Parameter values in experiment
Robotic systems are expected to engage in various types of tasks, such as housework, nursing and welfare work, and industrial work done by skilled workers. Although fully automated robots are desirable, it appears difficult to produce such robots from the viewpoints of cost efficiency and the technologies available currently. Human-operated robotic systems are a good compromise, and hence are widely studied. Objectives of these robots include extending human mechanical power (Kazerooni & Steger, 2006), providing precise and smooth operation for human workers in difficult tasks (Bettini et al., 2001) (Peshkin et al., 2001), and executing a task in remote or hazardous environment (Anderson & Spong, 1989) (Lawrence, 1993).
In human-operated robotics systems, controllers are required to incorporate the human operator's command and compensate for the operator's mistakes without reducing the ease of operation. For this purpose we propose a model reference control approach, in which the reference model generates a desired trajectory according to the operator's input and constraints such as collision avoidance. This approach is applied to a two wheeled mobile robot that transports an object. This type of robot has various applications in many areas. Because transporting objects is a fundamental task of robotic systems, we realize a function to prevent slip and tumble of the transported object even when the human operator makes mistakes during operation. Fixing the transported object to the robotic system to prevent the object from tumbling requires extra time to transport the object and reduces the operational ease. This is because fixing is a time-consuming and inconvenient task. In particular, supposing that the robot is operated by elderly or disabled people, this function will be necessary for providing easy and safe operations. In addition, a collision function is implemented by the proposed model reference approach.
Many studies have been conducted into the obstacle avoidance of mobile robots (Bonnafous & Lefebvre, 2004) (Fox et al., 1997) (Khatib, 1986
2. Human-Operated Mobile Robot
In this chapter, we consider a control problem of a general type two-wheeled mobile robot that transports an object as shown in Fig. 1. Human operators are enabled to handle the robot using control sticks. They can give command signals for driving forces of each wheel
3. Controller Design
3.1. Model reference control for obstacle avoidance
To consider the nonholonomicity of the robot and incorporate the operator's command, we propose an obstacle avoidance algorithm based on the model reference approach as shown in Fig. 2, where the reference model generates the desired angles of each wheel,
3.2 Stability analysis based on linear model
This section presents a stability analysis based on a linear model of the proposed reference model in Eqs. (3) and (4). In this analysis, we consider the case in Fig. 4, where the two parallel walls are obstacles. It is assumed that the mobile robot moves almost along the centerline between the two walls with a velocity
The distance between each sensor and walls are given by
The following linear approximation is also reasonable because
The dynamics on
Equation (4) is linearized as:
Because Eq. (11) has no coupling term on
Defining a vector
The characteristic polynomial of the system Eq. (12) is
Because all the coefficients of the right-hand side of Eq. (13) are positive, the stability condition is given by:
From Eqs. (7) and (14), the following sufficient condition for the stability is derived:
By assigning the coefficient
3.3 Object transportation control
Because transporting objects is a fundamental task of robotic systems, we include a function to prevent slip and tumble of the transported object in the reference model block in Fig. 2 even when the human operator makes mistakes during operation. Fixing the transported object to the robotic system to prevent the object from slip and tumble requires extra time to transport the object and reduces the operational ease.
Because the value of
In this study, we assume that the slip and tumble of the transported object is caused mainly by the translational acceleration, although the acceleration normally includes the centrifugal and the Coriolis terms. The slip of the object is prevented if the inertial force is smaller than the static friction force as follows:
Next, we consider the allowable acceleration to avoid the tumble. We assume that the object starts to rotate at the end point of the contacting surface with the robot as shown in Fig. 5. Considering the equation around the centre of rotation, we obtain the following condition for preventing the object from starting to tumble.
To avoid the tumble, we propose to adjust the mass coefficient
The effectiveness of the proposed controller is experimentally verified in a corridor-like space shown in Fig. 6. Parameter values for the experiment are given in Table 1. Parameters for obstacle avoidance
To verify the effect for the operational easiness, ten unskilled persons (students) are employed to operate the robot with the transported object
|0.056 [kgm 2]||3.0 [Nms/rad]||4 [Nm 5/4]|
|5.4 [kg]||10.0 [Ns/m]||10.0[Nm 1/4]|
|0.11 [m]||0.029 [m]||4|
(a1) Manual control
(a2) Control with the obstacle avoidance function presented in section 3.2.
(a3) Control with the obstacle avoidance and the tumble avoidance functions in section 3.3.
In (a3), only the tumble is considered because
Figures 7 - 9 show the obtained robot trajectories by one operator under conditions (a1) – (a3), respectively. In case (a1), as negative values of
In case (a2), although
In case (a3), the robot was enabled to smoothly pass through the course by an almost constant inputs in Fig. 9 (a) without requiring a large magnitude of acceleration as shown in Fig. 9 (b).
Table 2 summarizes experimental results by ten unskilled operators (students), where no collision occurs in cases (a2) and (a3), and no tumble occurs in case (a3), for all operators. Figure 10 summarizes the control time required to pass through the course. The control time is largely reduced for almost all operators by the model reference control approach, because they do not have to consider the obstacle or tumble avoidance during operation. The control time in case (a3) increases little compared to case (a2), although the acceleration magnitude is reduced to avoid the tumble.
: Not occur, ×: Occur
|Operator×fs No.||(a1) Manual control||(a2) Obstacle avoidance||(a3) Obstacle and tumble avoidance|
This chapter presents a model reference control approach for a human-operated mobile robot that transports an object. This type of robot has wide applications in industrial and household tasks. The operational easiness of the robot is verified by experiments where operators are required to operate the robot with a transported object to pass through a corridor-like space. Because even young students failed to operate the robot, a function to support the operation is obviously required. The operational easiness is improved by the proposed approach, with which all operators succeeded in transporting the object without collision nor tumble of the object.
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