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4D Spatio-Temporal Planning
A discipline of AI and robotics aiming to calculate an optimal sequence of actions for an agent, simultaneously optimizing its trajectory in three spatial dimensions and its progression through time, while respecting a set of dynamic constraints.
Time-Parameterized Configuration Space (TC-Space)
An extension of the classical configuration space where each point represents not only a position and orientation of the system, but also a precise instant, allowing temporal constraints to be modeled as obstacles in this augmented space.
Discretized-Time Graph (DTG)
A data structure used in planning to represent the reachable states of a system at discrete time intervals, where nodes are states (x, y, z, t) and edges represent valid transitions between these temporal states.
Temporally Feasible Trajectory
A trajectory in space-time that satisfies not only the kinematic and dynamic constraints of the system (e.g., max speed, acceleration), but also all imposed temporal constraints, such as deadlines or time windows.
RRT* (Rapidly-exploring Random Tree Star)
A sampling-based tree algorithm, asymptotically optimal, adapted for 4D planning by randomly exploring the time-parameterized configuration space and reorganizing the tree to guarantee convergence toward the shortest path in time or energy.
Time-Augmented State
A representation of a system that explicitly includes time as a component of its state vector, allowing planning algorithms to reason about when an action is undertaken in addition to the position and configuration of the system.
Spatio-Temporal Cost
An objective function used in 4D planning that is not limited to spatial distance, but combines multiple metrics such as travel time, energy consumption, risk, or comfort, often weighted to reflect mission priorities.
Time-Parameterized A* (A* with Time)
A variant of the A* pathfinding algorithm where the heuristic estimates the remaining cost not only in distance but also in time, and where explored nodes include a temporal component to avoid collisions with moving obstacles.
Dynamic Obstacle
Entity whose position and/or shape evolves over time, whose trajectory must be anticipated and integrated into 4D planning to guarantee a collision-free trajectory for the planning agent.
4D Trajectory Smoothing
Post-processing step that takes a discrete and potentially jerky trajectory, generated by a planner, and converts it into a continuous and differentiable curve in spacetime, respecting the vehicle's dynamic constraints.
Obstacle Trajectory Prediction
Essential module of 4D planning that uses models (e.g., Kalman, neural networks) to estimate the future positions of dynamic obstacles, allowing the planner to evaluate collision risk at future instants.
Multi-Agent Spatio-Temporal Planning
Planning problem where multiple agents must compute their 4D trajectories in a coordinated manner to achieve their respective objectives while avoiding collisions with each other and with static/dynamic obstacles in the environment.
Hybrid A*
Trajectory planning algorithm that combines the discrete search of A* with continuity checks and non-holonomic constraints (e.g., vehicle turning radius), often used in spatio-temporal contexts for autonomous driving.
Constrained-Time Goal State
Goal condition in a 4D planning problem that specifies not only a target position, but also a time interval or precise instant for reaching it, making the search for a valid path significantly more complex.