A Fault Tolerance Measure for Spatial Serial and Parallel Robotic Manipulators Driven by Single and Dual Actuators

Vittorio Monteverde and Sabri Tosunoglu

Florida International University
Department of Mechanical Engineering
Miami, Florida 33199 USA
E-mail: tosun@fiu.edu

Abstract - The state of the art technology of fault tolerance is becoming an important design issue in many applications of mechanical systems. Reliability is enhanced with the inclusion of fault tolerance in the mechanical design. With the added implementation of this technology, methods to distinguish how much fault tolerance is included in a manipulator has become necessary. In this work, a fault tolerance measure is developed to describe the fault-tolerant capacity of robotic manipulators. The mechanical design options that affect fault tolerance include the actuation of joints by single or dual motors; serial, parallel or hybrid structures; kinematic redundancy; and the use of multiple systems. The spectrum of mechanical designs is represented in a four-level, hierarchical fault-tolerant architecture. The measure is evaluated for a wide variety of robots which use various design elements from the four-level fault-tolerant architecture.

INTRODUCTION

Fault tolerance is state of the art technology currently receiving added attention in modern mechanical systems and robotics. Fault tolerance provides for completion of task requirements despite failures of individual components. These characteristics are especially important for robots when they operate in hazardous environments. These environments may be space, nuclear power plants, battlefields, mines, or deep sea worksites. As robots attempt to operate under these circumstances, their reliability becomes a primary concern. Should a robot encounter difficulty in a hazardous environment, it may not be able to complete the specified task or return to safety. The losses in such a situation could be devastating, especially if human lives are endangered in trying to retrieve the robot. The reliability of such systems therefore becomes extremely critical.

Fault tolerance can provide reliability for robotic systems as it has for computer hardware and software, where it has been used extensively. With the inclusion of fault tolerance, robots can sustain operation even with the occurrence of component failures. Ideally, a fault-tolerant system should continue to operate after a failure of one of its components with little or no effect on performance.

As robots become more readily available and fault tolerance further develops in robotics, a need to determine how much fault-tolerant capability a system contains has become necessary. Such a measure is developed in this paper. The measure is demonstrated in the analysis of serial and parallel, spatial robotic structures.

MECHANICAL FAULT TOLERANCE LEVELS IN ROBOT DESIGN

Four distinct levels of mechanical fault-tolerant robot designs are distinguished at joint, link, subsystem and system levels [8-9, 12-13].

Each level of design offers a fault tolerance enhancement at varying degrees of sophistication to isolate faults in the system. The levels are subsumptive with the lower levels providing fault isolation capability locally, whereas higher levels are more capable to mask faults globally.

Single and Dual Actuation at Joint Level

The joint level of fault tolerance deals with the actuation systems of the individual joints. Single actuators are the simplest and most common means of driving a link. However, a single actuator at a joint does not provide any fault tolerance for the robot at that particular joint.

To add fault tolerance at the joint level, an actuator can be duplicated at the joint [1]. This setup defines a dual-actuator system. A dual-actuator system incorporates two actuators to drive a single degree of freedom (DOF) of the robot as shown in Figure 1. During normal operation, the two actuators may compliment each other by applying torques in the same direction which can increase the payload capacity of the robot or one of the actuators may apply a small amount of counter-torque to reduce or eliminate joint backlash.

Figure 1. Dual Actuation System

The advantage of the dual-actuator system is in that a single actuator failure can be handled by disengaging the failed actuator with a clutch mechanism and allowing the second actuator to drive the joint. The remaining system may have to operate with a reduced load carrying capacity or increased backlash, depending on the normal operating condition strategy, but the operation will not have to be aborted. Thus, although some mechanical advantage is lost in the system with a single actuator failure, the task can still be completed successfully. Researchers at NASA have investigated the possibility for incorporating dual-actuators on the Space Shuttle Remote Manipulator System (SSRMS) and have had favorable results [19].

Serial and Parallel Mechanisms at Link Level

This level of fault tolerance involves the type of links used in the robot structure. The simplest and most common link type is the serial link. Similar to the single actuator, the serial link is the simplest and cheapest to incorporate. Also, a serial link does not provide any fault tolerance to the robotic system in this level. Fault tolerance at this level can be included by the use of parallel mechanisms, such as a four-bar mechanism as in Figure 2, to drive one DOF of the robot [15].

Parallel mechanisms are inherently more stable than serial links. The fault tolerance gained with a parallel mechanism is that upon failure, the added stability of the mechanism limits the error deterioration, and allows the system to recover more rapidly than a serial link. Parallel mechanisms are generally driven by two actuators at each of the ground joints, which also adds fault tolerance at the actuation or joint level acting similar to dual-actuators.

