This paper considers a wide number of time-stepping methods, and discusses their implications for convergence theory and the nature of the limiting solutions.

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this document is available under the understanding that it is to be used only for personal use, and is not to be sold or used for commercial exchange. 1.1 Introduction

Physically based simulation of rigid body dynamics is commonly done by time-stepping systems forward in time. In this paper, we propose methods to allow time-stepping rigid body systems backward in time. Unfortunately, reverse-time integration of rigid bodies involving frictional contact is mathematically ill-posed, and can lack unique solutions. We instead propose time-reversed rigid body integrators that can sample possible solutions when unique ones do not exist. We also discuss challenges related to dissipation-related energy gain, sensitivity to initial conditions, stacking, constraints and articulation, rolling, sliding, skidding, bouncing, high angular velocities, rapid velocity growth from micro-collisions, and other problems encountered when going against the usual flow of time.

Summary. In this paper, we report on the design of a model-based controller that can achieve dynamical self-righting of a hexapod robot. Extending on our earlier work in this domain, we introduce a tractable multi-point contact model with Coulomb friction. We contrast the singularities inherent to the new model with other available methods and show that for our specific application, it yields dynamics which are well-defined. We then present a feedback controller that achieves “maximal ” performance under morphological and actuation constraints, while ensuring the validity of the model by staying away from singularities. Finally, through systematic experiments, we demonstrate that our controller is capable of robust flipping behavior. Key words: legged robot, model based control, contact modeling, flipping, RHex 1