Robot Motion Planning & Trajectory Generation - Complete Guide

At its foundation, motion planning treats the robot as a rigid body moving in a high-dimensional configuration space (C-space), where each dimension corresponds to a controllable degree of freedom (e.g., joint angle). Obstacles are 'inflated' into C-space using collision checking algorithms (e.g., FCL, Bullet), transforming navigation into a graph search or optimization problem over free space. Early methods like A* on grids or visibility graphs work well for simple 2D mobile robots but scale poorly with dimensionality.

Modern industrial practice relies on sampling-based planners (e.g., RRT*, EST) that probabilistically explore C-space without explicit discretization. These are embedded within perception-aware pipelines: stereo vision or time-of-flight sensors update occupancy grids at 10–30 Hz, while calibration-aware forward kinematics ensure C-space queries reflect true physical reachability. Trajectory generation then converts the discrete path into a continuous, differentiable function — typically piecewise polynomials (cubic, quintic, or septimal) — whose coefficients are solved via constrained quadratic programming to meet boundary conditions (start/end pose, velocity, acceleration) and inequality constraints (torque, velocity, jerk).

At the frontier, learning-augmented planners (e.g., Diffusion-Planner, LMP) use offline-trained neural priors to guide sampling toward high-success regions, reducing online computation by 3–5×. However, certified real-time performance still requires deterministic fallbacks — hence hybrid architectures where learned components propose candidates, and formal verification tools (e.g., S-TaLiRo, dReach) validate safety-critical constraints before execution. ISO 10218-1:2011 and ISO/TS 15066:2016 mandate such verification for collaborative robot deployment.