Hostname: page-component-7b7567c8c-kwt9d Total loading time: 0 Render date: 2026-11-15T06:32:43.531Z Has data issue: false hasContentIssue false
  • English
  • Français

The tau of flight control

Published online by Cambridge University Press:  27 January 2016

G. D. Padfield
G. D. Padfield*
Affiliation:
The University of Liverpool, Liverpool, UK
*
gareth.padfield@liverpool.ac.uk
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

With this survey paper, the author proposes a new ‘tao’ – a new way of understanding – of how pilots do what they do. Research into the control of purposeful action in the natural world suggests that very rapid, efficient and ‘instinctive’ techniques have evolved based on the time to close on a goal, or close a gap, τ(t), and its derivatives. Purposeful actions involve the closure of one or more physical gaps, each with its own time to close, varying with time. Maintaining a constant rate of change of τ(t) with time (< 1) during an approach will ensure a successful arresting when the gap is closed, but an animal’s strategy can be adapted to the circumstances to achieve either a hard stop (aggressive action with ṫ > 0·5), or a soft stop (gentle action with ṫ < 0·5). Synchronous coupling of two motions, x(t) and y(t), such that the times to close are coupled, τx = kτy, results in the motion gaps x(t) and y(t) being related through a power law, x = Cy1/k, and closing smoothly together; examples of such coupling in the form of pursuit tracking in the natural world abound. Research has also shown that gaps can be closed by following ‘intrinsic’ guides, or self-generated mental models of desired motion, that have particular forms; for example, constant deceleration or constant acceleration. The gathering evidence from research into animal behaviour in the natural-world forms a background for the exploration of flight control in the man-made world. The implications for control theory, flight control developments and flight handling qualities, are considered to be profound. τ-theory suggests that natural control has a particular non-linear, albeit very simple, time varying form and that pilots learn control strategy skills by developing mental models, or internalised schemata, in the form of what are described as ‘τ guides’. In this context the author presents his perspective on flight control, briefly reviewing τ-theory and providing examples from research conducted at The University of Liverpool during the period 1999-2011, including the work of several PhD students. Concepts for guidance algorithms suitable for augmented manual or autonomous control are discussed and the implications for handling qualities developments, particularly relating to flight in degraded visual conditions, are presented. Some outstanding questions pointing directions for future research are raised.

Information

Type
Survey Paper
Information
The Aeronautical Journal , Volume 115 , Issue 1171 , September 2011, pp. 521 - 556
Copyright
Copyright © Royal Aeronautical Society 2011 

References

1 Padfield, G.D., Jones, J.P., Charlton, M.T., Howell, S. and Bradley, R. Where Does the Workload Go When Pilots Attack Manoeuvres? – An Analysis of Results from Flying Qualities Theory and Experiment, Proceedings of the 20th European Rotorcraft Forum, Amsterdam, The Netherlands, October 1994.Google Scholar
2 Jones, J.G., Padfield, G.D. and Charlton, M.T. Prediction of pilot workload in helicopter low level flying tasks through the application of adaptive wavelet decomposition, Aeronaut J, January 1999, 103, (1019).Google Scholar
3 Milne, R.D. and Padfield, G.D. The Strongly Controlled Aircraft, Aeronaut Q, May 1971, XXII, part 2, pp 146–168.Google Scholar
4 McRuer, D.e, Ashkenas, I. and Graham, D. Aircraft Dynamics and Automatic Control, Princeton University Press, Princeton, NJ, USA, 1973 Google Scholar
5 McRuer, D.T. and Krendel, E.S. Mathematical Models of Human Pilot Behaviour, AGARD AG-188, AGARD, Paris, France, 1974.Google Scholar
6 Krendel, E. and McRuer, D. A servomechanisms approach to skill development, J Franklin Institute, January 1960, 269, (1).Google Scholar
7 Padfield, G.D. Helicopter Flight Dynamics, 2nd ed, Blackwell Science, Oxford, UK, 2007.Google Scholar
