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This paper describes the evolution of our concept of hopping robot for planetary exploration, that combines coarse long range mobility achieved by hopping, with short range wheeled mobility for precision target acquisition.

This paper describes a minimalist hopping robot that can perform basic exploration tasks on Mars or other moderate gravity bodies.

The Mars Pathfinder mission illustrated the benefits of including a mobile robotic explorer on a plantary mission.

With the success of Mars Pathfinder's Sojourner rover, a new era of planetary exploration has opened, with demand for highly capable mobile robots.

Much prior work in mobile robot path planning has been based on assumptions that are not really applicable for exploration of planetary terrains.

A new method for unconstrained global function optimization, acronymed TRUST, is introduced.

The presence of redundant degrees of freedom in a manipulator structure leads to a physical phenomenon known as a self-motion, which is a continuous motion of the manipulator joints that leaves the end-effector motionless. In the first part of the paper, a global manifold mapping reformulation of manipulator kinematics is reviewed, and the inverse kinematic solution for redundant manipulators is developed in terms of self-motion manifolds. Global characterizations of the self-motion manifolds in terms of their number, geometry, homotopy class, and null space are reviewed using examples. Much previous work in redundant manipulator control has been concerned with the redundancy resolution problem, in which methods are developed to determine, or resolve, the motion of the joints in order to achieve end-effector trajectory control while optimizing additional objective functions. Redundancy resolution problems can be equivalently posed as the control of self-motions. Alternatives for redundancy resolution are briefly discussed.