Abstract—Finding a racing path that allows minimum lap time is the first and foremost step in overall autonomous race car planning. Minimum curvature path is the raceline that offers the highest …

Let C be a piecewise-smooth curve that is the graph of the vector described parametrically by R(t) = x(t)i + y(t)j + z(t)k, and let P0 = P (t0) be a particular point on C (called the base point).

We develop and test our algorithm in a multi-robot racing scenario, where the robot’s objective is to finish the race along a bounded track ahead of other robots and without collision.

Given the magnitude and the direction of a vector, it is possible to determine its components: 2D vector with magnitude | | and direction , =| | 〈cos ,sin 〉=〈| |cos ,| |sin 〉

Background: Saturn Vector Unit Compact vector unit with short vector lengths and wide SIMD datapath Targets DSP-core like deployments Vector chaining with out-of-order multi-issue Support for all RVV …

Using these representations, we can construct the components of all unit vectors in these coordinate systems and in this way define explicitly the unit vectors ˆr, ˆθ, ˆφ, etc.

Acceleration changes velocity, i.e. speed and direction of motion. Components of acceleration parallel and perpendicular to velocity have different effects. If only gravity acts on an object (free fall), then …