a quadrotor, and a medical steerable needle performing a liver biopsy procedure.

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