Kinodynamic Planning

A sampling-based motion planning algorithm that incrementally builds a space-filling tree from an initial state to explore high-dimensional configuration spaces. It is probabilistically complete and particularly effective for systems with non-holonomic and kinodynamic constraints.

• Core Mechanism: Randomly samples the state space and connects the nearest node in the tree to the new sample via a local planner that respects dynamics.
• Key Use Case: Planning for high-DOF robots, vehicles, and manipulators in complex, cluttered environments where analytic solutions are intractable.
• Variant: RRT* introduces a rewiring step for asymptotic optimality, continuously improving path cost.

A search-based motion planning algorithm that discretizes a vehicle's state space (e.g., x, y, heading, velocity) into a graph of pre-computed, short motion primitives. This creates a lattice structure enabling efficient graph search for smooth, dynamically feasible trajectories.

• Core Mechanism: Uses a set of feasible control inputs to generate a finite set of short trajectories from any state, building a predictable, searchable graph.
• Key Use Case: Autonomous vehicle navigation on roads, where motion is constrained to lanes and requires continuous curvature paths.
• Advantage: Provides strong guarantees on dynamic feasibility since all primitives are validated against the vehicle model.

An online optimization-based control strategy where, at each time step, a finite-horizon optimal control problem is solved using a dynamic model of the system. Only the first control action is executed before the horizon recedes and the process repeats (Receding Horizon Control).

• Core Mechanism: Solves a constrained optimization problem at each control cycle, minimizing a cost function (e.g., tracking error, control effort) subject to kinodynamic and obstacle constraints.
• Key Use Case: Real-time trajectory tracking and reactive obstacle avoidance for drones, legged robots, and autonomous vehicles.
• Strength: Naturally handles multivariable constraints and can incorporate predictions about the environment.

A local trajectory optimization method that deforms an initial, kinematically feasible path. It optimizes the pose and time sequence of a robot along the path, treating it as an elastic band subject to kinodynamic, obstacle, and temporal constraints.

• Core Mechanism: Formulates a nonlinear optimization problem over a sequence of robot states and the time intervals between them, minimizing objectives like path length, duration, and separation from obstacles.
• Key Use Case: Local, reactive navigation for mobile robots in dynamic environments, often used in conjunction with a global planner (e.g., RRT).
• Advantage: Optimizes the trajectory's timing directly, which is critical for dynamic feasibility and interaction with moving obstacles.

A formal verification framework for ensuring safety in real-time control. A CBF is a mathematical function derived from safety constraints (e.g., collision avoidance). The controller is synthesized or filtered to guarantee the function's value remains non-negative, thus keeping the system within a safe set.

• Core Mechanism: Transforms safety constraints (e.g., "stay 1m from obstacle") into a condition on the system's dynamics. At each control step, a quadratic program finds the minimal deviation from a desired control input that satisfies this condition.
• Key Use Case: Providing provable safety guarantees for reactive systems, such as ensuring a robot never collides despite sensor noise or unexpected agent movements.
• Integration: Often used as a safety filter for higher-level planners or MPC controllers.

Traditional graph search algorithms adapted for kinodynamic planning by incorporating a feasibility checker at their core. Instead of searching over a simple grid, they search over a discretized state space where each transition is validated by a local planner that ensures dynamic feasibility.

• Core Mechanism: Algorithms like A* search a graph where nodes are robot states and edges are motion primitives. D*, D Lite*, and Lifelong Planning A (LPA)** are incremental variants that efficiently replan when edge costs change (e.g., new obstacles).
• Key Use Case: Lattice planners are a prime example. D* Lite is famously used for real-time navigation in unknown terrain.
• Advantage: Provides optimality guarantees (within the discretization) and is highly efficient for replanning in dynamic environments.

A sampling-based motion planning algorithm that incrementally builds a space-filling tree from an initial state to explore high-dimensional configuration spaces. It is particularly effective for systems with non-holonomic and kinodynamic constraints because it does not require an explicit representation of the free space.

• Key Mechanism: Randomly samples the state space and connects the nearest node in the tree to the new sample via a local planner that respects dynamics.
• Use Case: Foundational for many kinodynamic planners due to its ability to handle complex differential constraints.

An advanced control method where a dynamic model of the system is used to predict future behavior. At each control step, it solves a finite-horizon optimization problem to determine a sequence of optimal control actions, executing only the first before re-planning.

• Relation to Kinodynamic Planning: MPC is often the execution layer for a kinodynamic plan, providing closed-loop, real-time control that respects dynamic constraints and reacts to disturbances.
• Core Concept: Receding Horizon Control is the implementation strategy that makes MPC suitable for dynamic environments.

A search-based motion planning algorithm that discretizes a vehicle's state space into a graph of pre-computed motion primitives. This lattice structure enables efficient planning of smooth, dynamically feasible trajectories.

• Motion Primitives: Short, feasible trajectory segments that form the edges of the lattice, encapsulating kinodynamic constraints.
• Advantage: Provides strong guarantees on dynamic feasibility and is highly compatible with graph search algorithms like A*.

A decentralized, reactive navigation algorithm where multiple agents independently compute velocity adjustments to avoid collisions. It assumes other agents employ a similar reciprocal strategy, enabling scalable local collision avoidance.

• Context: While not a full kinodynamic planner, ORCA operates on velocity space and is often integrated as a local collision avoidance layer within a broader kinodynamic planning stack.
• Limitation: Typically assumes simple, linear dynamics (e.g., holonomic point masses), requiring adaptation for full kinodynamic systems.

A mathematical tool used in control theory to formally guarantee that a dynamical system will remain within a safe set. It synthesizes controllers that enforce constraints derived from the function, providing safety certificates.

• Application: Used to enforce kinodynamic constraints (like acceleration limits) and safety constraints (like collision avoidance) in a provably correct manner, often in conjunction with MPC or other planners.

A local trajectory optimization method that deforms an initial, kinematically feasible path. It optimizes the positions and timestamps of a sequence of robot poses for smoothness, safety, and speed, adhering to kinodynamic constraints.

• Mechanism: Formulates the problem as a non-linear optimization over a band of connected poses, with constraints for velocity and acceleration.
• Use Case: Common for local replanning and refinement of global plans for mobile robots, explicitly optimizing the time parameterization of the path.