Big Brain Robotics

 Actuators are typically a combination of a motor and a gearbox. Motors usually have a rotating part (rotor) which transfers motion or driving power to a gearbox.  The gearbox (or reducer) reduces the motor speed and simultaneously amplifies motor torque. In fact, the gearbox does more than this - they inflate the inertia of the rotor and makes it feel significantly heavier. The inflated inertia of rotor is called 'reflected inertia'. Let's take an example of a bicycle at rest. If the gear train is set to higher gear ratio, it takes huge effort to turn the rear wheel in the beginning (feels heavy). Similarly, if a robot uses high-gear-ratio actuators, you need to push the robot quite hard to move it around. In case of industrial manipulators (e.g., UR3 manipulator), you need actuators' assistance when you manually grab the robot and move it around to your liking.  Let's briefly summarize what a gearbox (of gear ratio $n$) or a reducer does.  1. Velocity reduction: $...

This article is about the dynamics of 2-DoF manipulator, with a bit of twist. In textbooks, you will usually find a manipulator with magical actuators that can apply infinitely large torque and do not have any inertial properties. In reality, however, actuators can only apply limited torques and have velocity limits. Moreover, motors' (actuators') inertial properties may affect the dynamics greatly (as discussed here ). Let's derive a more realistic dynamics of a manipulator in following steps: 1. analyze motion (kinematics) 2. get the energy of the robot 3. derive dynamics using Euler-Lagrangian 1. Kinematics What we care, in fact, is simply the kinetic energy and the potential energy of the system. Meaning, we need to know how fast the masses are moving (velocity) and how high they are located (position). Let's define the coordinate system first, $$\begin{equation} \displaylines{ \hat{x} = \begin{bmatrix} 1\\0 \end{bmatrix}, \quad \hat{y} = \begin{bmatrix} 0\\1 \end{b...

My research goal is to build more capable robots that can apply explosive forces and accelerate like athletes. Basically, what I care about are forces and masses (inertia). Unfortunately, robots are quite complex. So, we need to up the level from the basics like $F=ma$, but the core concept does not differ too much from the Newton's law.  Roboticists' version of newton's law is called the manipulator equation, which is probably the first scary equation you learn from robotics intro courses:  $$M(q) \ddot{q} + c(q, \dot{q}) = J(q)^\top f + \tau.$$ I usually try to understand this equation by looking at the terms one by one and linking examples to them.  1. $M \ddot{q}$ is analogous to $ma$: larger mass makes it difficult to accelerate.  2. $c$ is a parasitic force required to maintain current pose $q$ and velocity $\dot{q}$. For example, it is difficult to maintain squatted pose because you need to fight against the gravity. Another example is the Coriolis force you ...