12

Miura and Shimoyama present a stilt-leg biped that walks

they are of less interest to animators.

dynamically in 3D on point feet [MS84].

Takanishi et al. [TIYK85] achieve a dynamic but very

rough, lurching 3D walk for a robot with anthropomorphic legs.

Furusho & Sano [FS90]

demonstrate the use of sensor-based feedback to produce smoother motions from a similar gait.

Raibert et al. [Rai+84] present an elegant three-way decomposition of control to accomplish

robust one-legged hopping in three dimensions which is later extended to bipedal and quadrupedal

models using the notion of a virtual leg[Rai86] [Rai86b].

2. 2. 4

Limit Cycle Control

A number of papers view bipedal walking and running motions as limit cycles in state space.

These are most closely related to the work in this thesis.

McGeer [McG89] [McG90] [McG90b]

demonstrates that various forms of passive legged locomotion, such as walking with and without

knees and running can exist as natural modes of a mechanical device. By using Newton's method

to search for motions which have identical initial and final system states, stable gaits could be

found for a system which uses only a small downhill slope as a source of energy.

Katoh and

Mori [KM84] use high-gain PD control to drive a biped's motion toward a prescribed cyclic state

space trajectory.

Hmam and Lawrence [HL91] use nonlinear feedback control to drive a running

biped onto a prescribed trajectory which is based on the passive motion of the system.

The

feedback is used to improve the robustness of the system to perturbation.

These latter two works

use very simple biped models and all three assume strictly planar dynamics.

2. 3

Pose Control

The fundamental control representation used throughout this thesis is the pose control graph, or

PCG [vKF94]. Figure 2.2 shows a typical PCG, which is essentially a specialized type of finite

state machine.

Pose control provides a compact way to specify the torques to be applied to an

articulated figure in order to attain a desired motion.

Each state in the PCG specifies a set of

desired joint angles for the creature with respect to some fixed reference position, called a desired