Multibody Dynamics

The study of how systems of rigid or flexible bodies, connected by joints, move under applied forces.

Multibody dynamics studies how systems of rigid or flexible bodies, connected by joints and possibly undergoing large translations and rotations, move under applied forces; it's used in aerospace, automotive engineering, biomechanics, and robotics. Each rigid body in space has 6 degrees of freedom (3 translational, 3 rotational), and joints remove some of them. Modeling follows one of two approaches: redundant coordinates, where every body is described by its full pose and constraint equations then tie them together, or minimal (generalized) coordinates, which use independent variables like joint angles directly, so the constraints are automatically satisfied. Robot dynamics is a branch of it, producing equations of the form M(q)q̈ + C(q,q̇)q̇ + g(q) = τ (q is the joint angles, M the mass matrix, C the Coriolis and centrifugal terms, g the gravity term, τ the joint torques). Both MuJoCo and Pinocchio compute dynamics using generalized coordinates.

ExampleA quadruped robot with 12 joints has 13 rigid bodies (the torso plus 12 leg segments). Generalized coordinates need only 6 (the torso's floating base) + 12 (joint angles) = 18 variables; redundant coordinates would need 13×6 = 78 variables, with 12 revolute joints each contributing 5 constraint equations — 60 in total — to eliminate the extra degrees of freedom.

Also called

Multibody System Dynamics

Related

Rigid-Body Dynamics · Generalized Coordinates · Recursive Newton-Euler Algorithm · Articulated Body Algorithm · Physics Engine · Kinematic Tree

Sources

Wikipedia: Multibody system
Lynch & Park, Modern Robotics（2017）第 8 章：机器人动力学是多体系统动力学的子领域 (Chinese)
MuJoCo 文档 Overview：广义坐标表示 (Chinese)