Mitsubishi Heavy Industries Technical Review Vol. 51 No. 1 (March 2014)
34

Development of Obstacle Avoidance Controlfor Robotic Products Using Potential Method

YUSUKE YASHIRO*1

KAZUKI EGUCHI*1SATOSHI IWASAKI*2

YOSHIAKI YAMAUCHI*3

MASAHIRO NAKATA*4

In the field of robot development used in areas into which human beings have difficultyentering such as deep water, space and irradiated areas, the need for autonomous products thatcan operate without being remotely control by a human being has increased. Considering
application to more general issues, it is important for autonomous operation to have the capability
to avoid unknown obstacles in three dimensional space. Accordingly, Mitsubishi Heavy Industries,Ltd. (MHI) has used the potential method to establish control logic and verified the effectiveness of
the logic through simulation. Specifically, the capability to improve the efficiency of avoidance
operations in three dimensional space by finding obstacle avoidance paths in horizontal andvertical directions based only on the coordinates of the obstacle was confirmed.

|1. Introduction
In the past, MHI developed several robotic products used for operations in harshenvironments into which human beings have difficulty entering such as deep water, space, nuclear
power plants, etc. In recent years, due to improvements in the performance of computers andsensors, the development of autonomous products has been made possible. Technology for theautonomous operation of robots is also in demand in the market as a customer need because it
allows the extension of the operational range of autonomous robots and the reduction of fatigue inhuman beings caused by many hours of control operation.
In areas where robotic products are used, there may be obstacles that are not indicated byinformation on a prepared map because of unexpected events such as disasters, etc. In such cases, arobot with the capability to avoid obstacles switches its operational mode to obstacle avoidance.
However, if the obstacle avoidance operation is based on a preset sequence, some obstacle shapes
cause repeating and/or exaggerated operation, resulting in a loss of efficiency.
Accordingly, to improve the efficiency of avoidance operation of robots, a method to findavoidance paths depending on the shape of obstacles is needed. Considering the application ofrobots to more general issues, it is favorable that the method is applicable to operations in three
dimensional space.
One of the methods to find avoidance paths is the potential method(1). This method defines
potential functions on a destination position and obstacle positions and determines the moving
direction based on the gradients of the functions in order to find a path for moving to thedestination position while avoiding the obstacles. The calculation of potential functions can beextended three-dimensionally. This method can also deal with unknown obstacles because the routecan be changed in real time based on observation data up to the point of time.
*1Nagasaki Research & Development Center, Technology & Innovation Headquarters*2

Chief Staff Manager, Nagasaki Research & Development Center, Technology & Innovation Headquarters*3

Ship & Ocean Engineering Department, Shipbuilding & Ocean Development Division, Commercial Aviation & Transportation Systems*4

Submarine Department, Naval Ship Division, Integrated Defense & Space Systems

Mitsubishi Heavy Industries Technical Review Vol. 51 No. 1 (March 2014)35

This paper presents the use of the potential method for the establishment of control logic forfinding an obstacle avoidance path of a robotic product and the results of its effectivenessverification through simulation. This control logic stores and updates a certain number of obstacle
coordinates detected by the sensor, and calculates potential functions and the gradients based on thecoordinates of the obstacles and the destination position to determine a moving direction. A
weighting coefficient is used for the potential function and increased or decreased depending on
conditions in order to improve the efficiency of avoidance paths and to resolve the issue where therobot stops at a certain position in some cases (deadlock) because a moving direction cannot be
successfully determined. In the verification of the control logic through a simulation using different
shapes of obstacles without changing the parameters, it was confirmed that an appropriate path
could be derived based only on sensor detection results, and efficient obstacle avoidance wasrealized.

|2. Potential method
The potential method defines potential functions on a destination position and obstacle
positions and determines the moving direction based on the gradients (partial differentiation of eachcoordinate component) of the functions. Figure 1 shows an image of a potential field(superposition of potential functions) designed on a two-dimensional plane. Smooth potentialfunctions are defined so that those of the obstacles diverge in the direction of positive infinity andthat of the destination position diverges in the direction of negative infinity. The gradient of thefunctions defined for obstacles are in a direction away from the obstacle. On the contrary, thegradient of the function defined for the destination position is in a direction approaching thedestination position. The potential field is the superposition of these functions. The gradient(differentiation) of the potential field is in a direction away from obstacles and approaching thedestination position. A robot can move to the destination position while avoiding obstacles, using
this gradient as the moving direction at that time. The potential method has the following threefeatures.
Prior information such as a topographic map is unnecessary because the moving direction isderived according to the information available at that time.
The moving path can be changed in real time because the potential field changes when anobstacle is found.
Application to three-dimensional space is easy because gradients are derived separately foreach of the coordinate components (x, y, …).

Figure 1 Example of deriving path based on potential method(two-dimensional plane)
This figure shows the derivation flow of the moving direction and path from thegradients of potential functions defined on a two-dimensional plane.

Mitsubishi Heavy Industries Technical Review Vol. 51 No. 1 (March 2014)36

The following formulas (1) and (2) show potential functions, formula (3) shows thecalculation of a potential field, and formula (4) shows the calculation of a gradient.
1( , , )=(1)2( − ) + ( − )2 +( − )2( , , )=−1( −)2 + ( −)2 +( −( , , )=+(3)−grad ( , , ) = −,,)2(2)(4)(x, y, z ) : Robot position (xo , y o , z o ) : Obstacle position (xd , yd , z d ) : Destination position(wo , wd ) : Weighting coefficient|3. Establishment of control logic
Figure 2 shows the control logic based on the potential method. The movement of the robot
depends on the actuators controlled according to the direction derived by the logic.