8 Bradley, R. The Flying Brick Exposed: Non-Linear Control of a Basic Helicopter Model, Glasgow Caledonian University Technical Report, TR/MAT/96-51, 1996.Google Scholar
9 Bradley, R. and Thomson, D.G. Inverse simulation as a tool for flight dynamics research – Principles and applications, Progress in Aerospace Sciences, May 2006, 42, (3), pp 174–210.Google Scholar
10 Gibson, J., et al, Parallax and perspective during aircraft landings, American J Psychology, 1955, 68.Google Scholar
11 Perrone, J.A. The Perception of Surface Layout During Low Level Flight, NASA CP 3118, 1991.Google Scholar
12 Lee, D.N. Tau in action in development, in Action as an Organizer of Learning and Development (pp 3–49) Rieser, J.J., Lockman, J.J. and Nelson, C.A. (Eds) (Hillsdale, N.J. Erlbaum), 2005.Google Scholar
13 Padfield, G.D. and White, M.D. Flight simulation in academia; HELIFLIGHT in its first year of operation, Aeronaut J, September 2003, 107, (1075), pp 529–538.Google Scholar
14 White, M., Perfect, P., Padfield, G.D. and Gubbels, A. Acceptance testing of a rotorcraft flight simulator for research and teaching: the importance of unified metrics, 35th European Rotorcraft Forum, Hamburg, Germany, September 2009.Google Scholar
15 Lee, D.N., Simmons, J.A., Saillant, P.A. and Bouffard, F. Steering by echolocation: a paradigm of ecological acoustics, J Comp Physiol A, 1995, 176, pp 347–354.Google Scholar
16 Davies, M.N.O. and Green, P.R. Optic flow-field variables trigger landing in hawk but not pigeons, Naturwissenschaften, 1990, 77, pp 142–144.Google Scholar
17 Lee, D.N. and Reddish, P.E. Plummeting gannets: a paradigm of ecological optics, Nature, 24 September 1981, 293.Google Scholar
18 Lee, D.N., Reddish, P.E. and Rand, D.T. Aerial docking by hummingbirds, Naturwissenschaften, 1991, 78, pp 526–527.Google Scholar
19 Lee, D.N., et al, Common principle of guidance by echolocation and vision, J Comp Physiol A, 1992, 171, pp 563–571.Google Scholar
20 Lee, D.N., Davies, M.N.O., Green, P.R. and van der Weel, F.R. Visual control of velocity of approach by pigeons when landing, J Experimental Biology, 1993, 180, pp 85–104.Google Scholar
21 Lee, D.N. Visual Information During Locomotion, Perception: Essays in Honor of James J. Gibson, MacLeod, R.B. and JnrPick, H.L. (Eds)(pp. 250–267), Ithaca and London: Cornell University Press, 1974.Google Scholar
22 Lee, D.N. A theory of visual control of braking based on information about time-to-collision, Perception, 1976, 5, pp 437–459.Google Scholar
23 Lee, D.N. The Optic Flow-field: the Foundation of Vision, Phil Trans R. Soc, London, USA, 1980, B 290, pp 169–179.Google Scholar
24 Gibson, J.J. Perception of the Visual World, The Riverside Press, Houghton Mifflen Company, Boston, Mass, USA, 1950.Google Scholar
25 Gibson, J.J. The Ecological Approach to Visual Perception, LEA Inc Publishers, NJ, USA, 1986.Google Scholar
26 Lee, D.N. Guiding movement by coupling taus, Ecological Psychology, 1998, 10, pp 221–250.Google Scholar
27 Lee, D.N., Young, D.S. and Rewt, D. How do somersaulters land on their feet? J experimental psychology, human perception and performance, 1998, 18, pp 1195–1202.Google Scholar
28 Lee, D.N. and Schogler, B. Music through movement, in Communicative Musicality: Narratives of Expressive Gesture and Being Human (Eds) Malloch, S and Trevarthen, C. (Oxford: Oxford University Press), 2006.Google Scholar
29 Lee, D.N., von Hofsten, C. and Cotton, E. ‘Perception in action approach to cerebral palsy’, in The Neurophysiology and Neuropsychology of Motor Development (pp 257–285) Connelly, K., Forrsberg, H (Eds) (London: Mac Keith Press), 1997.Google Scholar
30 JrWarren, W.H., Young, D.S. and Lee, D.N. Visual control of step length during running over irregular terrain, J Experimental Psychology: Human Perception and Performance, 1986, 12, pp 259–266.Google Scholar
31 van der Meer, A.L.H., van der Weel, F.R. and Lee, D.N. Prospective control in catching in infants, Perception, 1994, 23, pp 287–302.Google Scholar
32 Craig, C.M. and Lee, D.N. Neonatal control of nutritive sucking pressure: evidence for an intrinsic tau-guide, Experimental Brain Research 124 371-382, 1999.Google Scholar
