Lateral stability of the spring-mass hopper suggests a two-step control strategy for running.

This paper investigates the control of running gaits in the context of a spring loaded inverted pendulum model in three dimensions. Specifically, it determines the minimal number of steps required for an animal to recover from a perturbation to a specified gait. The model has four control inputs per step: two touchdown angles (azimuth and elevation) and two spring constants (compression and decompression). By representing the locomotor movement as a discrete-time return map and using the implicit function theorem we show that the number of recovery steps needed following a perturbation depends upon the goals of the control mechanism. When the goal is to follow a straight line, two steps are necessary and sufficient for small lateral perturbations. Multistep control laws have a larger number of control inputs than outputs, so solutions of the control problem are not unique. Additional constraints, referred to here as synergies, are imposed to determine unique control inputs for perturbations. For some choices of synergies, two-step control can be expressed as two iterations of its first step policy and designed so that recovery occurs in just one step for all perturbations for which one-step recovery is possible.

Optimal motor control may mask sensory dynamics.

Properties of neural controllers for closed-loop sensorimotor behavior can be inferred with system identification. Under the standard paradigm, the closed-loop system is perturbed (input), measurements are taken (output), and the relationship between input and output reveals features of the system under study. Here we show that under common assumptions made about such systems (e.g. the system implements optimal control with a penalty on mechanical, but not sensory, states) important aspects of the neural controller (its zeros mask the modes of the sensors) remain hidden from standard system identification techniques. Only by perturbing or measuring the closed-loop system "between" the sensor and the control can these features be exposed with closed-loop system identification methods; while uncommon, there exist noninvasive techniques such as galvanic vestibular stimulation that perturb between sensor and controller in this way.