Plant
Conventionally, the initial step in designing a control system is to model the dynamics of the plant. There are numerous proposed models in the neuromotor movement
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modeling literature. The literature provides evidence of that the human neuromotor system is easily capable of solving the inverse dynamics or kinematics for an extreme large scope of complex arm movement tasks. The human neuromotor system can almost effortlessly solve the inverse dynamics problem of a typical reaching task. Regardless of the various proposed models, the focus within this section is to describe the high-level issues that relate to designing a controller for a human plant.
The key notion that must be clear is that we wish to fully leverage the physical acuity of the user and issue motion cues that specify a stable trajectory between the reaching task terminal points. This should includes allowance for user comfort during the movement task.
The obvious initial inclination is to model the system as a visual servoing prob- lem, but there are some natural constraints that must be taken into account. Even though the human arm can be viewed as a +6-DOF manipulator with differing sets of holonomic constraints on the various joints, there are some natural movement tenden- cies the allow for a significant reduction in the number of DOFs for object tracking. As a simple example, consider the lateral flexion and extension of the wrist. While it is possible to laterally move the wrist through a moderate extension arc and a very limited flexion arc, in a pronated position the wrist is normally axially aligned with the forearm because it requires minimal exertion. Given this natural movement behavior, we can reduce the problem by 1-DOF under the reasonable assumption that the user will maintain a wrist orientation that has minimal deflection from the forearm axis. Similar cases can be made for further reductions.
Regardless, we still find it valuable to examine the system in the context of a visual servoing problem. Using the taxonomy introduced by Sanderson and Weiss [80] which classifies visual servoing systems into four main categories: Dy- namic Position-based Look and Move (PBLM),Dynamic Image-based Look and Move
(IBLM),Position-based Direct Visual Servo(PBVS),Image-based Direct Visual Servo
(IBVS); this type of visually guided reaching task is considered to be an IBLM sys- tem. It is categorized as such because the feature-space controller uses point features extracted from each image to generate the set-points for the joint-space controller (the user) even though that error signal is in terms of camera motion, in feature-space, as opposed joint-space variables. The IBLM model is illustrated in Figure 2.2.
Thus we can view the overall system in layers, where the plant for the assistive device control system is the human user, but that human plant is viewed as servoing
Chapter 2: Describing the System 23 USER- GLOVE Joint-Level Controller Feature Space Controller Visual Feature Extraction ± ˆ f f
Figure 2.2: A block diagram modeling the assistive application at an high level abstraction as a generic Image-Base Look and Move visual servoing system
manipulator with an unconventional joint-space control scheme. In this way, the block diagram given in Figure 2.1 is contained within the USER-GLOVE Joint-Level Controller block of Figure 2.2.
The system uses a monocular vision eye-in-hand configuration and the user’s hand is considered to be the end-effector. Eye-in-hand systems are said to be end- point open-loop because the system only observes the target object, while visual servoing systems that employ a camera at a distance to the end-effector are said to be end-point closed-loop as both the target object and end-effector are seen [31]. Without an external reference camera, precise contact registration between the end- effector and the target cannot necessarily be achieved. An external reference view is generally desirable for a servoing task, but for a wearable assistive device it can be untenable. There are a number of issues with providing a second camera view. It is cumbersome and impractical to rigidly mount a second camera to some other part of the user’s body that can clearly provide an external reference view of the end-effector proximity to the target. Providing a second camera view entirely external to the user is counter productive as it constrains the use of the assistive device to only that locale. However, we can leverage the user’s intelligence and fine motor control ability in place of a number of key control processes. If we redefine the reaching task target position as some region in task-space that is very close to, but not in contact with the target object, then the goal is get the end-effector close enough. Once the end- effector reaches a point within that target region, the system can “transfer” control to the user to probe for the physical object; determine the appropriate orientations and forces for the tool (fingers) necessary to grasp the physical object.
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Generally, an image based visual servoing system follows an proportional error control law that compensates for the difference between the goal-view feature vector ˆ
f and the current-view feature vector,f, through camera motion given by ˙
p=K·J+v (p)(ˆf −f) (2.1)
where K is a gain matrix, J+v is the pseudo-inverse of the image Jacobian, and ˙p is the velocity screw of the terminal point on the end-effector. It can be advantageous to use moments of image feature within the feature vector as IBLM visual servoing from point features alone can result in infeasible camera motion due to the coupling between translational and rotational degrees of freedom in orientation errors and trajectory traversal [81].
In a conventional visual servoing application we have known, consistent, and precise physical dimensions for the manipulator, focal length of the camera, etc. So assignment of various coordinate frames; tool, camera, joint(s), base, and world are made. Thus the velocity screw can be defined as
˙
p=TxTy Tz ωα ωβ ωγT (2.2) with Tx,Ty, Tz denoting the translation velocities of the end-effector terminal point with respect to the manipulator’s base frame andωα,ωβ, ωγ denoting the rotational velocities about the base frame’s X-, Y-, Z-axis, respectively. In this kind of wear- able application there is no consistency of physical parameters from one manipulator unit to another (different users). In essence the only physical parameters that are consistent are the camera related parameters: resolution, focal length, angle of view, etc. Hence we can only rely on a consistent image-space.
The transforms between the base and various joint frames are not known, but as everyday experience tells us, they are not required for a movement solution. The transforms are part of our internalized neuromotor representation for the movement. Given that we are working with a visually impaired person in an unmapped envi- ronment, the task space is not fixed. It can extend beyond the arms length to any distance at which the target object is identifiable. Since visually impaired persons’ perceptual frame of reference is themselves, the task space is anchored by a egocentric frame of reference and can easily move within the external environment.
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the manipulator (arm), all torque control is also handled by the user, and the end- effector (hand), during natural movements, moves in hand-space coordinate frame, we can view the problem as control of 6-DOF kinematic point at end-effector.
In previous sections reductions in degrees of freedom related to natural coar- ticulations and sequencing of movement tasks, but we can also employ functional reductions in the number of degrees to simply the problem. Consider the functional task space for the reaching task. There is no need for the system to guide the user’s hand toward their own body. Thus postures of the arm-hand that are not directed outward from the body are unnecessary. Therefore in the context of the reaching task, the plant in this problem should be viewed as a 3-DOF kinematic point.