Kinematic Tree

A tree structure with links as nodes and joints as edges, branching outward from a root to each end effector.

A kinematic tree describes the structure of a multi-link robot: links are nodes, and joints are the edges connecting a parent link to a child link; each link has only one parent and there are no closed loops, so the structure branches outward from a root node — a fixed base, or the pelvis for a humanoid — to each end. A single robot arm is the special case with just one branch (a serial chain), while humanoids, dexterous hands, and quadrupeds are trees with multiple branches. URDF (Unified Robot Description Format) can only describe tree structures and can't directly represent closed chains such as a Stewart platform; MuJoCo likewise organizes every rigid body into a tree rooted at 'world' with no loops allowed, so closed loops like four-bar linkages or parallel ankle mechanisms have to be added back in as extra equality constraints. Dynamics libraries such as Pinocchio recurse over this tree and exploit the sparsity that its structure provides to speed up computation.

ExampleIn a humanoid robot's URDF, the pelvis is the root, branching down into the left and right legs and up through the waist to the torso, which then branches into the two arms and the head; each dexterous hand further branches into five fingers, making the whole robot a multi-level branching tree.

Also called

Tree-Structured Kinematic Chain

Related

Kinematic Chain · Serial Mechanism · Parallel Mechanism · Unified Robot Description Format · Floating Base · Articulated Body Algorithm

Sources

Lynch & Park, Modern Robotics（2017）4.2 节：URDF 可表示任何树形结构机器人 (Chinese)
MuJoCo 文档 Overview：Kinematic tree（不允许运动学回路，用等式约束建模） (Chinese)
Pinocchio（GitHub）：利用运动学树稀疏性的刚体动力学算法库 (Chinese)