robotics Robotics is an interdisciplinary branch of computer science and engineering. Robotics involves design, construction, operation, and use of robots. The goal of robotics is to design machines that can help and assist humans. Robotics integrate ...

and

motion planning Motion planning, also path planning (also known as the navigation problem or the piano mover's problem) is a computational problem to find a sequence of valid configurations that moves the object from the source to destination. The term is use ...

, a velocity obstacle, commonly abbreviated VO, is the set of all

velocities Velocity is the directional speed of an object in motion as an indication of its rate of change in position as observed from a particular frame of reference and as measured by a particular standard of time (e.g. northbound). Velocity is a ...

of a

robot A robot is a machine—especially one programmable by a computer—capable of carrying out a complex series of actions automatically. A robot can be guided by an external control device, or the control may be embedded within. Robots may ...

that will result in a

collision In physics, a collision is any event in which two or more bodies exert forces on each other in a relatively short time. Although the most common use of the word ''collision'' refers to incidents in which two or more objects collide with great fo ...

with another robot at some moment in time, assuming that the other robot maintains its current velocity. If the robot chooses a velocity inside the velocity obstacle then the two robots will eventually collide, if it chooses a velocity outside the velocity obstacle, such a collision is guaranteed not to occur. This algorithm for robot collision avoidance has been repeatedly rediscovered and published under different names: in 1989 as a maneuvering board approach, in 1993 it was first introduced as the "velocity obstacle", in 1998 as collision cones, and in 2009 as forbidden velocity maps. The same algorithm has been used in maritime port navigation since at least 1903. The velocity obstacle for a robot

A

induced by a robot

B

may be formally written as :

VO_ = \

where

A

has

position Position often refers to: * Position (geometry), the spatial location (rather than orientation) of an entity * Position, a job or occupation Position may also refer to: Games and recreation * Position (poker), location relative to the dealer * ...

\mathbf_A

and

radius In classical geometry, a radius ( : radii) of a circle or sphere is any of the line segments from its center to its perimeter, and in more modern usage, it is also their length. The name comes from the latin ''radius'', meaning ray but also the ...

r_A

, and

B

has position

\mathbf_B

, radius

r_B

, and velocity

\mathbf_B

. The notation

D(\mathbf, r)

represents a disc with

center Center or centre may refer to: Mathematics *Center (geometry), the middle of an object * Center (algebra), used in various contexts ** Center (group theory) ** Center (ring theory) * Graph center, the set of all vertices of minimum eccentrici ...

\mathbf

and radius

r

. Variations include common velocity obstacles (CVO), finite-time-interval velocity obstacles (FVO), generalized velocity obstacles (GVO),

hybrid Hybrid may refer to: Science * Hybrid (biology), an offspring resulting from cross-breeding ** Hybrid grape, grape varieties produced by cross-breeding two ''Vitis'' species ** Hybridity, the property of a hybrid plant which is a union of two dif ...

reciprocal velocity obstacles (HRVO),

nonlinear In mathematics and science, a nonlinear system is a system in which the change of the output is not proportional to the change of the input. Nonlinear problems are of interest to engineers, biologists, physicists, mathematicians, and many othe ...

velocity obstacles (NLVO), reciprocal velocity obstacles (RVO), and

recursive Recursion (adjective: ''recursive'') occurs when a thing is defined in terms of itself or of its type. Recursion is used in a variety of disciplines ranging from linguistics to logic. The most common application of recursion is in mathematics ...

probabilistic velocity obstacles (PVO).

References

Geometric algorithms Multi-robot systems Robot kinematics {{robo-stub