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2017 | OriginalPaper | Chapter

7. Assistive Optimal Control-on-Request with Application in Standing Balance Therapy and Reinforcement

Authors : Anastasia Mavrommati, Alex Ansari, Todd D. Murphey

Published in: Trends in Control and Decision-Making for Human–Robot Collaboration Systems

Publisher: Springer International Publishing

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Abstract

This chapter develops and applies a new control-on-request (COR) method to improve the capability of existing shared control interfaces. These COR enhanced interfaces allow users to request on-demand bursts of assistive computer control authority when manual/shared control tasks become too challenging. To enable the approach, we take advantage of the short duration of the desired control responses to derive an algebraic solution for the optimal switching control for differentiable nonlinear systems. Simulation studies show how COR interfaces present an opportunity for human–robot collaboration in standing balance therapy. In particular, we use the Robot Operating System (ROS) to show that optimal control-on-request achieves both therapy objectives of active patient participation and safety. Finally, we explore the potential of a COR interface as a vibrotactile feedback generator to dynamically reinforce standing balance through sensory augmentation.

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previous chapter A Learning Algorithm to Select Consistent Reactions to Human Movements
next chapter Intelligent Human–Robot Interaction Systems Using Reinforcement Learning and Neural Networks
Footnotes
1
In this chapter a control action is a control vector with constant values applied for a (possibly infinitesimal) duration of time.
 
2
The notation, \(||\cdot ||_{M}^2\), indicates a norm on the argument where matrix, M, provides the metric (i.e., \(||x(t) ||_{Q}^2 = x(t)^T \, Q \, x(t)\)).
 
3
\(D_{x}f(\cdot )\) denotes the partial derivative \(\frac{\partial f(\cdot )}{\partial x}\).
 
4
At any specified application time, \(\tau _m\), of the COR interface, \(u_2^*(\tau _m)\) represents the optimal action that balances control authority and drives the mode insertion gradient to \(\alpha _d\) if activated around that time. Thus, \(u_2^*(t)\) is a schedule of optimal actions that can be switched to from NC, u(t), to produce a desired change in mode insertion gradient at \(\tau _m\).
 
5
Practically, this is not a very stringent requirement. Most spaces of interest are RKHS. Refer to [7] for more detail.
 
6
For equivalence, \(||\cdot ||\) refers to the \(\mathcal {L}_2\) norm and \(\mathcal {H}\) is additionally assumed to be an \(\mathcal {L}_2\) space.
 
7
A quadratic cost is assumed so that resulting equations emphasize the local similarity between burst control and LQR [2].
 
8
Interestingly, this scheme of intermittent instead of sustained control has been suggested to be natively used by the central nervous system (CNS) in human posture control in [31, 32].
 
9
As shown in Sect. 7.2, it is possible to provide parameters that guarantee local stability and convergence in the case when the Assistive Controller is continuously activated.
 
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Metadata
Title
Assistive Optimal Control-on-Request with Application in Standing Balance Therapy and Reinforcement
Authors
Anastasia Mavrommati
Alex Ansari
Todd D. Murphey
Copyright Year
2017
Book
Trends in Control and Decision-Making for Human–Robot Collaboration Systems

Print ISBN: 978-3-319-40532-2

Electronic ISBN: 978-3-319-40533-9

Copyright Year: 2017

DOI
https://doi.org/10.1007/978-3-319-40533-9_7