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 integrat ...

and motion planning, kinodynamic planning is a class of problems for which

velocity 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 ...

acceleration In mechanics, acceleration is the rate of change of the velocity of an object with respect to time. Accelerations are vector quantities (in that they have magnitude and direction). The orientation of an object's acceleration is given by the ...

, and force/torque bounds must be satisfied, together with kinematic constraints such as avoiding obstacles. The term was coined by

Bruce Donald Bruce Randall Donald (born 1958) is an American computer scientist and computational biologist. He is the James B. Duke Professor of Computer Science and Biochemistry at Duke University. He has made numerous contributions to several fields in Comp ...

, Pat Xavier, John Canny, and John Reif. Donald et al. developed the first polynomial-time approximation schemes (PTAS) for the problem. By providing a provably

polynomial-time In computer science, the time complexity is the computational complexity that describes the amount of computer time it takes to run an algorithm. Time complexity is commonly estimated by counting the number of elementary operations performed by t ...

ε-approximation algorithm, they resolved a long-standing open problem in optimal control. Their first paper considered time-optimal control ("fastest path") of a point mass under Newtonian dynamics, amidst polygonal (2D) or polyhedral (3D) obstacles, subject to state bounds on position, velocity, and acceleration. Later they extended the technique to many other cases, for example, to 3D open-chain kinematic robots under full

Lagrangian dynamics In physics, Lagrangian mechanics is a formulation of classical mechanics founded on the stationary-action principle (also known as the principle of least action). It was introduced by the Italian-French mathematician and astronomer Joseph-Loui ...

. More recently, many practical heuristic algorithms based on stochastic optimization and iterative sampling were developed, by a wide range of authors, to address the kinodynamic planning problem. These techniques for kinodynamic planning have been shown to work well in practice. However, none of these heuristic techniques can guarantee the optimality of the computed solution (i.e., they have no performance guarantees), and none can be mathematically proven to be faster than the original PTAS algorithms (i.e., none have a provably lower computational complexity).

References

{{reflist Robot control Automated planning and scheduling Robot kinematics Algorithms