AN ADAPTIVELY SAMPLED PATH PLANNER USING WAYPOINTS: AN ANY-ANGLE VARIANT

This thesis develops a low-cost grid-based path planner that intrinsically supports smooth, curved vehicle dynamics. There are many advantages to grid-based planners, including working natively in the digital space of most sensors, and efficiency in low dimensional space. However, discrete planners create jaggedness in most paths. Further, the dimensionality must be limited for efficiency, usually by limiting vehicle steering angles to a small finite set. The algorithm presented here, Waypoint-A*, extends A* to produce low-cost curved trajectories, taking the dynamics of the vehicle into account explicitly post-planning. Considering the path generated by A* as composed of a set of waypoints, Waypoint-A* calculates the minimum-cost heading on a continuum, to direct the vehicle to the waypoint at the location resulting in the lowest total cost. Smoothness of these curves is invariant to terrain resolution and computation

Synthesizing a Fractional v=2/3 State from Particle and Hole States

Topological edge-reconstruction occurs in hole-conjugate states of the fractional quantum Hall effect. The frequently studied polarized state of filling factor v=2/3 was originally proposed to harbor two counter-propagating edge modes: a downstream v=1 and an upstream v=1/3. However, charge equilibration between these two modes always led to an observed downstream v=2/3 charge mode accompanied by an upstream neutral mode (preventing an observation of the original proposal). Here, we present a new approach to synthetize the v=2/3 edge mode from its basic counter-propagating charged constituents, allowing a controlled equilibration between the two counter-propagating charge modes. This novel platform is based on a carefully designed double-quantum-well, which hosts two populated electronic sub-bands (lower and upper), with corresponding filling factors, vl & vu. By separating the 2D plane to two gated intersecting halves, each with different fillings, counter-propagating chiral modes can be formed along the intersection line. Equilibration between these modes can be controlled with the top gates' voltage and the magnetic field. Our measurements of the two-terminal conductance G2T and the presence of a neutral mode allowed following the transition from the non-equilibrated charged modes, manifested by G2T=(4/3)e2/h, to the fully equilibrated modes, with a downstream charge mode with G2T=(2/3)e2/h accompanied by an upstream neutral mode.Comment: 16 pages,4 figure