A Class of SDRE-RRT Based Kinodynamic Motion Planners
A variety of LQR-RRT kinodynamic motion planners are built on the idea of solving a two point boundary value problem in an LQR manner for affine systems. These planners can also be used for controllable nonlinear systems only if its linearized model at the equilibrium state is also controllable, and the cost function reflects only a time/control trade-off. We propose a class of RRT planners based on the SDRE (State Dependent Riccati Equation) control paradigm. The SDRE control is used both for finding the nearest state in the tree and for the tree expansion. By solving an LQR tracking problem for nonlinear systems within the SDRE framework, instead of a two point boundary value problem, the proposed planners deal with a wider range of controllable nonlinear systems and cost functions. We compare the proposed planners with LQR-RRT-like algorithms by observing the results obtained from the three specific benchmark examples.