33 Lee, D.N. and Young, D.S. Visual timing of interceptive action, Brain mechanisms and spatial vision, Dordrecht, The Netherlands, 1985.Google Scholar
34 Padfield, G.D., Clark, G. and Taghizard, A. How long do pilots look forward? Prospective visual guidance in terrain hugging flight, J American Helicopter Society, April 2007, 52, (2).Google Scholar
35 Clark, G. Helicopter Handling Qualities in Degraded Visual Environments, PhD thesis, The University of Liverpool, Liverpool, February 2007.Google Scholar
36 Jump, M. Prospective Sky Guides; developing guidelines for pilot vision aids, PhD thesis, The University of Liverpool, Liverpool, April 2007.Google Scholar
37 Jump, M. and Padfield, G.D. Investigation of flare manoeuvres using optical tau, AIAA J Guidance, Control and Dynamics, October 2006, 25, (5), pp 1189–1200.Google Scholar
38 Jump, M. and Padfield, G.D. Progress in the development of guidance strategies for the landing flare manoeuvre using tau-based parameters, Aircraft Engineering and Aerospace Technology, 2006, 78, (1), pp 4–12.Google Scholar
39 Jump, M. and Padfield, G.D. Development of a nature-inspired flare command algorithm, AIAA Guidance, Navigation and Control Conference, Hilton Head, N. Carolina, USA, August 2007.Google Scholar
40 Heffley, R. Closed Loop analysis of manual flare and landing, AIAA paper 74-834, Mechanics and Control of Flight Conference, Anaheim, California, USA, 1974.Google Scholar
41 Heffley, R.K. et al An analysis of airline landing flare data based on flight and training simulator measurements, STI Tech Report, 1172-1R, Mountain View, California, USA, 1982.Google Scholar
42 anon, Aeronautical Design Standard – 33E PRF, Performance Specification, Handling Qualities Requirements for Military Rotorcraft, US Army AMCOM, Redstone, AL, USA, March 2000.Google Scholar
43 Padfield, G.D., Lee, D.N. and Bradley, R. How do pilots know when to stop, turn or pull-up? Developing guidelines for the design of vision aids, J American Helicopter Society, April 2003, 48, (2), pp 108–119 (also proc of 57th AHS annual forum, May 2001).Google Scholar
44 Moen, G.C., DiCarlo, D.J. and Yenni, K.R. A parametric analysis of visual approaches for helicopters, NASA TN-8275, December 1976.Google Scholar
45 Lockett, H.A. The role of tau guidance during decelerative helicopter approaches, PhD thesis, The University of Liverpool, Liverpool, February 2010.Google Scholar
46 Cooper, G.E. and Jr.Harper, R.P., The use of pilot ratings in the evaluation of aircraft handling qualities, NASA TM D-5133, 1969.Google Scholar
47 Key, D.L., Blanken, C.L. and Hoh, R.H. Some lessons learned in three years with ADS-33C, Piloting Vertical Flight Aircraft; a NASA/AHS conference on flying qualities and human factors, San Francisco, USA, January 1993.Google Scholar
48 Hoh, R.H. Lessons learned concerning the interpretation of subjective handling qualities pilot rating data, AIAA paper 902824, AIAA Atmospheric Flight Mechanics Conference, Portland, Oregon, USA, August 1990.Google Scholar
49 Padfield, G.D. The Contribution of Handling Qualities to Flight Safety, Royal Aeronautical Society Conference of Rotorcraft Flight Safety, London, UK, November 1998.Google Scholar
50 Padfield, G.D. The making of helicopter flying qualities; A requirements perspective, Aeronaut J, December 1998.Google Scholar
51 Hoh, R.H. New Developments in Flying Qualities Criteria with Application to Rotary-Wing Aircraft, Helicopter Handling Qualities, NASA CP 2219, April 1982.Google Scholar
52 Hoh, R.H. Investigation of Outside Visual Cues Required for Low Speed and Hover, AIAA Paper 85-1808 CP, 1985.Google Scholar
53 Hoh, R.H. Handling Qualities for Very Low Visibility Rotorcraft NoE Operations, AGARD CP 423, Oct 1986.Google Scholar
54 Johnson, W.W. and Kaiser, M.K. (Eds), Visually guided control of movement, NASA CP 3118, 1991.Google Scholar
55 Blanken, C.L. and Whalley, M.S. (Eds), Piloting Vertical Flight Aircraft: a conference on flying qualities and human factors, NASA CP 3220, 1993.Google Scholar
56 Kaiser, M.K. Visual information for judging temporal range, proceedings of ‘Piloting Vertical Flight Aircraft: a conference on flying qualities and human factors’, NASA CP 3220, 1993.Google Scholar