Figure 2. Link Level Fault Tolerance


Non-Redundant and Redundant Manipulators at
Subsystem Level

This level of fault tolerance is defined by the kinematic redundancy of a robotic arm. Kinematic redundancy is achieved by the addition of DOFs greater than the amount necessary for the robot to complete its task [7, 10]. Figure 3 illustrates two kinematically redundant robots. The Robotics Research arm is a 7-DOF robot that is partially modular. users can not disassemble them, but the company can with relative ease. The second robot is the Odetics 7-DOF robot that has dual-actuators (14 total) placed at every joint. This robot incorporates the joint and subsystem levels of fault tolerance.

For instance, a three dimensional workspace requires a six DOF robot and any added links provide fault tolerance capabilities at this level. When a failure occurs at a joint of a 7-DOF manipulator, the robot loses its mobility by one DOF. The brake is applied to the failed link and the controller reconfigures the 7-DOF robot as a 6-DOF system. The robot may be able to maneuver itself around the workspace and complete the task even after failure. However, the full range of motions may be limited after failure if the redundancy of the robot is not well designed, and the robot may not be able to complete the task in the case of undesirable failure conditions.

Figure 3. Robotics Research K-807i Robot (left)
and Odetics 7-DOF Manipulator (right)

Single and Multiple Manipulators at System Level

This level of fault tolerance is incorporated when the other levels are not available. System level fault tolerance involves an additional robot placed nearby the original serving as either a backup or cooperating system. The additional robot can either take over the job entirely of a fully failed robot or cooperate with a partially failed robot. This level of fault tolerance allows for task completion even after full failure of a robot.

Figure 4. Two 7-DOF Robotics Research
Dual Manipulator System

FAULT TOLERANCE CAPACITY

The fault tolerance measure to provide a measure of the capacity of different robotic mechanical architectures to tolerate system faults is defines as

(1)

where FTM represents the fault tolerance capacity of the robot, w_i is the weighting factor for the i'th component,
and a_i stands for the total number of the i'th component included.

This relationship limits the fault-tolerant capacity of robotic manipulators to a value between 0 and 100 percent. Over-constrained robots (not enough DOFs for the workspace) automatically have a capacity of 0 percent as they are insufficient to carry out the operation when fully operational regardless of what structure they encompass. The maximum of 100 percent in the measure is a theoretical limit describing a robot with an infinite number of fault-tolerant components and thus foolproof of failure.

Methods for measuring the dexterity of manipulators have been previously developed [5, 7, 20]. Measures for fault-tolerant characteristics of manipulators have also previously been researched. In [6], a kinematic failure tolerance measure is developed that insures local desired velocity satisfaction in the vicinity of a failure if the measure value is large. In [11], a numerical method for fault-tolerant workspace determination is developed that can be used as an aid in the design of redundant robots. However, these methods focus on the subsystem level fault tolerance, where one failed joint actuator is locked in place, of a kinematically redundant serial manipulator.

The fault tolerance capacity measure proposed in this paper is a tool for comparison of different manipulators in terms of their fault tolerance and unites all four levels of the fault-tolerant mechanical architecture to apply to most manipulators. However, the measure is exclusive to these four levels and does not account for fault tolerance in sensors, fault detection and identification schemes, nor fault tolerant controllers, but these are essential components of any fault tolerant system [2-4, 14-18]. The measure is based only on the kinematic framework of the manipulators. We now define the base system and the weighting system used in the development of fault tolerance measure.

Definition of Base System: The base system is described as the simplest robotic architecture necessary relative to the robot being evaluated. The base system may be defined as the minimum configuration robot required to perform a task. The minimum configuration robot is defined by the least amount of DOFs necessary to complete the required task and is represented by its mobility m_b. For example, in the case of a planar robot, 3 DOFs will be necessary, and in the case of a spatial robot, 6 DOFs will be necessary, where m_b = 3 and 6, respectively. In the base system, each DOF is driven by a single actuator, and the structure contains only serial links as this is the most basic mechanical architecture for manipulators.

Definition of Weighting System: The weighting system provides numerical weights for the fault tolerance of robotic system components. The values of the weights in Table 1 indicate the relative advantages obtained from the different components when utilized in the design of a fault-tolerant robot. The numerical weights are relative values selected for fitting the component's fault tolerance enhancement to a system. Therefore, the values of the weighting terms describe the relative improvement in fault tolerance gained with the addition of the particular component.

The base weight being used is 1 and is therefore inherited by the base system components: actuators and serial links as shown in Table 1. The parallel linkage weight of 1.3 represents the relative advantage of using a parallel mechanism in place of a serial link. Values deviating from this weight give the parallel mechanism unreasonable fault tolerance enhancement. The redundant link weight is described as a function of the mobility of the base system. This is because it needs to accomodate all systems: planar, spatial, or any other. The mobility term compensates for the number of terms added so that the addition of the redundant link is not negligible or overwhelming for the cases of large and small robots, respectively. In the case of a spatial robot, m_b = 6 and so the redundant link weight becomes

w₄ = m_b / 3 = 6 / 3 = 2

which is twice as much as that due to a serial link. For planar robots, this weight is only 1. The difference is due to the fact that equal values have a smaller effect on larger robots, and therefore the term must be a function of the robot size.

