Kinodynamische

Kinodynamische planning, or kinodynamic planning, is a branch of motion planning in robotics that seeks trajectories which are not only collision-free and geometrically feasible but also dynamically feasible given the robot’s dynamics and actuators. In kinodynamic problems, the state space includes positions and velocities (and sometimes higher derivatives), and the system evolves according to differential equations ẋ = f(x, u). The planner must ensure that control inputs u(t) respect actuator limits, inertia, and other physical constraints, while achieving the goal within a given time or energy budget.

Common approaches combine dynamics with planning methods. Sampling-based kinodynamic planners extend algorithms such as RRT, RRT*, and PRM by propagating states through the system dynamics via forward simulation or integration. This requires evaluating whether the resulting trajectory is feasible and collision-free. Optimization-based methods formulate the problem as a trajectory optimization or direct transcription, solving for a time-parameterized path that minimizes a cost (time, energy, or a combination) under dynamic and collision constraints. Hybrid methods mix planning and optimization, using a rough geometric path as a seed and refining it to meet dynamics.

Challenges in kinodynamic planning include high-dimensional state spaces, nonlinear and nonholonomic dynamics, uncertainty in model parameters, and the need for real-time computation in dynamic environments. Effective planning often relies on accurate dynamic models, efficient simulation, and careful handling of time parameterization.

Applications are widespread in robotics and automation, including mobile robots with nonholonomic constraints, robotic manipulators with torque limits, drones, and legged robotics, where both the geometry of the scene and the physics of motion must be considered to produce feasible, efficient trajectories. Kinodynamic planning sits at the intersection of geometric planning and optimal control, often bridging planning with model predictive control and learning-based methods.