Figure 2Obstacle avoidance logic based on potential method

This figure shows the logic flow using the potential method and its positional relationship to theactual equipment and the actuator.

The following capabilities are added to the logic in order to move the robot efficiently to thedestination position while avoiding obstacles.
Capability to update the list storing obstacle coordinates
Capability to adjust the weighting coefficients of the potential field
Updating the obstacle coordinate list allows the elimination of obstacles already avoided andthe creation of a potential field that covers only considerable obstacles. Adjusting the weighting
coefficients allows more rapid obstacle avoidance and the reduction of the influence of obstacles
having lower avoidance priority on the determination of a path.
Figure 3 shows the procedures for the prevention of deadlocks using capabilities to store
obstacle coordinates and to adjust the weighting coefficients. In some cases, the potentials of thedestination position and the obstacles reach equilibrium when the potential gradient is calculated
from all potential functions. In such cases, a small value with the opposite sign in the moving
direction is derived repeatedly, resulting in a path that makes the robot almost stop at that position.
This is referred to as a deadlock, one of the issues with the use of the potential method. To resolve
this issue, the reduction of the weighting coefficient of the destination position with theapproaching obstacle kept stored allows the robot to move away from the obstacle temporarily.
Then once again returning the weighting coefficient of the destination position to the original value
makes the robot move to the destination position while avoiding the stored obstacle, resulting in apath that prevents deadlocks.

Mitsubishi Heavy Industries Technical Review Vol. 51 No. 1 (March 2014)37

Figure 3

Deadlock avoidance logic

This figure shows the flow of the logic that changes weighting coefficients to prevent deadlocks, theequilibrium of the potential gradients of the obstacle and the destination position.

|4. Simulation
The effectiveness of the control logic was confirmed using simulation. Figure 4 shows theresults of the functional confirmation of the control logic in two-dimensional space. The obstacleand destination position were set so that a deadlock would result. Because this was the verificationof only the control logic, the sensor was defined to be able to detect the obstacle in all directions
and the robot was defined to have no dynamic characteristics and be able to move in the moving
direction without delay. As a result, the robot moved to the destination position while avoidingobstacles and deadlocks, thereby confirming the validity of the control logic.

Figure 4

Result of simulation on two-dimensional plane

Next, simulation in three-dimensional space including vertical directional movement wasperformed. This simulation considers the dynamic characteristics of the robot and therefore thesimilar characteristics as an actual robot were reproduced. The sensor was defined as to be able todetect the obstacle only in three directions (to the front, and left and right obliquely downward).
Figure 5 and Figure 6 show the results of horizontal and vertical directional obstacle
avoidance simulation, respectively. The result of obstacle avoidance using sequential operationconsisting of a change of direction, moving up, moving straight and moving down is shown
together for a comparison of avoidance efficiency improvement. For both simulations, the design
parameters of the control logic were the same. The obstacle positions were not given in advanceand the robot could only acquire the obstacle positions that existed within the detection range ofthe sensor.

Mitsubishi Heavy Industries Technical Review Vol. 51 No. 1 (March 2014)
38Figure 5 Result of vertical directional
obstacle avoidance simulation inthree-dimensional space (Red:Sequential operation, Blue: Operationaccording to potential method)

Figure 6 Result of horizontal directional
obstacle avoidance simulation inthree-dimensional space (Red: Sequentialoperation, Blue: Operation according topotential method)

In vertical directional obstacle avoidance using sequential operation, the robot moved up to
avoid the obstacle and then moved down to the destination position. When the control logic basedon the potential method was used, the robot moved up while turning to avoid the obstacle and thenmoved down to the destination position.
In horizontal directional obstacle avoidance using sequential operation, the robot moved tothe destination position through a path including unnecessary turning. This was because the acting
time of each operation was tuned for vertical directional obstacle avoidance. This result indicatesthat sequential operation causes unnecessary avoidance for different obstacles. On the other hand,the avoidance path that was made according to the potential method included no unnecessaryturning. This result indicates that the potential method can derive an appropriate avoidance patheven with the same parameters because potential functions were made depending on the shape ofobstacles. The undulating shape of the path that was made based on the potential method wascaused by the fact that the robot could not change the moving direction instantaneously due to its
dynamic characteristics.
Figures 7 and 8 compare the efficiency of avoidance operation numerically. For both thevertical and horizontal directions, the control logic based on the potential method resulted in ashorter required time and the further reduction of the energy consumption index determined fromthe actuator travel. In this way, it can be said that the control logic based on the potential method
improves the efficiency of obstacle avoidance operation.

Figure 7 Comparison of time required foravoiding obstacles (Red: Sequential
operation, Blue: Operation according
to potential method)

Figure 8 Comparison of energy consumption
for avoiding obstacles (Red: Sequentialoperation, Blue: Operation according topotential method)

Mitsubishi Heavy Industries Technical Review Vol. 51 No. 1 (March 2014)39|5. Conclusion
MHI used the potential method to establish logic for the avoidance of obstacles applicable tothree-dimensional space and verified its capability to find a path depending on the shape of anobstacle and to improve the efficiency of avoidance operations through simulation. This method
enables the efficient avoidance of unknown obstacles, resulting in the autonomous movement ofrobots in areas with complicated geography.
In the future, MHI will proceed with research of the elements necessary for application toactual equipment such as a weighting coefficients design method in consideration of the detectionrange of the sensor and the dynamic characteristics of the robot, and contribute to actual operation.

References
1. Jen-Hui Chuang et al., An Analytically Tractable Potential Field Model of Free Space and Its Applicationin Obstacle Avoidance, IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS-PART B:
CYBERNETICS, Vol. 28 No. 5 (1998) pp. 729-736