*Corresponding Author: Nadeem Javaid, COMSATS Institute of IT, Islamabad, www.njavaid.com. 
Control Strategies for Mobile Robot With Obstacle Avoidance 
 
 
M. Zohaib1, M. Pasha1, R. A. Riaz1, N. Javaid1, M. Ilahi1, R. D. Khan2 
 
1COMSATS Institute of Information Technology, Islamabad, Pakistan. 
2COMSATS Institute of Information Technology, Wah Cant, Pakistan. 
ABSTRACT 
 
Obstacle avoidance is an important task in the field of robotics, since the goal of autonomous robot is 
to reach the destination without collision. Several algorithms have been proposed for obstacle 
avoidance, having drawbacks and benefits. In this survey paper, we mainly discussed different 
algorithms for robot navigation with obstacle avoidance. We also compared all provided algorithms 
and mentioned their characteristics; advantages and disadvantages, so that we can select final efficient 
algorithm by fusing discussed algorithms. Comparison table is provided for justifying the area of 
interest 
KEYWORDS: Autonomous control, safe Navigation. 
 
I. 
INTRODUCTION 
 
Obstacle avoidance is the back bone of autonomous control as it makes robot able to reach to 
destination without collision. Path planning is involved to generate the shortest path from source to 
destination on the basis of sensorial information of environment. Many obstacle avoidance algorithms 
are proposed, some of them are discussed in this paper. Bug algorithms are the earliest methods [1]. 
They are easy to tune but more time consuming. They are not goal oriented algorithms, as they follow 
the edge without considering the goal. Same as, Artificial Potential is also a easy technique for 
obstacle avoidance but they get stuck in local minima [1][2]. Vector Field Histogram (VFH) is used 
by [2][8], that is an improved algorithm. It selects a shorter path than bug algorithms but it takes more 
time to manipulate. Follow the gap (FGM) method is a novel algorithm that is proposed in 2012 but it 
also unable to avoid U-shaped obstacle [1]. New Hybrid Navigation algorithm (NHNA) is a complete 
algorithm, which proves convergence but it is unable to apply in an unknown environment as it 
requires prior information of environment [3]. Same as “NHNA”, a Hybrid Navigation Algorithm 
(HNA) with roaming trails is an obstacle avoidance algorithm for partially known environment [4]. It 
used APF in its reactive layer so it can also get stuck in local minima. It is also a time consuming 
algorithm as robot may stop in front of obstacle until it moves. The characteristics of different 
algorithms are compared in table1.  The main algorithms that we have studied are discussed in coming 
sections (Latest Journal and research papers are preferred to study). 
II. 
ARTIFICIAL POTENTIAL FIELD METHOD 
 
This algorithm is based on the principle of Potential field in which robot and obstacles are act as a 
positive charge where as goal act as a negative charge. Thus, obstacles repel robot by generating 
repulsive force and goal attracts robot due to opposite change. Final force on robot is the vector sum 
of all repulsive and attractive force. However the magnitude of force is described by the distance, i.e. 
the obstacle near to robot will affect more similarly when the robot is at a far distance from goal its 
speed will be high and it will become slow as it comes close to goal. As mention in [2] attractive force 
is –ve gradient of attractive potential. 
𝐹𝑎𝑡𝑡𝑟= − ∇𝑈𝑎𝑡𝑡𝑟= −𝐾𝑎𝑡𝑡𝑟 (𝑞−𝑞𝑔𝑜𝑎𝑙) 
Where 𝑞−𝑞𝑔𝑜𝑎𝑙 is Euclidean distance from current position to goal and 𝐾𝑎𝑡𝑡𝑟 is scaling factor. 
Zohaib et al.,2013 
 
Obstacle1
Obstacle2
qgoal
Fattr
Frep1
Frep2
Local minimum
qgoal
q
Robot path
Repulsive force can be calculated by adding a repulsive effect on robot by the obstacles. This can be 
done by calculating the distance of obstacles from robot and their direction (angle). The obstacle near 
to robot has high repulsive force. The formula that [3] described is, 
𝑈𝑟𝑒𝑝= ෍𝑈𝑟𝑒𝑝 𝑖 (𝑞)
𝑛
𝑖=1
 
