#### Multi-dimensional trajectory

lesson

We learn to compute a trajectory that involves simultaneous smooth motion of many robot joints.

lesson

We learn to compute a trajectory that involves simultaneous smooth motion of many robot joints.

lesson

The Jacobian matrix provides powerful diagnostics about how well the robot’s configuration is suited to the task. Wrist singularities can be easily detected and the concept of a velocity ellipse is extended to a 3-dimensional velocity ellipsoid.

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A body moving in 3D space has a translational velocity and a rotational velocity. The combination is called spatial velocity and is described by a 6-element vector.

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We introduce the relationship between the velocity of the robot’s joints and the velocity of the end-effector in 3D space.

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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.

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We consider the most general type of serial-link robot manipulator which has six joints and can position and orient its end-effector in 3D space.

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We consider a robot with four joints that moves its end-effector in 3D space.

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We will learn the essentials of inertial navigation, about sensors such as accelerometers, gyroscopes and magnetometers and how we can use the information they provide to estimate our motion and orientation in 3D space.

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The orientation of a body in 3D can also be described by a single rotation about a particular axis in space.

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We extend the idea of relative pose, introduced in the last lecture, to 3D. We learn another right-hand rule that indicates the direction of rotation about an axis, and we see how we can attach 3D coordinate frames to objects to determine their pose in 3D space.