Full Code of MengGuo/RVO_Py_MAS for AI

Repository: MengGuo/RVO_Py_MAS
Branch: master
Commit: e656e88294e9
Files: 8
Total size: 31.9 KB

Directory structure:
gitextract_kaateia7/

├── .gitignore
├── LICENSE
├── README.md
├── RVO.py
├── __init__.py
├── data/
│   └── mkmovie.sh
├── example.py
└── vis.py

================================================
FILE CONTENTS
================================================

================================================
FILE: .gitignore
================================================
.DS_Store
*.pyc
*.avi
snap*.png
data/*.jpg


================================================
FILE: LICENSE
================================================
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================================================
FILE: README.md
================================================
RVO_Py_MAS
========

Python Implementation of Reciprocal Velocity Obstacle (RVO) for Multi-agent Systems

```
@ARTICLE{8361450,
  author={M. {Guo} and M. M. {Zavlanos}},
  journal={IEEE Transactions on Robotics}, 
  title={Multirobot Data Gathering Under Buffer Constraints and Intermittent Communication}, 
  year={2018},
  volume={34},
  number={4},
  pages={1082-1097},
  doi={10.1109/TRO.2018.2830370}}
```

-----
Description
-----
This package contains a **_plug-and-play_** Python package for collision-avoidance in multi-agent system, based on reciprocal velocity obstacles ([RVO](https://www.cs.unc.edu/~geom/RVO/icra2008.pdf)) and hybrid reciprocal velocity obstacles ([HRVO](https://www.cs.unc.edu/~geom/RVO/icra2008.pdf)).

It has _minimal impact_ on your control objective and requires _minimal integration_. 



<p align="center">  
  <img src="https://github.com/MengGuo/RVO_Py_MAS/blob/master/data/snapshots.png" width="800"/>
</p>

-----
Features
-----
* Takes a 2D workspace with _any number_ of non-overlaping circular or square obstacles
* _Any number_ of dynamic agents with non-zero volume.
* Allow the choice of VO, RVO, HRVO.
* **Direct plug-and-play** and **fully integrate-able  with your control objective**, i.e., the output velocity is a minimal modification of the desired velocity.

```python
from your_module import compute_desired_V, Update_V
from RVO import RVO_update

# your control objective here 
V_desired = compute_desired_V(X, control_objective, V_max)

# plug in the RVO controller from this package
V = RVO_update(X, V_desired, workspace_model)

# let the robot move
X = Update_X(X, V, step)
```

* Scalable and fast, see examples below. 
* See [example.py](https://github.com/MengGuo/RVO_Py_MAS/blob/master/example.py) for test run. [[Video1]](https://vimeo.com/185405407), [[Video2]](https://vimeo.com/185408368)


----
References 
----
* Papers on [RVO](https://www.cs.unc.edu/~geom/RVO/icra2008.pdf), [HRVO](https://www.cs.unc.edu/~geom/RVO/icra2008.pdf)
* There are [Python bindings](https://github.com/sybrenstuvel/Python-RVO2) of the C++ implementation from the algorithm developers. For my purposes, the formality is too _heavy_ to be integrated into my own project, so I have my own try.
* This package does _not_ depend on the [Clearpath geometric package](http://pcl.intel-research.net/publications/clearpath_sca2009.pdf) to compute velocity obstacles.


----
Discussion
----
* For **very** clustered workspace with a large number of robots, you may need to limit the `maximal velocity` and use very `small step size`.
* You may add additional constraints in `RVO_update` such as the change rate of `V`, the lower bound of `V`.
* When applying this module to experimental robot control, you may need to set the **step size** higher due to hardware constraints.
* In most practical experiments, this scheme should still work by limiting the _maximal velocity_.  



