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Actuators have finite capability, that is they have a maximum torque, velocity and power rating.

A more efficient trajectory has a trapezoidal velocity profile.

We summarise the important points from this lecture.

We learn the principles behind accelerometers, sensors that measure acceleration due to motion and due to the Earth’s gravitational field.

We describe inertia of the robot as a matrix which represents how inertia of a joint depends on the position of all the joints, and how the torque on one joint depends on the acceleration of other joints.

So far we have worked out the torques on a robot’s joints based on joint position, velocity and acceleration. For simulation we want the opposite, to know its motion given the torques applied to the joints. This is called the forward dynamics problem.

So far we have taken a linear combination of pixels in the box around the input pixel, but non-linear operations like sorting and ranking the pixel values also prove to be very useful. We look at the median filter which is much better at removing salt and pepper noise from image than simple smoothing.

A number of strategies exist to reduce the effect of these coupling torques between the joints, from introducing a gearbox between the motor and the joint, to advanced feedforward strategies.

The simplest smooth trajectory is a polynomial with boundary conditions on position, velocity and acceleration.

For real robots such as those with 6 joints that move in 3D space the inverse kinematics is quite complex, but for many of these robots the solutions have been helpfully derived by others and published. Let’s explore the inverse kinematics of the classical Puma 560 robot.