From quail to ostrich: modeling methods for deducing control priorities in running birds

Ground-running birds have a striking ability to run over uneven terrain with agility and efficiency. In our HFSP supported work, we seek the fundamental task-level control priorities that underlie this suite of locomotion behaviors. We address this question with a novel combination of cross-species obstacle experiments and trajectory optimization modeling analysis. We deduce that birds from quail to ostrich, a 540-fold mass range, achieve such dynamic locomotion primarily by regulating leg safety and energy economy, and surprisingly, without any direct behavioral objective for steadying their gait.

HFSP Young Investigator Grant holders Monica Daley and Jonathan Hurst and colleagues
authored on Sat, 01 November 2014

Cursorial birds run with impressive robustness even when confronted with highly variable terrain geometry. However, it’s difficult to determine if this apparent stability is a direct priority of control or achieved implicitly by intrinsic stabilizing dynamics in their legs.  To answer questions about control priorities and more rigorously analyze data from obstacle experiments, we built a mathematical model of the intrinsic leg dynamics of birds from quail to ostrich.  With this model, we use trajectory optimization techniques to optimize control in simulation, thereby testing if a hypothesized control priority replicates data collected from obstacle-negotiating birds.

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Our criterion for a successful model was its ability to explain key features of locomotion across species while using relatively few fitting parameters. For our target locomotion feature, we sought to explain a pronounced asymmetry in ground-reaction forces (GRF) observed across our sample of bird species.  Typical reduced-parameter running models, such as the energetically conservative spring-mass model, are fundamentally incapable of producing such asymmetric GRF.  To account for gait energy fluctuations, we added leg dissipation and a thrusting actuator to the spring-mass model, and used trajectory optimization to minimize the work applied by the time-varying actuator thrust (a proxy for overall energy economy).  This addition was able to closely fit our measured level-ground running data from ostrich to quail by fitting just two parameters (spring and dissipation coefficients).  Further, this model explains the general phenomenon of locomotion asymmetry as a work-optimal response to dissipation.

Having validated this model on level ground, we employed it to test specific hypotheses regarding obstacle negotiating priorities in birds.  Our bird experiments probed for the relative control priorities between body stability, energy economy, and leg injury avoidance by running birds over platform-like obstacles. Initial statistics on observed obstacle negotiation suggested that no species seemed to target body stability by steadying their gait.  Trajectory optimization analysis of our bird model further indicated why: that a hypothetical gait-steadying strategy would come at a cost in both energy economy and magnified leg forces (a source of injury risk).  Both our optimization-based modeling and statistical analyses suggest that the control priorities of all these species are the same, in spite of stark musculoskeletal and postural differences.  We believe this broad similarity in control priorities lends insight into the co-evolution of behavior and morphology in cursorial birds, their theropod dinosaur ancestors, and vertebrate locomotion in general.

Text by Christian Hubicki

Reference

Don’t break a leg: Running birds from quail to ostrich prioritise leg safety and economy in uneven terrain. A. V. Birn-Jeffery*, C. M. Hubicki*, Y. Blum, D. Renjewski, J. Hurst and M. Daley.  (*equal contribution).Journal of Experimental Biology, 217, 3786-3796, 2014.

Link to article

Teaching robots to run like birds: Comparative biomechanics inspire novel robot control - by Monica Daley and Jonathan Hurst