Stable control of a simulated one-legged running robot with hip and leg compliance

Abstract

We present a control strategy for a simpli ed model of a one-legged running robot which features compliant elements in series with hip and leg actuators. For this model, proper spring selection and initial conditions result in \passive dynamic" operation close to the desired motion, without any actuation. However, this motion is not stable. Our controller is based on online calculations of the desired passive dynamic motion which is then parametrized in terms of a normalized \locomotion time." We show in simulation that the proposed controller stabilizes a wide range of velocities and is robust to modelling errors. It also tracks changes in desired robot velocity and remains largely passive despite a xed set of springs, masses, and inertias. Comparisons of simulated runs with direct hip actuation show 95% hip actuation energy savings at 3m=s. Such energy savings are critical for the power autonomy of electrically actuated legged robots.

Nonlinear control of mechanical systems with one degree of underactuation

“…Though not indicated in the figure, massless springs may be attached between links and between links and the inertial reference frame; prismatic joints between links are also allowed. This class of systems clearly includes the Acrobot [2,36,52], the brachiating robots of [15,34,35,46], the gymnast robots of [32,39,57] when pivoting on a high bar, and the stance phase models of Raibert's onelegged hopper [1,6,14,26,33,42] as well as RABBIT [7][8][9][10]41]. The control objectives will be to stabilize the system about an equilibrium point or to track a set of reference trajectories with internal stability.…”

“…Figure 2 shows an example of such a system. This class of systems clearly includes the gymnast robot of [32] when dismounting from the high bar, the planar diver of [17], the flip gait of the robot in [16], the ballistic phase of the 4-link planar robot in [47], and the ballistic phase of running in planar biped robots [8] and Raibert's hopper [1,6,14,26,42]. The control objective will be to maximally linearize the system so as to facilitate the construction of a trajectory that transfers the state of the system from one point to another in finite time.…”

“…Let the potential energy, V, depend only on the configuration variables and be smooth. Denote the Lagrangian by L = K − V and assume that the system is actuated according to (1). The model can then be written as in (2).…”

“…are the entries in the first row of D. The definition of R(q,q) and the required 1 Recall that simple means that the kinetic energy is quadratic in the velocities and the potential energy depends only on the configuration variables.…”

The Spring Loaded Inverted Pendulum as the Hybrid Zero Dynamics of an Asymmetric Hopper

“…Instead, many empirical control procedures have been employed over the past twenty years to control hopping and running robots or robot models; see [36], [1], [17], [14], [30], [24], [10], [2] for examples of one-legged robots. In many cases, e.g.…”