The –ve gradient of 𝑈𝑟𝑒𝑝 is a repulsive force. So, 
𝐹𝑟𝑒𝑝= − 𝑈𝑟𝑒𝑝 𝑖  (𝑞) 
 APF is a goal oriented algorithm and selects shorter path from source to destination, however it has a 
local minima problem. Symmetric and U-shaped obstacles are the dead end scenarios for APF as 
illustrated in Fig.1. Symmetric obstacles are shown in Fig.1a, in which attractive force of goal is equal 
and opposite to the sum of repulsive forces by obstacles. So the final heading force becomes zero and 
robot stops its motion, this is the case of local minima. Another crucial scenario is shown in Fig.1b, 
which also cases the local minima and APF fails to avoid it.  
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Fig.1. Dead end scenario of Artificial Potential Field method (symmetric obstacles) 
 
 
 
 
 
 
 
 
 
 
 
 
 
Fig.2. Dead end scenario of Artificial Potential Field method (U-shaped obstacle) 
III. 
VECTOR FIELD HISTOGRAM 
 
Vector field Histogram is a three stage method of obstacle avoidance. In first stage 2D histogram 
is generated around the robot that represents the obstacles. 2D histogram is updated with new coming 
percepts from sensors.  In the second step, this 2D histogram is converted to 1D histogram and then 
polar histogram. Finally in a third step, the algorithm selects the most suitable sector with low polar 
obstacle density, and calculates the steering angle and velocity in that direction. The Fig.2 is taken by 
the work of [8] which illustrates the 2D histogram grid. Conversion from 2D to 1D histogram is 
depicted in Fig. 3a and Fig. 3b is the representation of 1D polar histogram.  
          
 
 
 
 
 
 
 
 
 
 
 
 
 
Fig. 3. Construction of 2D histogram grid map 
 
 
 
 
 
 
 
 
 
 
 
 
 
Fig. 4. Representation of 1D and polar histogram (1D Histogram) 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Fig. 5. Representation of 1D and polar histogram (1D Polar histogram) 
IV. 
BUG ALGORITHM 
 
One of the earliest algorithms is Bug algorithm, which plans direct path from source to 
destination until it faces an obstacle. Algorithm is sub divided into three main versions on the basis of 
their behaviour of obstacle avoidance is mentioned below;  
 
• 
VERSION 1: BUG-1 ALGORITHM 
In this algorithm when robot detects an obstacle it start moving around it until 
Zohaib et al.,2013 
 
reaches to starting point from where it has started. During its movement around an obstacle, it 
calculates a leaving point with minimum distance to destination and generates new path from 
calculated leaving point to destination. After its one complete circle, it restarts its motion around 
obstacles until reaches to leaving point and starts moving on new generated path to reach the 
destination. Fig. 4a is the simulation results of [7] that shows the trajectory of robot under bug1 
algorithm.  
 
• 
VERSION 2: BUG-2 ALGORITHM 
Bug-2 algorithm generates slope from an initial position to destination and robot 
starts following it until it interrupted by obstacle. When it interrupted, it follows the edge of obstacle 
and calculates new slop from every new position until the new slop becomes equal to the original 
slope. After reaching on point having same slope as previous, it starts moving to destination by 
following pervious generated path. The scenario is illustrated in Fig. 4b [7].  
 
• 
VERSION 3: DIST-BUG ALGORITHM 
This algorithm is based on distance, in which robot moves from source to 
destination on path having minimum distance. When robot faces an obstacle in path, it starts following 
the edge of obstacle simultaneously; it calculates the distance of destination from each point. The 
point with the minimum distance is known as leaving point. When it finds the leaving point during its 
motion around an obstacle, it generates a new path and starts following it until reaches to destination 
as shown in Fig. 4c [7]. 
 
 
 
 
 
 
 
 
 
Fig.6. Obstacle avoidance with Bug algorithms (Trajectory of Bug-1 algorithm) 
 
 
 
 
 
 
Fig.7. Obstacle avoidance with Bug algorithms (Trajectory of Bug-2 algorithm) 
 
          
 
 
 
 
 
