Skip to content
Reachability-based Trajectory Design
Branch: master
Clone or download
Fetching latest commit…
Cannot retrieve the latest commit at this time.
Type Name Latest commit message Commit time
Failed to load latest commit information.

RTD (Reachability-based Trajectory Design)

This repository presents the tools required to implement RTD, which is a method of trajectory planning for autonomous mobile robots that can guarantee safety (in static environments) and not-at-fault behavior (in dynamic environments).


To run the files in this repository, you will need the following:

You will need to install the following MATLAB toolboxes as well:

  • Mapping Toolbox
  • Bioinformatics Toolbox
  • Robotics System Toolbox (to use with ROS)


All examples currently are for the FRS computation. We'll be adding examples of tracking error and online planning soon.

To run the FRS computation examples, make sure that this repository is on your MATLAB path, and that spotless and MOSEK are installed correctly and on your MATLAB path. Then, in the MATLAB command window, run


You should see MOSEK get called in the command window, and then a plot of an FRS in the state and parameter space will pop up. If this works, then you can also try running examples 2 -- 4 (see RTD/examples/offline_FRS_computation/).

To run the current online planning example, make sure simulator is on your MATLAB path, then run


You should see a simulation start plotting, with a little Segway robot scurrying around obstacles (and occasionally getting stuck, since right now it's using a really simple high-level planner that you can find in the simulator/planners folder). The Segway might have weird behavior currently, because there are some bugs that are a result of adapting old code to the new simulator framework, so please let us know if you find any.

RTD Overview

RTD is a way of controlling a robot, described by a "high-fidelity" dynamic model, by generating "desired trajectories" with a lower-dimensional "trajectory-producing" model. The robot uses a tracking controller (e.g., PID or MPC) to track the desired trajectories. We estimate a worst-case bound on the tracking error dynamics, then use it with the trajectory-producing model to compute a Forward Reachable Set (FRS) offline. The FRS then contains all points in the robot's state space that are reachable while tracking the desired trajectories.

We use the FRS for online planning by first intersecting it with obstacles that we want the robot to avoid. Since the FRS contains all possible trajectories of the robot (when tracking the parameterized desired trajectories), this lets us identify all of the trajectories that could cause a crash. Then, we optimize over the remaining safe trajectories.

The online planning algorithm runs in a "receding horizon" fashion, where a desired trajectory is executed while a new one is computed. This is because robots have limited sensor information at any time, so they have to move through the world to gain more information (about the things they aren't supposed to hit). In RTD, we enforce a planning time constraint, so each planning iteration only has some limited amount of time to try and find a new trajectory. If a new trajectory can't be found, then the robot has to execute a "fail-safe" maneuver; in our prior work (see the references below), we've used coming to a stop as a fail safe since it is widely applicable. Notice that this means every desired trajectory must include a fail-safe maneuver! We ensure this is possible by making the duration of the trajectories large enough for the robot to stop.

This repo demonstrates simple examples of RTD to illustrate how it works both offline and online. We'll be updating it with more examples as we make 'em!


This repository implements the methods presented in the following papers:

[1] Shreyas Kousik, Sean Vaskov, Matthew Johnson-Roberson, Ramanarayan Vasudevan, "Safe Trajectory Synthesis for Autonomous Driving in Unforeseen Environments," available at

[2] Shreyas Kousik, Sean Vaskov, Fan Bu, Matthew Johnson-Roberson, Ram Vasudevan, "Bridging the Gap Between Safety and Real-Time Performance in Receding-Horizon Trajectory Design for Mobile Robots," available at

[3] Sean Vaskov, Utkarsh Sharma, Shreyas Kousik, Matthew Johnson-Roberson, Ramanarayan Vasudevan, "Guaranteed Safe Reachability-based Trajectory Design for a High-Fidelity Model of an Autonomous Passenger Vehicle," available at


Shreyas Kousik

Sean Vaskov

Ram Vasudevan

Visit our website:

You can’t perform that action at this time.