The four different components shown on the table can be used to describe the fault tolerance of any robotic manipulator. The summation for the base system can now be given by

(2)

but a₃ = a₄ = 0 and a₁ = a₂ = m_b for the base system since it does not include any redundant links or parallel links and has only one actuator and serial link per DOF. Also, w₁ = w₂ = 1 for the serial links and actuators so that the base system is described as

(3)

and the final formulation for the fault-tolerant capacity measure is defined as

(4)

SPATIAL ROBOT SYSTEMS

For three-dimensional manipulators the minimum configuration robot necessary for full operation is a 6-DOF serial robot. Thus, the base system mobility of planar arms is m_b = 6, as demonstrated previously. This fact further reduces the fault tolerant capacity measure for planar robots to:

(5)

This is the final form of the measure when applied to spatial manipulators. The following section will step through examples incorporating the levels of fault tolerance in their kinematic structure.

EXAMPLES OF THE FAULT TOLERANT CAPACITY MEASURE FOR SPATIAL ROBOTS

Example 1

The robot labeled 1 in Figure 5 is a 6-DOF, serial manipulator. This robot is the most common in industry and represents the minimum configuration robot for 3-dimensional manipulation. Thus, it also represents the base system for spatial manipulators and has no fault tolerance capacity. This is can be seen from the measure since the summation of the actual system from Equation 1 is the same as the summation of the base system. Thus, the quotient term from Equation 1 becomes 1 and FTM is 0:

Example 2

Robot 2 in this figure demonstrates the implementation of the link level of fault tolerance. The manipulator has 3 parallel mechanisms, 3 serial links, and 6 actuators in its structure. The summation of its components yields

and the fault tolerance capacity of this manipulator can be found to be

The fault tolerance gained by this manipulator demonstrates the effects of the addition of parallel mechanisms in place of serial links.

Example 3

Robot 3 in Figure 5 demonstrates the addition of a dual-actuator to the configuration of a 6-DOF manipulator. This robot has 6 serial links and 7 actuators and is therefore described by

giving a fault tolerance capacity of

which is greater than the manipulator in Example 1 that had 3 parallel mechanisms. This demonstrates the superior fault tolerance enhancement of the joint level over the link level. This significant advantage is due to the fact that the joint level provides fault tolerance against a particular actuator's failure while the link level only adds stability to aid in the recovery process once a failure has occurred. However, it should be noted that when parallel mechanisms are implemented, one actuator is usually placed at each of the base joints, which can behave as a dual-actuator driving a single DOF. Thus, the system would have added fault tolerance from joint level as well as from the link level.

Example 4

Robot 9 in this group exhibits a combination of the joint and link level of fault tolerance. This manipulator has 2 parallel links in its structure, along with 4 serial links and 10 actuators. These components result in

which result in

The higher fault tolerance of this manipulator is attributed to both the additional parallel mechanisms and dual-actuator systems in the configuration.

Example 5

Robots 13 through 24 demonstrate the implementation and fault tolerance gained by introducing the subsystem level fault tolerance to the lower levels. Robot 13 demonstrates the fault tolerance gained (20%) by the addition of a single redundant link to a minimum configuration spatial manipulator. This gain is much greater than that gained by inclusion of the lower levels. This significant increase in fault tolerance with the subsystem level is because it guards against the failure of any actuator failure, not just a particular actuator's failure as was the case for the joint level of fault tolerance.

Robot 23 illustrates a combined implementation of the first three levels of fault tolerance. This manipulator has 8 DOFs. It includes 10 actuators, 2 parallel mechanisms, 4 serial-non-redundant links and 2 redundant links. The manipulator is therefore described as

with a fault tolerance measure of

As expected, this manipulator shows a drastic increase in FTM relative to the previous case as it includes the subsystem level of fault tolerance. Robot 24 in the figure has a fault tolerance measure of 50%, the largest of any of the other robots in the figure. This robot has 4 redundant links in its configuration and thus demonstrates the supremacy of the subsystem level fault tolerance over the joint and link levels.

Fault tolerance at the system level may not be an attractive design option unless extraordinary reliability is required. This is so due to the high cost of backup systems. However, it may be a feasible option in a case where an additional arm is already available at close proximity (on an assembly line for instance) which is not originally installed for the purpose of fault tolerance. This level's fault tolerance capacity can be measured in the same manner as the previous levels. If one robot is capable of performing the task on its own, then all of the second robot's DOFs are redundant.

CONCLUSIONS

A fault tolerance measure is introduced and employed extensively to spatial robotic architectures encompassing the four levels of the fault tolerant mechanical architecture. The measure accounts for the advantages gained from using different components in a robot's mechanical structure such as the use of single and dual actuators at joints, single and parallel kinematic structures, redundant arms and multiple robots. The fault tolerance measure developed in this paper is used as a comparative tool to describe the fault-tolerant characteristics possessed by manipulators.

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