Probabilistic Feasibility for Nonlinear Systems with Non-Gaussian Uncertainty using RRT

For motion planning problems involving many or unbounded forms of uncertainty, it may not be possible to identify a path guaranteed to be feasible, requiring consideration of the trade-o between planner conservatism and the risk of infeasibility. Recent work developed the chance constrained rapidly-exploring random tree (CC-RRT) algorithm, a real-time planning algorithm which can e ciently compute risk at each timestep in order to guarantee probabilistic feasibility. However, the results in that paper require the dual assumptions of a linear system and Gaussian uncertainty, two assumptions which are often not applicable to many real-life path planning scenarios. This paper presents several extensions to the CC-RRT framework which allow these assumptions to be relaxed. For nonlinear systems subject to Gaussian process noise, state distributions can be approximated as Gaussian by considering a linearization of the dynamics at each timestep; simulation results demonstrate the e ective of this approach for both open-loop and closed-loop dynamics. For systems subject to non-Gaussian uncertainty, we propose a particle-based representation of the uncertainty, and thus the state distributions; as the number of particles increases, the particles approach the true uncertainty. A key aspect of this approach relative to previous work is the consideration of probabilistic bounds on constraint satisfaction, both at every timestep and over the duration of entire paths.United States. Air Force (USAF, grant FA9550-08-1-0086)United States. Air Force Office of Scientific Research (AFOSR, Grant FA9550-08-1-0086

Nuclear Inelastic X-Ray Scattering of FeO to 48 GPa

The partial density of vibrational states has been measured for Fe in compressed FeO (w\"ustite) using nuclear resonant inelastic x-ray scattering. Substantial changes have been observed in the overall shape of the density of states close to the magnetic transiton around 20 GPa from the paramagnetic (low pressure) to the antiferromagnetic (high pressure) state. Our data indicate a substantial softening of the aggregate sound velocities far below the transition, starting between 5 and 10 GPa. This is consistent with recent radial x-ray diffraction measurements of the elastic constants in FeO. The results indicate that strong magnetoelastic coupling in FeO is the driving force behind the changes in the phonon spectrum of FeO.Comment: 4 pages, 4 figure

Reliable robust path planning with application to mobile robots

This paper is devoted to path planning when the safety of the system considered has to be guaranteed in the presence of bounded uncertainty affecting its model. A new path planner addresses this problem by combining Rapidly-exploring Random Trees (RRT) and a set representation of uncertain states. An idealized algorithm is presented first, before a description of one of its possible implementations, where compact sets are wrapped into boxes. The resulting path planner is then used for nonholonomic path planning in robotics

DOI: RELIABLE ROBUST PATH PLANNING

This paper is devoted to path planning when the safety of the system considered has to be guaranteed in the presence of bounded uncertainty affecting its model. A new path planner addresses this problem by combining Rapidly-exploring Random Trees (RRT) and a set representation of uncertain states. An idealized algorithm is presented first, before a description of one of its possible implementations, where compact sets are wrapped into boxes. The resulting path planner is then used for nonholonomic path planning in robotics

Sampling-based path planning: a new tool for missile guidance

A new missile midcourse guidance algorithm is proposed in this paper. It is a combination of sampling based path planning, Dubins' curves and classical guidance laws. Moreover, a realistic interceptor missile model is used. It allows to anticipate the future changes of flight conditions along the trajectory, especially the loss of maneuverability at high altitude. Simulation results are presented to demonstrate the substantial performance improvements over classical midcourse guidance laws

Multi-agent motion planning for nonlinear Gaussian systems

In this paper, a multi-agent motion planner is developed for nonlinear Gaussian systems using a combination of probabilistic approaches and a rapidly exploring random tree (RRT) algorithm. A closed-loop model consisting of a controller and estimation loops is used to predict future distributions to manage the level of uncertainty in the path planner. The closed-loop model assumes the existence of a feedback control law that drives the actual system towards a nominal system. This ensures the uncertainty in the evolution does not grow significantly and the tracking errors are bounded. To trade conservatism with the risk of infeasibility and failure, we use probabilistic constraints to limit the probability of constraint violation. The probability of leaving the configuration space is included by using a chance constraint approach and the probability of closeness between two agents is imposed using an overlapping coefficient approach. We augment these approaches with the RRT algorithm to develop a robust path planner. Conflict among agents is resolved using a priority-based technique. Numerical results are presented to demonstrate the effectiveness of the planner