Velocity Ellipse in 2D
In Robotics | No commentThe end-effector is not able to move equally fast in all directions, and that in fact depends on the pose of the robot. We will introduce the velocity ellipse to illustrate this.
The end-effector is not able to move equally fast in all directions, and that in fact depends on the pose of the robot. We will introduce the velocity ellipse to illustrate this.
By inverting the Jacobian matrix we can find the joint velocities required to achieve a particular end-effector velocity, so long as the Jacobian is not singular.
For a simple 2-link planar robot we introduce and derive its Jacobian matrix, and also introduce the concept of spatial velocity.
We introduce the relationship between the velocity of the robot’s joints and the velocity of the end-effector in 3D space.
We will learn about the relationship, in 2D, between the velocity of the joints and the velocity of the end-effector — the velocity kinematics. This relationship is described by a Jacobian matrix which also provides information about how easily the end-effector can move in different Cartesian directions.
This video gives summary of inverse kinematics.
An alternative for smooth motion between poses is Cartesian interpolated motion which leads to straight line motion in 3D space.
To move a robot smoothly from one pose to another we need smooth and coordinated motion of all the joints. The simplest approach is called joint interpolated motion but it has some limitations.
For a redundant robot the inverse kinematics can be easily solved using a numerical approach.
For real robots there are a few extra things to think about. Is a particular point actually reachable? Our old friend, singularity or gimbal lock reappears in the wrist.
Let’s look at numerical approaches to inverse kinematics for a couple of different robots and learn some of the important considerations.
To simplify the inverse kinematics most robots have a spherical wrist, a particular mechanical wrist design. For robots where the inverse kinematics is too hard to figure out we can solve the problem numerically, treating it as an optimisation problem.
A characteristic of inverse kinematics is that there is often more than one solution, that is, more than one set of joint angles gives exactly the same end-effector pose.
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.
A really important function when performing inverse kinematics is the inverse tangent or arctan function. We revise how this function works for angles in all quadrants of the circle and introduce a useful variant known as atan2.
We repeat the process of the last section but this time consider it as an algebraic problem.
We revisit the simple 2-link planar robot and determine the inverse kinematic function using simple geometry and trigonometry.
We will learn about inverse kinematics, that is, how to compute the robot’s joint angles given the desired pose of their end-effector and knowledge about the dimensions of its links. We will also learn about how to generate paths that lead to smooth coordinated motion of the end-effector.
This video gives summary of Robot Manipulator Arms.
This lecture has been about kinematics and we define that term.