Description
Objectives
The goal of this lab is to explore build autonomy into a simple two-wheeled non-holonomic robot. You will develop
an RRT-based planner designed to get your robot to a desired goal state.
Deliverables
This project will require you to write code. Make sure the well commented code for this lab is committed and
pushed, and submit a link to the repository. For some possible resources on git, see the previous pset.
You may work in teams on this assignment. As a team, you will create a well documented git repository containing
all your code and data. You will also create a team writeup describing the mathematical formulation, experimental
setup, and experimental results.
As an individual, you will create your own one-page slide summarizing the key contributions of your personal
efforts primarily using equations and/or figures. You will be assessed on both the clarity and completeness of your
content.
Include a link to your code repository / website in your report, as well as a complete list of references you’ve used
and in what manner, and submit pdfs by 4pm Mon. Nov. 4, 2019.
Preliminaries
0(a). What is the link to your (fully commented) github repo for this pset?
0(b). Who did you collaborate with?
0(c). What other resources did you use?
0(d). What was the aggregate % contributions of each team member?
1 Robot model
You will consider a two-wheeled robot similar to the one shown in Fig. 1. It has two wheels of radius r = 25mm,
separated by a distance w = 90mm. It drags a tail for stability, at a distance l = 75mm behind the centerpoint of
the wheels. The position of this robot in the environment is defined relative to the centerpoint of the wheels.
Each wheel is powered independently by a continuous rotation servo, with the angular velocity of the wheel
controlled by a PWM signal from the microcontroller. Assume each input prescribes the respective angular speed of
the wheel, from -60 to +60 RPM. This allows the robot to drive forwards or backwards at variable speed, or turn
with any turning radius.
1(a). What is the dimensionality of the input (action) space, robot state (configuration) space, and operational
space?
1(b). Define the (continuous space) system model. Assume a fully observable system, i.e. the state itself is directly
accessible with no sensor model.
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Figure 1: Two wheeled tank-drive robot, with dimensions as specified
2 Trajectory planning
The robot must move through a cluttered rectangular environment representing a parking lot, ultimately achieving a
prescribed goal, i.e. attaining a state within a desired region in C-space. You will consider geometric obstacles defined
by rectangles specified within the operational space. For an additional challenge, you may also include “one-way”
regions in the space that only permit motion in one direction.
Implement an RRT based algorithm to take the robot from a given initial state to the desired goal state while
avoiding obstacles, and use that to simulate a planner / controller specifying the inputs to the actuators as a function
of time.
2(a). Given a set of points V in C-space and a single target point xt, define and justify a metric that can be used
to determine which of the points in V is closest to xr.
2(b). Given arbitrary initial robot state xi and target robot state xt (in C-space), generate a smooth achievable
trajectory (that matches the metric you defined above) from the xi towards xt lasting 1 second. What are the
control inputs for this trajectory?
2(c). Given a smooth robot trajectory in C-space and obstacles defined in operational space, determine whether
this trajectory is collision free.
2(d). Combine the above to implement an RRT planner generating a trajectory from a specified initial state to a
desired goal region. Visualize the evolution of the RRT.
3 Evaluation and Extensions
3(a). Run some examples that demonstrate the performance (in terms of computational efficiency, trajectory efficiency, and obstacle avoidance) of your planner as your robot tries to achieve various goals (such as head-in
parking and parallel parking between other such parked vehicles). Clearly describe the experiments that were
run, the data that was gathered, and the process by which you use that data to characterize the performance
of your planner. Include figures; you may also refer to animations uploaded to your git repo.
3(b). How much relative computational cost is associated with the various operations of the RRT planner?
3(c). Improve on your planner using the RRT* algorithm, and compare to your original RRT planner using the
above metrics.
3(d). Qualitatively describe some conclusions about the effectiveness of your planner for potential tasks your robot
may encounter. For example, what happens to your planner in the presence of process noise, i.e. a stochastic
system model? How might you modify your algorithm to better handle noise?
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