================================================
FILE: RVO.py
================================================
from math import ceil, floor, sqrt
import copy
import numpy

from math import cos, sin, tan, atan2, asin

from math import pi as PI



def distance(pose1, pose2):
    """ compute Euclidean distance for 2D """
    return sqrt((pose1[0]-pose2[0])**2+(pose1[1]-pose2[1])**2)+0.001


def RVO_update(X, V_des, V_current, ws_model):
    """ compute best velocity given the desired velocity, current velocity and workspace model"""
    ROB_RAD = ws_model['robot_radius']+0.1
    V_opt = list(V_current)    
    for i in range(len(X)):
        vA = [V_current[i][0], V_current[i][1]]
        pA = [X[i][0], X[i][1]]
        RVO_BA_all = []
        for j in range(len(X)):
            if i!=j:
                vB = [V_current[j][0], V_current[j][1]]
                pB = [X[j][0], X[j][1]]
                # use RVO
                transl_vB_vA = [pA[0]+0.5*(vB[0]+vA[0]), pA[1]+0.5*(vB[1]+vA[1])]
                # use VO
                #transl_vB_vA = [pA[0]+vB[0], pA[1]+vB[1]]
                dist_BA = distance(pA, pB)
                theta_BA = atan2(pB[1]-pA[1], pB[0]-pA[0])
                if 2*ROB_RAD > dist_BA:
                    dist_BA = 2*ROB_RAD
                theta_BAort = asin(2*ROB_RAD/dist_BA)
                theta_ort_left = theta_BA+theta_BAort
                bound_left = [cos(theta_ort_left), sin(theta_ort_left)]
                theta_ort_right = theta_BA-theta_BAort
                bound_right = [cos(theta_ort_right), sin(theta_ort_right)]
                # use HRVO
                # dist_dif = distance([0.5*(vB[0]-vA[0]),0.5*(vB[1]-vA[1])],[0,0])
                # transl_vB_vA = [pA[0]+vB[0]+cos(theta_ort_left)*dist_dif, pA[1]+vB[1]+sin(theta_ort_left)*dist_dif]
                RVO_BA = [transl_vB_vA, bound_left, bound_right, dist_BA, 2*ROB_RAD]
                RVO_BA_all.append(RVO_BA)                
        for hole in ws_model['circular_obstacles']:
            # hole = [x, y, rad]
            vB = [0, 0]
            pB = hole[0:2]
            transl_vB_vA = [pA[0]+vB[0], pA[1]+vB[1]]
            dist_BA = distance(pA, pB)
            theta_BA = atan2(pB[1]-pA[1], pB[0]-pA[0])
            # over-approximation of square to circular
            OVER_APPROX_C2S = 1.5
            rad = hole[2]*OVER_APPROX_C2S
            if (rad+ROB_RAD) > dist_BA:
                dist_BA = rad+ROB_RAD
            theta_BAort = asin((rad+ROB_RAD)/dist_BA)
            theta_ort_left = theta_BA+theta_BAort
            bound_left = [cos(theta_ort_left), sin(theta_ort_left)]
            theta_ort_right = theta_BA-theta_BAort
            bound_right = [cos(theta_ort_right), sin(theta_ort_right)]
            RVO_BA = [transl_vB_vA, bound_left, bound_right, dist_BA, rad+ROB_RAD]
            RVO_BA_all.append(RVO_BA)
        vA_post = intersect(pA, V_des[i], RVO_BA_all)
        V_opt[i] = vA_post[:]
    return V_opt


