A vector-integration-to-endpoint model for performance of viapoint movements

Daniel Bullock1, Raoul M. Bongers, Marnix Lankhorst

  • 1Department of Cognitive and Neural Systems, Boston University, 677 Beacon Street, Boston, USA

Summary

Viapoint (VP) movements deviate early in direction, unlike point-to-point (PTP) movements. The extended vector-integration-to-endpoint (VITE) model explains these complex movement trajectories without precomputation.

Related Concept Videos

Velocity and Position by Integral Method01:13

Velocity and Position by Integral Method

If acceleration as a function of time is known, then velocity and position functions can be derived using integral calculus. For constant acceleration, the integral equations refer to the first and second kinematic equations for velocity and position functions, respectively.
Consider an example to calculate the velocity and position from the acceleration function. A motorboat is traveling at a constant velocity of 5.0 m/s when it starts to decelerate to arrive at the dock. Its acceleration is...
Position and Displacement Vectors01:00

Position and Displacement Vectors

To describe the motion of an object, one should first be able to describe its position (where it is at any particular time). More precisely, the position needs to be specified relative to a convenient frame of reference. A frame of reference is an arbitrary set of axes from which the position and motion of an object are described. Earth is often used as a frame of reference to describe the position of an object in relation to stationary objects on Earth.
Further, several important kinds of...
Position Vectors01:29

Position Vectors

A position vector is a fundamental concept in mathematics that helps determine the position of one point with respect to another point in space. It is a vector that describes the direction and distance between two points. Position vectors are highly useful in the field of math and science, as they help represent spatial relationships and make calculations easier.
For instance, we want to locate a point P(x, y, z) relative to the origin of coordinates O. In that case, we can define a position...
Vector Transformation in Rotating Coordinate Systems01:16

Vector Transformation in Rotating Coordinate Systems

Consider a vector rotating about an axis with an angular velocity, such that its tip sweeps a circular path.
Integrals of Vector Functions01:23

Integrals of Vector Functions

Vector-valued functions provide a convenient framework for describing motion in space when both magnitude and direction are important. A drone’s velocity at any instant has a direction and a speed, and as the drone moves, both can change. A vector-valued function captures this behavior by assigning to each time a vector whose components are real-valued functions. Each component represents motion along a particular axis in space. Such functions can describe motion in either two-dimensional or...
Vector Functions and Motion: Problem Solving01:30

Vector Functions and Motion: Problem Solving

Accurate position tracking is fundamental to the safe and effective operation of unmanned aerial vehicles (UAVs), particularly during precision maneuvers near complex structures. In this scenario, a drone is programmed to perform a high-precision inspection of a vertical structure, starting at position ((x, y, z) = (3, 0, 0)), with an initial velocity oriented in the positive z-direction. The trajectory of the drone is governed by a time-dependent acceleration function a(t), which is predefined...