^{1}

^{1}

^{1}

^{2}

^{1}

^{*}

This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

In working environments with large manipulators, accidental collisions can cause severe personal injuries and can seriously damage manipulators, necessitating the development of an emergency stop algorithm to prevent such occurrences. In this paper, we propose an emergency stop system for the efficient and safe operation of a manipulator by applying an intelligent emergency stop algorithm. Our proposed intelligent algorithm considers the direction of motion of the manipulator. In addition, using a new regression method, the algorithm includes a decision step that determines whether a detected object is a collision-causing obstacle or a part of the manipulator. We apply our emergency stop system to a two-link manipulator and assess the performance of our intelligent emergency stop algorithm as compared with other models.

Increasing the safety of robots, especially industrial manipulators, is just as important as improving their performance. A collision between a manipulator and a person, for example, may cause severe personal injury as well as damage to the machinery. Thus, it is necessary to develop an algorithm that can detect collisions before they occur and make the manipulator stop before damage is done.

Various emergency stop or obstacle avoidance algorithms for robots, particularly those utilizing distance-measuring sensors [

In order to develop an efficient emergency stop algorithm, we consider two special cases in which the emergency stop is not needed. The first is the case that the detected object is not in the manipulator's path. The second is the case that detected object is not a collision-causing obstacle,

An efficient emergency stop algorithm using a fuzzy lookup table method to determine whether a detected object is an obstacle was previously presented and showed good performance [

In this section, we propose an intelligent emergency stop system for manipulators using distance-measuring sensors.

If one or more objects are sensed in the danger area, the algorithm verifies whether the detected object is a part of the manipulator (e.g., a link) or an obstacle that could cause a collision with the machine. If the detected object is judged to be an obstacle, the manipulator is shut down.

In this section, we consider the direction of movement of the manipulator in order to develop an efficient emergency stop algorithm. Obviously, accidents can occur if there is an obstacle—e.g., a person—in the manipulator's path; however, the manipulator does not need to stop when it does not move towards the obstacle.

Hence, our emergency stop algorithm, which considers the direction of motion of the manipulator, not only solves the safety problem but also helps to establish a more efficient operation of the manipulator.

The information provided by the distance-measuring sensor, e.g., an ultrasonic and an infrared sensor, is limited to a distance value, which is not sufficient information for the emergency stop algorithm to distinguish a part of the manipulator from true obstacles. Consequently, this limitation not only affects the efficient operation of the manipulator since it cannot work at specific motor positions where sensors detect parts of the manipulator in danger areas, but it also can result in unnecessary stops.

In order to solve this problem, we propose an intelligent decision method that can determine whether the sensed object is an obstacle that could cause a collision with the manipulator or not. We develop the intelligent decision method by applying a new regression method, which we introduce in Section 3.

For the decision step mentioned in Section 2.3, we apply a new regression method to the emergency stop algorithm. The regression method generates a function model of the motor positions and distance values, and then the function is used to predict a distance value. Next, the algorithm compares this predicted (estimated) distance value to a real distance value measured by a sensor and determines whether a stop is necessary. In this section, we introduce our proposed regression method—

The regression method determines the relationship between variables, and then uses that information to predict unknown variables. More specifically, the regression method generates an approximated function model using sample data (variables), and values of specific variables can be estimated by the function model. We call this function model the regression model, and the linear regression model has the form:

In order to apply a regression method to our emergency stop algorithm, we need a training procedure that will generate a function model of the motor position and distance values—hence the use of sample data pairs for this purpose. We collect motor position and corresponding distance data pairs by operating the manipulator under working conditions, but without obstacles. Because we cannot collect every motor position and distance data pair, we collect data at regular intervals of the position. We then apply the motor position values as inputs and the distance values as outputs to a regression method and a function model is generated for each sensor. After a function model for each sensor is generated by the regression method, distance values corresponding to specific motor position values can be estimated. Note that the distance-measuring sensors used for our experiment are ultrasonic sensors, which are typical distance-measuring sensors and have been widely employed in robotic applications [

After an object is sensed in a danger area, the algorithm determines whether the object is an obstacle or not by using the new regression method, as shown in the flowchart in

Because the function model generated by the regression method is approximated by sample data pairs, the estimated distance values provided by the regression model are not identical to the real distance values, producing experimental error. Consequently, when the difference between a measured value and an estimated value is larger than the allowed error range, the detected object is regarded as an obstacle that is not a part of the manipulator. We call this allowed error range the “permissible error region”, and note that it is not fixed region but is directly proportional to the distance values, as shown in

The black dotted line represents the permissible error region boundary of the regression model (red line), and region between the red line and the blue dotted line is the permissible error region. For object 1 in

In

In

In

In summary, if the value estimated by a regression model is larger than the real distance value, as shown in

In response to this paradox, we propose a new regression method in this section that minimizes the SRI. As shown in

The risk and inefficiency can be represented as follows:
_{r}_{i}_{n}_{n}_{n}^{t}_{n}_{n}_{n}_{n}_{n}_{n}_{n}_{r}_{i}

