forward dynamics
Forward dynamics answers a 'what happens if' question: given how hard each motor is pushing right now, and how the robot is currently posed and moving, how will it speed up or slow down in the next instant? In plain terms, you feed in the forces and torques, and it predicts the resulting accelerations. It is the robot version of pushing a shopping cart: you know how hard you are shoving and how full the cart is, and forward dynamics tells you how quickly the cart will pick up speed.
The math behind it follows Newton's old rule that force equals mass times acceleration, but generalized to a whole linked body where every joint affects every other. The robot starts from its current state — each joint's angle and how fast it is turning — plus the applied torques and the steady pull of gravity, then solves for the acceleration at each joint. Crucially, this is the reverse of inverse dynamics: inverse dynamics asks 'what torques do I need for this motion?', while forward dynamics asks 'what motion will these torques produce?'
Where this really shines is simulation. To rehearse a robot's behavior on a computer before risking real hardware, you run forward dynamics over and over in tiny time steps: apply torques, compute accelerations, nudge the speeds and angles forward by a sliver of a second, and repeat. Stitched together, these steps become a believable virtual robot — the engine inside video-game physics and robot training simulators alike.
A robot-training simulator uses forward dynamics thousands of times per second: each frame it takes the commanded motor torques and gravity, computes how every joint accelerates, and advances the virtual robot one tiny step so its fall, swing, or stride looks real.
Torques in, accelerations out — repeated tiny steps make a simulation.
Forward dynamics needs the robot's mass model (its inertia matrix); inverting that matrix at every time step is the costly part of running a physics simulation.