Body Lift and Drag for a Legged Millirobot in Compliant Beam Environment

Much current study of legged locomotion has rightly focused on foot traction forces, including on granular media. Future legged millirobots will need to go through terrain, such as brush or other vegetation, where the body contact forces significantly affect locomotion. In this work, a (previously developed) low-cost 6-axis force/torque sensing shell is used to measure the interaction forces between a hexapedal millirobot and a set of compliant beams, which act as a surrogate for a densely cluttered environment. Experiments with a VelociRoACH robotic platform are used to measure lift and drag forces on the tactile shell, where negative lift forces can increase traction, even while drag forces increase. The drag energy and specific resistance required to pass through dense terrains can be measured. Furthermore, some contact between the robot and the compliant beams can lower specific resistance of locomotion. For small, light-weight legged robots in the beam environment, the body motion depends on both leg-ground and body-beam forces. A shell-shape which reduces drag but increases negative lift, such as the half-ellipsoid used, is suggested to be advantageous for robot locomotion in this type of environment.Comment: First three authors contributed equally. Accepted to ICRA 201

Exact solution of position dependent mass Schroedinger equation by supersymmetric quantum mechanics

A supersymmetric technique for the solution of the effective mass Schr\"{o}% dinger equation is proposed. Exact solutions of the Schroedinger equation corresponding to a number of potentials are obtained. The potentials are fully isospectral with the original potentials. The conditions for the shape invariance of the potentials are discussed

Remarks on the Solution of the Position Dependent Mass (PDM) Schr\"odinger Equation

An approximate method is proposed to solve position dependent mass Schr\"odinger equation. The procedure suggested here leads to the solution of the PDM Schr\"odinger equation without transforming the potential function to the mass space or vice verse. The method based on asymptotic Taylor expansion of the function, produces an approximate analytical expression for eigenfunction and numerical results for eigenvalues of the PDM Schr\"odinger equation. The results show that PDM and constant mass Schr\"odinger equations are not isospectral. The calculations are carried out with the aid of a computer system of symbolic or numerical calculation by constructing a simple algorithm