Unit 3: Planning and Kinematics for Robotic Arms

Question 1

Probabilistic roadmaps methodology (PRM)

Answer 1

• Randomly sample n points in a configuration space.
• Check if the robot would be in collision at these configurations.
• Throw away samples that are in collision.

Create a visibility graph from the non-colliding samples.
This is done by connecting two samples and checking for collision at every small step along the connection.

Question 2

Probabilistic roadmaps
Are they complete / optimal?

Answer 2

Not complete. They could miss a narrow passage, as they only draw n samples.

Not optimal because the random sampling method means that the planner does not necessarily identify the shortest path.

Question 3

Rapidly-Exploring Random Tree (RRT) Algorithm

Answer 3

1. Set “start” as the root of your tree.
2. Loop:
   - Randomly sample a configuration q_{rand}. Every few iterations, use the goal instead of a random sample.
   - Find the nearest node in the tree to q_{rand}. Name it q_{near}.
   - Grow the tree by taking fixed size steps from q_{near} to q_{rand}. At each step, check collision. Stop when a configuration is in collision.
3. The planned path is given by the trace back from the goal to the start.

Question 4

Strengths of PRMs and RRTs

Answer 4

• No need to explicitly represent obstacles because collision checking of individual configurations is sufficient.
• Suitable for planning in high-dimensional spaces (e.g. robot arm c-spaces).
• Practical and fast solutions.
• Easy to implement.

PRM and RRT-based planners are state-of-the-art and are used in most of the current autonomous robot manipulators.

Question 5

Weaknesses of PRMs and RRTs

Answer 5

• Not complete … but probabilistically complete because - as time goes to infinity - it becomes complete.
• Not optimal. Planned paths may have a lot of random motion.

Question 6

Forward kinematic model

Answer 6

Describes how the robot as a whole moves as a function of its geometry and individual wheel behaviour.

Question 7

Kinematics

Answer 7

Study of how mechanical systems behave.

Question 8

End-effector

Answer 8

The more generic name for a robot hand, because we could also replace this with a gripper, a multi-fingered hand or another tool.

Question 9

Links

Answer 9

The name for the parts of a robot arm between the joints.

Question 10

Reachable workspace

Answer 10

The space in the environment which can be reached by the robot’s hand.

Question 11

Redundancy

Answer 11

When the area is reachable with many different joint angle.

I.e. the inverse kinematics may have many solutions.