| Kira Dmitrieva, Majid Abbasov Application of the RRT Algorithm to Solve Control Theory Problems |
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| Abstract. This paper presents a modified Rapidly-exploring Random Tree (RRT) algorithm for solving optimal control problems in nonlinear dynamical systems. The key innovation lies in integration of system dynamics direct into the tree expansion process. Unlike the classical RRT, which samples points in the configuration or state space, the proposed approach samples controls from a mixed continuous-discrete probability distribution. Each sampled control is applied to the nearest node in the tree, and the resulting child state is computed by numerically integrating the system's ordinary differential equations over a fixed time step. To explicitly track and minimize the objective functional, the state vector is augmented with the accumulated cost, forming an extended state space. This framework transforms the RRT from a path-planning tool into a stochastic optimizer capable of approaching a control trajectory that satisfies the necessary conditions for optimality while respecting state and control constraints. The method is validated through numerical simulation, demonstrating its effectiveness in generating feasible and near-optimal control policies for complex dynamical systems. |
| Keywords: optimal control, graph tree, fast growing graph trees, control theory |
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| DOI: https://doi.org/10.54381/itta2026.1.03 |