MoveIt - Open source general-purpose motion planning framework built on top of ROS. MoveIt combines kinematic solvers, collision checking, path planning, trajectory optimization, perception, and control in a unified framework for robotic manipulation.
OMPL - Open Motion Planning Library, a collection of sampling-based motion planning algorithms. It provides implementations of PRM, RRT, and many variants used for planning robot arm motions in complex environments.
Drake - Model-based design and verification toolbox for robotics developed at MIT and now maintained by Toyota Research Institute. It provides multibody dynamics, mathematical optimization, and control algorithms for planning and control of robotic systems.
Pinocchio - Fast and flexible C++ library for rigid body dynamics algorithms. It provides efficient implementations of forward/inverse kinematics, dynamics, and their analytical derivatives for articulated robotic systems.