57 Hoyle, F. The Black Cloud, Penguin Classics, 2010 (originally published by Heinmann in 1957).Google Scholar
58 Padfield, G.D. et al An integrated methodology manual for the evaluation of rotorcraft day/night all weather systems; 1st edition – preliminary guidelines based on DRA best practice in operational effectiveness, handling qualities and human factors, DRA/AS/SID/580/CR96221/1, June 1996.Google Scholar
59 Hoh, R.H., Bailey, S.W. and Morgan, J.M. Flight Investigation of the Tradeoff between Augmentation and Displays for NoE Flight in Low Visibility, Rotorcraft Flight Controls and Avionics, AHS National Specialists Meeting, Cherry Hill, NJ, USA, October 1987.Google Scholar
60 Blanken, C.L., Hart, D.C. and Hoh, R.H. Helicopter Control Response Types for Hover and Low Speed Near-Earth Tasks in Degraded Visual Conditions, Proceedings of the 47th Annual Forum of the American Helicopter Society, Pheonix, USA, May 1991.Google Scholar
61 Kimberley, A.M. and Padfield, G.D, An Evaluation of Flying Qualities in UCE 3, Workshop on Helmet Mounted Displays, NASA Ames Research Center, February 1994.Google Scholar
62 Hoh, R., ACAH Augmentation as a means to Alleviate Spatial Disorientation for Low Speed and Hover in Helicopters, American Helicopter Society International Conference on Advanced Rotorcraft Technology and Disaster Relief, Heli Japan, Gifu City, Japan, April 1998.Google Scholar
63 McRuer, D.T. and Graham, D. Flight control theory; triumphs of the systems approach, J Guidance, Control and Dynamics, March–April 2004, 27, (2).Google Scholar
64 Heffley, R.K. A pilot-in-the-loop analysis of several kinds of helicopter acceleration-deceleration maneuvers, Proceedings of specialists meeting on Helicopter Handling Qualities, NASA 2219, April 1982.Google Scholar
65 Padfield, G.D. and White, M.D. Measuring simulation fidelity through an adaptive pilot model, Aerospace Science and Technology, May 2005, 9, pp 400–408.Google Scholar
66 White, M.D., Padfield, G.D. and Armstrong, R. Progress with the Adaptive Pilot Model in Simulation Fidelity, 50th Annual Forum of the American Helicopter Society, Baltimore, MD, USA, June 2004.Google Scholar
67 Armstrong, R. Simulation Fidelity through an Adaptive Pilot Model, PhD thesis, The University of Liverpool, Liverpool, UK, October 2009.Google Scholar
68 Manimala, B.J., Walker, D.J., Padfield, G.D., Voskuijl, M. and Gubbels, A.W. Rotorcraft simulation modelling and validation for control law design, Aeronaut J, February 2007, 111, (1116), pp 77–88.Google Scholar
69 White, M.D., Perfect, P., Padfield, G.D., Gubbels, A.W. and Berryman, A.C. ‘Progress in the development of unified fidelity metrics for rotorcraft flight simulators’, 66th Annual Forum of the American Helicopter Society, Phoenix, AZ, USA, May 2010.Google Scholar
70 Perfect, P., White, M.D. and Padfield, G.D. Integrating Predicted and Perceived Fidelity for Flight Simulators, proc 36th European Rotorcraft Forum, Paris, France, September 2010.Google Scholar
71 Baker, H. An investigation of Pilot Modelling for Helicopter Handling Qualities Analysis, PhD Thesis, The University of Liverpool, Liverpool, November 2010.Google Scholar
72 Milne, R.D. The analysis of weakly coupled dynamical systems, Int J Control, 1965, 2, (2).Google Scholar
73 Neumark, S. Problems of longitudinal stability below minimum drag speed and theory of stability under constraint, Aeronautical Research Council ARC R&M 2983, 1957.Google Scholar
74 Pinsker, W.J.G. Directional stability in flight with bank angle constraint as a condition defining a minimum acceptable value for Nv , RAE Tech Report 67 127, June 1967.Google Scholar
75 Jr.Curtiss, H.C. Stability and Control modelling, proc of the 12th European Rotorcraft Forum, Garmisch-Partenkirchen, Germany, September 1986.Google Scholar
76 Dryfoos, J.B., Kothmann, B.D. and Mayo, J. An Approach to Reducing Rotor-Body Coupled Roll Oscillations on the RAH-66 Comanche Using Modifed Roll Rate Feedback,’ 55th Annual Forum Proceedings of the American Helicopter Society, 1999.Google Scholar