In

By substituting the quadratic function in _{r}_{i}_{r}_{i}_{r}_{i}^{2}_{2} is the regularized term, and

We also consider the fact that the risk and inefficiency values should adapt to the real measured distance value, _{n}_{n}_{n}_{n}_{n}_{1}_{2}_{1}_{2}_{1}_{2}_{1}_{2}

The optimality condition of

Then,

Finally, the optimal solution of the regression parameter

For performance verification of our proposed emergency stop algorithm, we apply the algorithm to a two-link robot and attach two ultrasonic sensors to each link, as shown in

We assume that _{i}^{th} data pair, and that _{i}_{1} and _{i}_{2} are the distance values measured by sensors 1 and 2 of the i^{th} data pair, respectively. We generate two regression function models of the data pairs (_{i}_{i}_{1}) and (_{i}_{i}_{2}).

As shown in

We construct regression models using SRI minimization to determine whether a detected object is an obstacle or not. Two regression models are generated—one for sensor 1 and another for sensor 2. We apply the motor position vectors _{i}_{i}_{i}^{2}_{i}^{3}_{i}^{p}_{i}

_{r}_{i}_{r}_{i}_{1}_{2}

As shown in

Finally, we compare the results of the proposed SRI regression, ridge regression, support vector regression, and fuzzy lookup table methods [_{n}

For implementation as an emergency stop algorithm, the decision speed is one of the most important factors. Hence, the decision time of the system using the fuzzy lookup table method applying five membership functions is 874.38 μs, and is 1,074.32 μs when the lookup table method with 10 membership functions is applied; however, when we apply regression methods, e.g., ridge regression, support vector regression and SRI regression, the decision time averages only 6.37 μs.

_{1}_{2}_{1}_{2}_{1}_{2}

We apply our proposed emergency stop algorithm to a two-link manipulator with ultrasonic sensors (

In this paper, we have proposed an emergency stop system for manipulators using distance-measuring sensors. Our proposed intelligent emergency stop algorithm considered the direction of motion of the manipulator. In addition, it was able to decide whether the detected objects were obstacles that could cause a collision with the manipulator or not by applying a new regression method. We applied our system to a two-link manipulator and verified the performance of our algorithm by comparing it with other regression methods. Consequently, we expect that the application of our emergency stop algorithm will enhance the safety and efficiency of working environments with industrial robots.

This work was supported by the R&D Program of the MKE (Ministry of Knowledge Economy).

Flowchart of the proposed efficient emergency stop algorithm. After an object is detected in the danger area, the algorithm determines whether the object is an obstacle or a part of the manipulator.

Consideration of moving direction.

Intelligent decision step: The algorithm determines whether to stop or not by comparing a distance value estimated by the regression model to a distance value measured by the sensor.

Permissible error region.

Two different regression results: (

Risk and inefficiency.

Loss function

Two-link manipulator.

Sample motor position and measured distance data pairs for a training procedure of the new regression method for (

Function models generated by the SRI regression method for (

Function models generated by two SRI regression methods for (

(

(

Regression results of fuzzy lookup table method, ridge regression, support vector regression, and SRI regression (_{r}_{i}_{r}_{i}_{1}_{2}

_{n} | |||||
---|---|---|---|---|---|

| |||||

Fuzzy lookup table | 5 Fuzzy membership functions | 0.9146 | 0.8403 | 0.5978 | 0.4423 |

10 Fuzzy membership functions | 0.5977 | 0.5219 | 0.2297 | 0.3395 | |

Ridge regression | 1 regression | 1.1713 | 0.9134 | 0.7044 | 0.4606 |

2 regression | 0.3579 | 0.3595 | 0.2143 | 0.2355 | |

Support vector regression | 1 regression | 1.4196 | 1.2219 | 0.66 | 0.6032 |

2 regression | 0.7497 | 0.677 | 0.3923 | 0.3595 | |

SRI regression | 1 regression | 1.2804 | 0.8616 | 0.5922 | 0.3821 |

2 regression |

SRI regression results according to different _{1}_{2}_{r}_{i}_{r}_{i}

| ||||
---|---|---|---|---|

_{1}, C_{2} |
_{1}, C_{2} |
_{1}, C_{2}) | ||

RMS error | 1 | 0.6744 | 0.7572 | |

2 | 0.7767 | 0.7007 | ||

RMS risk | 1 | 0.1752 | 0.7143 | |

2 | 0.129 | 0.6352 | ||

RMS inefficiency | 1 | 0.1781 | 0.6684 | |

2 | 0.2257 | 0.7704 | ||

RMS error × _{n} |
1 | 0.3626 | 0.3923 | |

2 | 0.489 | 0.4286 | ||

RMS risk × _{n} |
1 | 0.0921 | 0.3607 | |

2 | 0.0804 | 0.3838 | ||

RMS inefficiency × _{n} |
1 | 0.1093 | 0.3577 | |

2 | 0.15 | 0.4843 |