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Walking in Narrow Spaces: Safety-critical Locomotion Control for Quadrupedal Robots with Duality-based Optimization

<p align="center"> <img width="98.0%" src="docs/label.png"> <img width="24.0%" src="docs/distance.gif"> <img width="24.0%" src="docs/dcbf.gif"> <img width="24.0%" src="docs/duality.gif"> <img width="24.0%" src="docs/duality_dcbf.gif"> <img width="48.0%" src="docs/exp_straight.png"> <img width="48.0%" src="docs/exp_l.png"> <img width="48.0%" src="docs/exp_v.png"> <img width="48.0%" src="docs/exp_random.png"> </p>

Introduction

Open source code of Walking in Narrow Spaces: Safety-critical Locomotion Control for Quadrupedal Robots with Duality-based Optimization.

Files structure:

├── cbf_duality             # Main implementation of this paper
│   ├── cbf_controllers     # Controller interface 
│   ├── cbf_geometry        # Polytopes and QP distance implementation
│   ├── cbf_interface       # Duality and DCBF constraints OCS2 implementation
│   └── cbf_msgs            # Polytopes msgs definition
├── docs                    # Document assets
├── legged_control          # Basic controller framework
│   ├── docs                # Document assets
│   ├── legged_common       # Common interface for controller framework
│   ├── legged_control      # Metapackage
│   ├── legged_controllers  # Controller interface
│   ├── legged_estimation   # State estimation module
│   ├── legged_examples     # URDF and hardware interface of A1
│   ├── legged_gazebo       # Simulation interface
│   ├── legged_hw           # Hardware interface
│   ├── legged_interface    # Cost and constraints OCS2 implementation
│   ├── legged_wbc          # Whole body control module
│   ├── LICENSE
│   ├── qpoases_catkin      # QP solver wrapper
│   └── README.md
└── README.md

Getting Started

Dependency

The main dependency with recommended building type are shown below

Build

Check this document legged_control and make sure you can successfully run the simulation.

Then clone and build the cbf_controllers:

git clone git@github.com:HybridRobotics/Quadruped-NMPC-DCBF-Duality.git
catkin build cbf_controllers

Test

Launch the Gazebo simulation

roslaunch legged_unitree_description empty_world.launch

Spawn the controller with exponential DCBF constraints

roslaunch cbf_controllers test_simple_dcbf.launch

OR the controller with exponential DCBF duality constraints

roslaunch cbf_controllers test_simple_duality.launch

Then set a 2D Nav Goal in the RViz for the robot standup, and type "trot" to set the gait. You can command the robot by move_base_simple/goal or cmd_vel or use the goal_sender.launch to send a goal (recommended).

roslaunch cbf_controllers goal_sender.launch

Implementation Details

The OCS2 only supports continuous time formulation and is discrete in the solver internally. So the exponential DCBF duality constraints are formulated as follows:

$$ \begin{align} -\boldsymbol{\lambda}_{\mathcal{R}}^T \mathbf{b}_{\mathcal{R}}(\mathbf{x}) -\boldsymbol{\lambda}_{\mathcal{O}_i}^T\mathbf{b}_{\mathcal{O}_i} &\geq \alpha + e^{-\gamma (t-t_0)} d_i^*(\mathbf{x}_0), \ A_{\mathcal{R}}^T(\mathbf{x}) \boldsymbol{\lambda}_{\mathcal{R}} + A_{\mathcal{O}_i}^T \boldsymbol{\lambda}_{\mathcal{O}_i} &= 0, \ \lVert A_{\mathcal{O}_i}^T \boldsymbol{\lambda}_{\mathcal{O}_i} \rVert_2 &= 1, \ \boldsymbol{\lambda}_{\mathcal{R}} \geq 0, \boldsymbol{\lambda}_{\mathcal{O}_i} &\geq 0. \end{align} $$

The equality constraints are handled through a projection method, and the inequalities are handled either through a relaxed-barrier method. More details.