77 Pavel, M. and Padfield, G.D. Understanding the peculiarities of rotor-craft-pilot couplings, Proc of the 64th Annual Forum of the American Helicopter Society, Montreal, Canada, May 2008.Google Scholar
78 Lantzsch, R., Wolfram, J. and Hamers, M. Increasing handling qualities and flight control performance using an air resonance controller, Proc American Helicopter Society 64th Annual Forum, Montréal, Canada, May 2008.Google Scholar
79 Davidson, B.R. Aircraft Pilot Couplings: Causes and Cures, PhD Thesis, The University of Liverpool, Liverpool, UK, December 2006.Google Scholar
80 McRuer, D.T. et al Aviation Safety and Pilot Control; Understanding and Preventing Unfavourable Pilot-Vehicle Interactions, National Academy Press, ASEB National Research Council, Washington DC, USA, 1997.Google Scholar
81 Gray, W.R. III Boundary-Avoidance Tracking: A New Pilot Tracking Model, AIAA Atmospheric Flight Mechanics Conference, San Francisco, California, USA, 15–18 August 2005, pp 86–97.Google Scholar
82 Padfield, G.D., Lu, L. and Jump, M. Optical Tau in Boundary Avoidance Tracking – a new perspective on pilot induced oscillations, to appear in the AIAA J Guidance, Control and Navigation , 2011 (see also proc 36th European Rotorcraft Forum, Paris, France September 2010).Google Scholar
83 Meyer, M. and Padfield, G.D. First steps in the development of handling qualities criteria for a civil tilt rotor, J American Helicopter Society, January 2005, 50, (1), pp 33–46.Google Scholar
84 Voskuijl, M., Rotorcraft Flight Control For Improved Handling, Loads Reduction And Envelope Protection, PhD Thesis, The University of Liverpool, Liverpool, UK, March 2007.Google Scholar
85 Voskuijl, M., Padfield, G.D., Walker, D.W., Manimala, B. and Gubbels, A.W. Simulation of automatic helicopter deck landings using nature inspired flight control, Aeronaut J, January 2010, 114, (1151), pp 25–34.Google Scholar
86 Childs, S., Active Control Technologies for Tilt Rotor Aircraft, PhD thesis, The University of Liverpool, Liverpool, UK, 2005.Google Scholar
87 Manimala, B., Padfield, G.D., Walker, D. and Childs, S. Synthesis and Analysis of a Multi-Objective Controller for Tilt-Rotor Structural Load Alleviation, 1st international conference on innovation and integration in aerospace sciences, Belfast, August 2005.Google Scholar
88 Nannoni, F., Giancamilli, G. and Cicale, M. ‘ERICA – The European Advanced Tilt Rotor’, proceedings of the 27th European Rotorcraft Forum, Moscow, Russia, September 2001.Google Scholar
89 Bruce, V., Green, P.R. and Georgeson, M.A. Visual Perception, Physiology, Psychology and Ecology, 3rd edn, Psychology Press, Hove, UK, 1996.Google Scholar
90 Gibson, J.J. and Crookes, L.E. A theoretical field analysis of automobile driving, American J Psychology, July 1938, LI, (3).Google Scholar
91 Gibson, J.J. Visually controlled locomotion and visual orientation in animals, British J Psychology, 1958, 49.Google Scholar
92 Dailey, M.J. Apparatus and method for self calibrating visual time to contact sensor, US Patent No. 5,559,695, 24 September 1996.Google Scholar
93 Stein, G.P. System and method for detecting obstacles to vehicle motion and determining time to contact therewith using sequences of images, US Patent No. 7,113,867 B1, 26 September 2006.Google Scholar
94 Kaneta, Y., Katsuyama, Y. and Ito, K. Determination of time to contact using a compound eye sensor, Artif Life and Robotics, 14, 279–283, 2009 (also proc of 14th International Symposium on Artificial Life and Robotics, Oita, Japan, 5-7 February 2009).Google Scholar
95 Cameron, N. and Padfield, G.D. Tilt rotor pitch/flight-path handling qualities, J American Helicopter Society, October 2010.Google Scholar
96 Gibson, J.J. The Senses Considered as Perceptual Systems, Houghton Mifflin, 1966.Google Scholar
97 Lee, D.N. Lee’s 1976 Paper (inc author’s update, General Tau Theory: evolution to date), Perception, 2009, 38, pp 837–858.Google Scholar
98 Lee, D.N. How movement is guided, unpublished note, The University of Edinburgh Perception, Motion and Action Research Centre, http://www.pmarc.ed.ac.uk, March 2011.Google Scholar
99 Jung, C.G. and Wilhelm, R. The Secret of the Golden Flower, reprinted by Book Tree Publishing, USA, November 2010.Google Scholar