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We present a muscle-based control method for simulated bipeds in which both the muscle routing and control parameters are optimized. This yields a generic locomotion control method that supports a variety of bipedal creatures. All actuation forces are the result of 3D simulated muscles, and a model of neural delay is included for all feedback paths. As a result, our controllers generate torque patterns that incorporate biomechanical constraints. The synthesized controllers find different gaits based on target speed, can cope with uneven terrain and external perturbations, and can steer to target directions.

We present an efficient and simple paradigm for motion planning amidst fat obstacles. The paradigm fits in the cell decomposition approach to motion planning and exploits workspace properties that follow from the fatness of the obstacles. These properties allow us to decompose the workspace, subject to some constraints, rather than to decompose the higherdimensional free space directly. A sequence of uniform steps transforms the workspace decomposition into a free space decomposition of asymptotically the same (expectedly small) size. The approach applies to robots with any fixed number of degrees of freedom and turns out to be successful in many cases: it leads to nearly optimal O (n log n) algorithms for motion planning in 2D, and for motion planning in 3D amidst obstacles of comparable size. In addition, we obtain algorithms for planning 3D motions among polyhedral obstacles, running in 0(n2 log n) time, and among arbitrary obstacles, running in time O(n3).

Many algorithms developed in computational geometry are needlessly complicated and slow because they have to be prepared for very complicated, hypothetical inputs. To a void this, realistic models are needed that describe the properties that realistic inputs have, so that algorithms can de designed that take advantage of these properties. This can lead to algorithms that are provably e cient in realistic situations. We obtain some fundamental results in this research direction. In particular, we h a ve the following results. We show the relations between various models that have been proposed in the literature. For several of these models, we give algorithms to compute the model parameters for a given scene; these algorithms can be used to verify whether a model is appropriate for typical scenes in some application area. As a case study, w e give some experimental results on the appropriateness of some of the models for one particular type of scenes often encountered in geographic information systems, namely certain triangulated irregular networks.

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