Rapid and Robust Trajectory Optimization for Humanoids Safe Planning for Articulated Robots Using Reachability-based Obstacle Avoidance With Spheres Conformalized Reachable Sets for Obstacle Avoidance With Spheres System Identification For Constrained Robots Serving Time; Real-Time, Safe Motion Planning and Control for Manipulation of Unsecured Objects Can`t Touch This; Real-Time, Safe Motion Planning and Control for Manipulators Under Uncertainty Safe, Optimal, Real-time Trajectory Planning with a Parallel Constrained Bernstein Algorithm