Nilpotent Bases for a Class of Non-Integrable Distributions with Applications to Trajectory Generation for Nonholonomic Systems

This paper develops a constructive method for finding a nilpotent basis for a special class of smooth nonholonomic distributions. The main tool is the use of the Goursat normal form theorem which arises in the study of exterior differential systems. The results are applied to the problem of finding a set of nilpotent input vector fields for a nonholonomic control system, which can then used to construct explicit trajectories to drive the system between any two points. A kinematic model of a rolling penny is used to illustrate this approach. The methods presented here extend previous work using "chained form" and cast that work into a coordinate-free setting

Unstitching Scarlet Letters?: Prosecutorial Discretion and Expungement

This Article argues that scholarly discussions about prosecutorial discretion need to extend their focus beyond the exercise of prosecutorial judgment pretrial or questions of factual and legal guilt. Given that the primary role of the prosecutoris to do “justice,” this Article calls for increased attention to the exercise of discretion after the guilt phase is complete, specifically in the context of expungement of nonconviction andconviction information. It offers a framework for exercising such discretion and, in doing so, hopes to initiate additional conversation about the role of prosecutors during the phases that follow arrest and prosecution

Safety Verification of Fault Tolerant Goal-based Control Programs with Estimation Uncertainty

Fault tolerance and safety verification of control systems that have state variable estimation uncertainty are essential for the success of autonomous robotic systems. A software control architecture called mission data system, developed at the Jet Propulsion Laboratory, uses goal networks as the control program for autonomous systems. Certain types of goal networks can be converted into linear hybrid systems and verified for safety using existing symbolic model checking software. A process for calculating the probability of failure of certain classes of verifiable goal networks due to state estimation uncertainty is presented. A verifiable example task is presented and the failure probability of the control program based on estimation uncertainty is found

Conversion and verification procedure for goal-based control programs

Fault tolerance and safety verification of control systems are essential for the success of autonomous robotic systems. A control architecture called Mission Data System, developed at the Jet Propulsion Laboratory, takes a goal-based control approach. In this paper, a method for converting goal network control programs into linear hybrid systems is developed. The linear hybrid system can then be verified for safety in the presence of failures using existing symbolic model checkers. An example task is developed and successfully verified using HyTech, a symbolic model checking software for linear hybrid systems

A group-theoretic approach to formalizing bootstrapping problems

The bootstrapping problem consists in designing agents that learn a model of themselves and the world, and utilize it to achieve useful tasks. It is different from other learning problems as the agent starts with uninterpreted observations and commands, and with minimal prior information about the world. In this paper, we give a mathematical formalization of this aspect of the problem. We argue that the vague constraint of having "no prior information" can be recast as a precise algebraic condition on the agent: that its behavior is invariant to particular classes of nuisances on the world, which we show can be well represented by actions of groups (diffeomorphisms, permutations, linear transformations) on observations and commands. We then introduce the class of bilinear gradient dynamics sensors (BGDS) as a candidate for learning generic robotic sensorimotor cascades. We show how framing the problem as rejection of group nuisances allows a compact and modular analysis of typical preprocessing stages, such as learning the topology of the sensors. We demonstrate learning and using such models on real-world range-finder and camera data from publicly available datasets