Fig.7. Obstacle avoidance with Bug algorithms (Trajectory of Dist-Bug algorithm) 
V. 
FOLLOW THE GAP METHOD (FGM) 
Follow the gap method avoids obstacles by finding the gap between them. It calculates the gap 
angle. It has a threshold gap, the minimum gap between obstacles from which robot can move. If the 
measured gap is greater than the threshold gap then robot will follow calculated gap angle. Obstacle 
avoiding using “FGM” is done in three main steps. 
• 
STEP-1: CALCULATING THE GAP ARRAY AND FINDING THE MAX. 
GAP 
In step 1, When robot face obstacles it calculates the distance of obstacle from robot and stores 
these distance in distance array. After finding the distances of all obstacles, gap array is generated, 
which includes the gap between obstacles. Gap array is being traversed to find a maximum gap 
between obstacles. If more than one Maximum gap exists with the same value, then first gap will be 
selects as a maximum gap. The method used by author, to generate gap array is shown in Fig. 5a [1]. 
The pink lines are indicating the nonholonomic constraints of robot where as doted green lines are the 
field of view of robot. 𝑑𝑛ℎ𝑜𝑙_𝑙  and  𝑑𝑛ℎ𝑜𝑙_𝑟 are the distances of obstacles from left and right 
nonholonomic constraints lines and 𝑑𝑓𝑜𝑣_𝑙   and 𝑑𝑓𝑜𝑣_𝑟  are the distances of obstacles from left and 
right field of view lines respectively. ∅𝑛ℎ𝑜𝑙_𝑙  and ∅𝑛ℎ𝑜𝑙_𝑙  are the angles of left and right nonholonomic 
constraint lines and ∅𝑓𝑜𝑣_𝑙   and  ∅𝑓𝑜𝑣_𝑟  are the angles of left and right field of view lines of robot. The 
distance with less value is stored and avoided first. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Fig.8. Representation of Gap border parameter and center gap angle (Gap border parameters) 
 
 
 
 
Zohaib et al.,2013 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Fig.9. Representation of Gap border parameter and center gap angle (Center gap angle) 
 
• 
STEP-2 : CALCULATION OF GAP CENTER ANGLE 
The second step of FGM is to calculate center angle of the maximum gap, which 
ensures the safe trajectory from the center of obstacles. This is an angle of vector having tail at robot's 
current position and head on the center point of maximum gap. Gap center angle can be calculated by 
using Apollonius theorem and law of cosine as being done by [1]. Final equation of ∅𝒈𝒂𝒑𝒄 is shown 
below; 
∅𝒈𝒂𝒑𝒄= 𝒂𝒓𝒄𝒄𝒐𝒔ቌ
𝒅𝟏+𝒅𝟐𝒄𝒐𝒔(∅𝟏+∅𝟐)
ට𝒅𝟏
𝟐+ 𝒅𝟐
𝟐+𝟐𝒅𝟏𝒅𝟐𝒄𝒐𝒔(∅𝟏+∅𝟐)
ቍ− ∅𝟏   (111) 
Where 𝒅𝟏and 𝒅𝟐 are the distances of obstacle 1 and 2 from robot respectively. ∅𝟏 𝒂𝒏𝒅 ∅𝟐 are angles 
of obstacle 1 and 2 respectively. ∅𝒈𝒂𝒑𝒄is the final calculated gap center angle. Fig. 5b illustrates the 
gap center angle.  
 
• 
Step-3 : Calculation the final heading Angle 
The last stage of “FGM” is to calculate the final heading angle. This can be achieved by combining 
the gap center angle with the goal angle. The combining structure is distance of obstacles and weight 
dependent, i.e. the obstacle nearer to robot has more weight. In case, when obstacle is at very short 
distance to robot then robot must move to gap angle rather than goal angle. It is due to fact that 
obstacle avoidance is the main task of path planning. Formula to calculate the final angle is given 
bellow:  
 
 
∅𝒇𝒊𝒏𝒂𝒍= 
𝜶
𝒅𝒎𝒊𝒏∅𝒈𝒂𝒑𝒄+ 𝜷 ∅𝒈𝒐𝒂𝒍
𝜶
𝒅𝒎𝒊𝒏+ 𝜷
    (222) 
 
Where, 𝒅𝒎𝒊𝒏 = 
(𝒅𝒏)
𝒊=𝟏:𝒏
𝒎𝒊𝒏  
,  ∅𝒈𝒂𝒑𝒄 and ∅𝒈𝒐𝒂𝒍 are calculated gap and goal angle, 𝜶  and  𝜷   areweight 
coefficients of gap and goal angle respectively. (For simplicity, 𝜷 can be consider 1). 
In short “FGM” when robot encounters the obstacle, it starts finding the gap between obstacles and 
save these calculated gap vales in an array. Algorithm finds the maximum gap from calculated gap 
array. If the maximum gap is greater than the threshold value then it calculates the gap angle, while 
simultaneously it considers goal angle. Finally gap angle is added into goal angle with their weight 
          
coefficients to find final angle to avoid obstacles. After these entire calculations robot starts moving 
along final calculated angle in order to avoid an obstacle. 
VI. 
NEW HYBRID NAVIGATION ALGORITHM (NHNA) 
 
