Kinodynamic

Kinodynamic planning, or kinodynamic motion planning, is a field in robotics and computer science that seeks to compute trajectories for dynamical systems while respecting both kinematic and dynamic constraints. It extends traditional kinematic planning by incorporating the system's dynamics, such as velocity, acceleration, torque, and actuator limits. In kinodynamic planning, the state typically includes position (and orientation) coordinates together with velocities and possibly higher-order derivatives.

The problem is usually formulated as finding a control signal u(t) and a time-parameterized state trajectory x(t) that satisfies a differential equation ẋ = f(x,u), initial and goal states, state and control constraints, and collision avoidance with the environment. The objective may be to minimize path length, time, energy, or a combination, yielding a trajectory and feasible control profile.

Solution methods: two main families — sampling-based approaches that extend RRT/RRT* to respect dynamics, often by integrating the plant dynamics during extension steps, and optimization-based methods that discretize the trajectory via direct methods (direct transcription or direct collocation) and solve a constrained optimization problem. Hybrid methods and problem-specific models are common. Real-time kinodynamic planning remains challenging due to nonlinearity, high dimensionality, and nonconvex constraints.

Applications include mobile robots, autonomous vehicles, aerial drones, robotic manipulators, and legged robots, where feasible dynamic behavior is essential. The term is sometimes used interchangeably with dynamic motion planning or trajectory optimization when focusing on dynamic feasibility.