def intersect(pA, vA, RVO_BA_all):
    # print '----------------------------------------'
    # print 'Start intersection test'
    norm_v = distance(vA, [0, 0])
    suitable_V = []
    unsuitable_V = []
    for theta in numpy.arange(0, 2*PI, 0.1):
        for rad in numpy.arange(0.02, norm_v+0.02, norm_v/5.0):
            new_v = [rad*cos(theta), rad*sin(theta)]
            suit = True
            for RVO_BA in RVO_BA_all:
                p_0 = RVO_BA[0]
                left = RVO_BA[1]
                right = RVO_BA[2]
                dif = [new_v[0]+pA[0]-p_0[0], new_v[1]+pA[1]-p_0[1]]
                theta_dif = atan2(dif[1], dif[0])
                theta_right = atan2(right[1], right[0])
                theta_left = atan2(left[1], left[0])
                if in_between(theta_right, theta_dif, theta_left):
                    suit = False
                    break
            if suit:
                suitable_V.append(new_v)
            else:
                unsuitable_V.append(new_v)                
    new_v = vA[:]
    suit = True
    for RVO_BA in RVO_BA_all:                
        p_0 = RVO_BA[0]
        left = RVO_BA[1]
        right = RVO_BA[2]
        dif = [new_v[0]+pA[0]-p_0[0], new_v[1]+pA[1]-p_0[1]]
        theta_dif = atan2(dif[1], dif[0])
        theta_right = atan2(right[1], right[0])
        theta_left = atan2(left[1], left[0])
        if in_between(theta_right, theta_dif, theta_left):
            suit = False
            break
    if suit:
        suitable_V.append(new_v)
    else:
        unsuitable_V.append(new_v)
    #----------------------        
    if suitable_V:
        # print 'Suitable found'
        vA_post = min(suitable_V, key = lambda v: distance(v, vA))
        new_v = vA_post[:]
        for RVO_BA in RVO_BA_all:
            p_0 = RVO_BA[0]
            left = RVO_BA[1]
            right = RVO_BA[2]
            dif = [new_v[0]+pA[0]-p_0[0], new_v[1]+pA[1]-p_0[1]]
            theta_dif = atan2(dif[1], dif[0])
            theta_right = atan2(right[1], right[0])
            theta_left = atan2(left[1], left[0])
    else:
        # print 'Suitable not found'
        tc_V = dict()
        for unsuit_v in unsuitable_V:
            tc_V[tuple(unsuit_v)] = 0
            tc = []
            for RVO_BA in RVO_BA_all:
                p_0 = RVO_BA[0]
                left = RVO_BA[1]
                right = RVO_BA[2]
                dist = RVO_BA[3]
                rad = RVO_BA[4]
                dif = [unsuit_v[0]+pA[0]-p_0[0], unsuit_v[1]+pA[1]-p_0[1]]
                theta_dif = atan2(dif[1], dif[0])
                theta_right = atan2(right[1], right[0])
                theta_left = atan2(left[1], left[0])
                if in_between(theta_right, theta_dif, theta_left):
                    small_theta = abs(theta_dif-0.5*(theta_left+theta_right))
                    if abs(dist*sin(small_theta)) >= rad:
                        rad = abs(dist*sin(small_theta))
                    big_theta = asin(abs(dist*sin(small_theta))/rad)
                    dist_tg = abs(dist*cos(small_theta))-abs(rad*cos(big_theta))
                    if dist_tg < 0:
                        dist_tg = 0                    
                    tc_v = dist_tg/distance(dif, [0,0])
                    tc.append(tc_v)
            tc_V[tuple(unsuit_v)] = min(tc)+0.001
        WT = 0.2
        vA_post = min(unsuitable_V, key = lambda v: ((WT/tc_V[tuple(v)])+distance(v, vA)))
    return vA_post 

def in_between(theta_right, theta_dif, theta_left):
    if abs(theta_right - theta_left) <= PI:
        if theta_right <= theta_dif <= theta_left:
            return True
        else:
            return False
    else:
        if (theta_left <0) and (theta_right >0):
            theta_left += 2*PI
            if theta_dif < 0:
                theta_dif += 2*PI
            if theta_right <= theta_dif <= theta_left:
                return True
            else:
                return False
        if (theta_left >0) and (theta_right <0):
            theta_right += 2*PI
            if theta_dif < 0:
                theta_dif += 2*PI
            if theta_left <= theta_dif <= theta_right:
                return True
            else:
                return False

def compute_V_des(X, goal, V_max):
    V_des = []
    for i in range(len(X)):
        dif_x = [goal[i][k]-X[i][k] for k in range(2)]
        norm = distance(dif_x, [0, 0])
        norm_dif_x = [dif_x[k]*V_max[k]/norm for k in range(2)]
        V_des.append(norm_dif_x[:])
        if reach(X[i], goal[i], 0.1):
            V_des[i][0] = 0
            V_des[i][1] = 0
    return V_des
            
def reach(p1, p2, bound=0.5):
    if distance(p1,p2)< bound:
        return True
    else:
        return False
    
    


================================================
FILE: __init__.py
================================================


================================================
FILE: data/mkmovie.sh
================================================
#!/bin/sh

ffmpeg -r 3 -f image2 -i snap%d.png -s 1000x1000 -y simulation.avi


================================================
FILE: example.py
================================================
import sys


from RVO import RVO_update, reach, compute_V_des, reach
from vis import visualize_traj_dynamic


#------------------------------
#define workspace model
ws_model = dict()
#robot radius
ws_model['robot_radius'] = 0.2
#circular obstacles, format [x,y,rad]
# no obstacles
ws_model['circular_obstacles'] = []
# with obstacles
# ws_model['circular_obstacles'] = [[-0.3, 2.5, 0.3], [1.5, 2.5, 0.3], [3.3, 2.5, 0.3], [5.1, 2.5, 0.3]]
#rectangular boundary, format [x,y,width/2,heigth/2]
ws_model['boundary'] = [] 