“New Hybrid navigation” algorithm based on two layers, deliberative layer and reactive layer.  
Both layers are independent to each other. Deliberative layer planed a reference path on the basis of 
stored prior information. Reactive layer is an independently steers robot on the path planed by the 
deliberative layer. 
Hybrid algorithm required prior information of environment, which is stored in the form of binary 
grid map. In map, states of every grid are either free of occupied that depends on obstacles around i.e. 
free for no obstacle and occupied for obstacle. Unknown information is also taken as a free. In 
deliberative layer, A* search algorithm is used to generate a reference path. Reference path is 
temporary and not necessary to follow through out motion, it can be changed by the reactive layer. 
Fig. 6 is the results of [3] which shows the planned and shortest paths generated by A* search 
algorithm. 
Reactive layer takes reference path from deliberative layer and controls the motion of robot. 
It also receives the percepts of sensors and take decision to avoid an obstacle if found. For the purpose 
of obstacle avoidance, this layer uses D-H bug algorithm (Distance Histogram bug). This is a version 
of bug-2 algorithm which is improved by [2], which allows robot to rotate freely at angle less than 90° 
to avoid an obstacle. If the rotation of 90° or greater is required to avoid an obstacle; it acts as bug-2 
algorithm and starts moving to destination when path is clear from obstacles. Fig. 7a shows the robot 
trajectory with Dist-Bug algorithm where as Fig. 7b illustrates the robot's behavior with D-H bug 
algorithm [3]. 
 
 
 
 
 
 
 
 
 
 
 
 
 
Fig.10. Grid Map and Trajectory of robot with (NHNA) 
 
 
 
 
 
 
 
 
 
 
 
 
Fig. 11: strategy of obstacle avoidance (Trajectory of Dist-bug algorithm)  
 
Zohaib et al.,2013 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Fig. 11: strategy of obstacle avoidance (Trajectory of robot with Distance Histogram (D-H) bug 
algorithm) 
 
Reactive layer can change the path on the basis of current percept. Sensors provide current 
percepts to reactive layer as well as it updates the prior knowledge. In case on conflict between layers, 
the result of reactive layer is taken into an account. It is due to the present and updated nature of the 
results of reactive layer and hence incomplete knowledge of deliberative layer may contain errors. 
 
VII. 
ZYBRID NAVIGATION ALGORITHM WITH ROAMING TRAILS (HNA) 
 
The Hybrid Navigation algorithm with roaming trails is related to new NHNA. The main 
difference is that it used APF instead of D-H BUG in reactive layer. NHNA has not described any 
limit for robot to deviate from reference path but HNA used the concept of roaming trails for the same 
purpose. Fig. 8a shows the roaming trails with prior map and Fig. 8b illustrates the safe trajectory of 
robot in roaming trails [4]. 
According to the work of [4], other Hybrid algorithms may get stuck into cul-de-sac scenario as 
shown by the table in Fig. 8b. However it may stops in front of obstacle until it moves. 
 
 
 
 
 
 
 
 
 
 
 
  
Fig.12. Trajectory of robot with Roaming Trails (HNA) (Priori map with Roaming Trails) 
 
 
 
 
 
 
 
 
 
 
          
 
 
 
 
Fig.13.Trajectory of robot with Roaming Trails (HNA) (Trajectory of the robot (dotted line)) 
VIII. 
COMPARISON BETWEEN ALGORITHMS 
 
The above mentioned algorithms on obstacle avoidance are different with each other in some aspects. 
The main characteristics are compared and depicted in table shown in table-1. 
“Dist-Bug algorithm” is efficient then “Potential Field Method” because it has no local minimum 
problem. It covers short distance as compared to previous versions but it may take robot away from 
the goal because it is not a goal oriented while following the wall. Where as Potential Field Method is 
easy to tune, but it is not preferred since it get stack into local minimum error. Vector Field Histogram 
is time, space consuming algorithm as in 1st step, it generates 2D histogram and then converted it into 
1D histogram for further calculation. 
“Vision based sensor” method is best for upper level control i.e. with the use of beagle board, FPGA 
or any high processor because it requires dedicated application, high memory and calculations. Since 
we are working with Micro controller which is unable to interface camera, and cannot run any 
software relating to image processing. 
Algorithm 
Implementation 
Performance 
Remarks 
Hardware 
Required 
Parameters 
Required 
Efficiency 
Convergence 
Time 
Complexity 
Bug 
Algorithm 
[2][7] 
Distance 
sensors (IR, 
sonar) 
Microcontroller 
Current and 
destination 
position 
Low, may take robot 
away from 
destination 
Yes, but take more 
time to achieve 
goal 
Always move 
in one 
direction to 
avoid obstacle 
which 
increases the 
time 
complexity 
No local 
minima occur 
Select longest 
path 
Potential 
Field 
Method 
(VFF) 
[2][10] 
Distance 
sensors(IR, 
sonar) 
Microcontroller 
Target and 
obstacle 
distance 
Low, calculation are 
not accurate, 
constraints are not 
taken into account 
No, (in case U-
shaped and 
symmetrical 
obstacles) 
Less time 
required as it 
selects shorter 
path 
Local minima 
can occur 
Zohaib et al.,2013 
 
 
IX. 
CONCLUSION 
Collision free algorithm is a requirement of autonomous vehicle, since it provides the safe 
trajectory and proves the convergence. Some of the main algorithms that can use for obstacle 
avoidance are discussed in this paper. Dist-bug algorithm is an efficient algorithm in Bug series but it 
still takes more time to reach to destination. It is not a goal oriented; it may take robot for away from 
goal position. It can be improve by applying some condition as, if path is free towards goal, stops edge 
Vector Field 
Histogram 
[8] 
Sonar sensor 
Processor, high 
memory 
Obstacle 
distance 
Low, calculation 
may accurate but 
consumes more 
resources like 
memory, processor 
and power 
No, (in case U-
shaped and 
symmetrical 
obstacles) 
Required 
more time to 
generate a 2D 
grid and 
conversion 
from 2D to 1D 
polar 
histogram 
Difficult for 
Microcontrolle
r as high 
computations 
are required 
Vision 
sensor based 
method 
[11] 
Camera, sonar 
sensor, 
Processor, 
beagle board, 
laptop 
Obstacles 
position, angle 
and distance 
High, calculations 
are real and accurate 
(depends on 
equipment)  
May or may not 
(depend on Nature 
of algorithm) 
Depends on 
the resolution 
of camera and 
application 
used, mostly 
take more 
time for 
calculations 
Not best for 
mini vehicle 
with micro 
controller, It 
requires laptop 
or Processor 
and specific 
application 
like 
MATLAB.  
Follow the 
Gape 
Method 
[1] 
Ultrasonic and 
lidar Sensors, 
camera optical 
velocity sensor, 
NIPXI-
811108RT 
processor, PXi-
7954R FPGA 
Obstacle 
distance and 
angle 
High, Easy to tune, 
always select 
shortest path, able to 
avoid symmetric 
obstacles 
No, (In dead end 
scenario like U-
shaped obstacle) 
Less time 
consuming as 
decision are 
made on the 
basis of 
currents 
percepts, 
Fails for U 
shaped 
obstacle 
Hybrid 
Navigation 
Algorithm  
With  
Roaming 
trails 
[4] 
Laser and sonar 
sensors, Pioneer 
3-AT robots 
 
Prior 
information of 
information 
 
Medium, generates 
shortest path but no 
limit to deviate from 
path 
Yes, but in some 
scenarios, robot 
may stop in front 
of obstacle  
Consume 
more time 
generate 
reference path 
(A* search is 
required) 
Minutes or 
seconds 
Requires 
High 
calculation 
Consume 
more time 
In seconds  
and minutes 
New Hybrid 
Navigation 
Algorithm 
(NHNA) 
[3] 
Laser sensor, 
Micro processor 
Prior 
information of 
information 
Medium 
and 
efficient 
then 
Hybrid, use DH-Bug 
algorithm 
Yes, mostly 
converges except 
some scenarios 
like cul-de-sac 
Consume 
more time  as  
A* search is 
required to 
generate path 
High 
calculation 
Consume 
more time 
In seconds 
          
detecting and regenerate new path to move forward. From the above table, we conclude that “Follow 
the gap” method is better algorithm than others since it takes less time to reach the destination and 
does not require any dedicated software or extra memory. It has an important problem (due to its local 
characteristics), as it is unable to avoid U and H-shaped obstacles. So, there is a need of an algorithm 
which cannot get stuck into local minima and can able to tackle obstacles of U and H shaped. This can 
be achieved by fusing discussed algorithms with some upper level intelligence. This is our future task 
to design an algorithm that can avoid U and H-shaped obstacles and has no local minima issue. 
 
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