#------------------------------
#initialization for robot 
# position of [x,y]
X = [[-0.5+1.0*i, 0.0] for i in range(7)] + [[-0.5+1.0*i, 5.0] for i in range(7)]
# velocity of [vx,vy]
V = [[0,0] for i in range(len(X))]
# maximal velocity norm
V_max = [1.0 for i in range(len(X))]
# goal of [x,y]
goal = [[5.5-1.0*i, 5.0] for i in range(7)] + [[5.5-1.0*i, 0.0] for i in range(7)]

#------------------------------
#simulation setup
# total simulation time (s)
total_time = 15
# simulation step
step = 0.01

#------------------------------
#simulation starts
t = 0
while t*step < total_time:
    # compute desired vel to goal
    V_des = compute_V_des(X, goal, V_max)
    # compute the optimal vel to avoid collision
    V = RVO_update(X, V_des, V, ws_model)
    # update position
    for i in range(len(X)):
        X[i][0] += V[i][0]*step
        X[i][1] += V[i][1]*step
    #----------------------------------------
    # visualization
    if t%10 == 0:
        visualize_traj_dynamic(ws_model, X, V, goal, time=t*step, name='data/snap%s.png'%str(t/10))
        #visualize_traj_dynamic(ws_model, X, V, goal, time=t*step, name='data/snap%s.png'%str(t/10))
    t += 1
    


================================================
FILE: vis.py
================================================
#!/usr/bin/env python
import matplotlib
import matplotlib.pyplot as pyplot
from matplotlib.path import Path
import matplotlib.patches as patches
from matplotlib.patches import Polygon
import matplotlib.cm as cmx
import matplotlib.colors as colors

from math import pi as PI
from math import atan2, sin, cos, sqrt



def visualize_traj_dynamic(ws_model, X, U, goal, time = None, name=None):
    figure = pyplot.figure()
    ax = figure.add_subplot(1,1,1)
    cmap = get_cmap(len(X))
    # plot obstacles
    for hole in ws_model['circular_obstacles']:
        srec = matplotlib.patches.Rectangle(
                (hole[0]-hole[2], hole[1]-hole[2]),
                2*hole[2], 2*hole[2],
                facecolor= 'red',
                fill = True,
                alpha=1)
        ax.add_patch(srec)
    # ---plot traj---
    for i in range(0,len(X)):
        #-------plot car
        robot = matplotlib.patches.Circle(
            (X[i][0],X[i][1]),
            radius = ws_model['robot_radius'],
            facecolor=cmap(i),
            edgecolor='black',
            linewidth=1.0,
            ls='solid',
            alpha=1,
            zorder=2)
        ax.add_patch(robot)
        #----------plot velocity
        ax.arrow(X[i][0], X[i][1], U[i][0], U[i][1], head_width=0.05, head_length=0.1, fc=cmap(i), ec=cmap(i))
        ax.text(X[i][0]-0.1, X[i][1]-0.1, r'$%s$' %i, fontsize=15, fontweight = 'bold',zorder=3)
        ax.plot([goal[i][0]], [goal[i][1]], '*', color=cmap(i), markersize =15,linewidth=3.0)
    if time:
        ax.text(2,5.5,'$t=%.1f s$' %time,
                fontsize=20, fontweight ='bold')                
    # ---set axes ---
    ax.set_aspect('equal')
    ax.set_xlim(-1.0, 6.0)
    ax.set_ylim(-1.0, 6.0)
    ax.set_xlabel(r'$x (m)$')
    ax.set_ylabel(r'$y (m)$')
    ax.grid(True)
    if name:
        pyplot.savefig(name, dpi = 200)
        #pyplot.savefig(name,bbox_inches='tight')
    pyplot.cla()
    pyplot.close(figure)
    return figure

def get_cmap(N):
    '''Returns a function that maps each index in 0, 1, ... N-1 to a distinct RGB color.'''
    color_norm  = colors.Normalize(vmin=0, vmax=N-1)
    scalar_map = cmx.ScalarMappable(norm=color_norm, cmap='hsv') 
    def map_index_to_rgb_color(index):
        return scalar_map.to_rgba(index)
    return map_index_to_rgb_color