# The three-cubic method: An optional online robot joint trajectory generator under velocity, acceleration, and wandering constraints

## Abstract

An original method called the three-cubic method is proposed to generate online robot joint trajectories interpolating given position points with associated velocities. The method is based on an acceleration profile composed of three cubic polynomial segments, which ensure a zero acceleration at each intermediate point. Velocity and acceleration continuity is obtained, and this three-cubics combination allows the analytical solution to the minimum time trajectory problem under maximum velocity and acceleration constraints. Possible wandering is detected and can be overcome. Furthermore, the analytical solution to the minimum time trajectory problem leads to an online trajectory computation.

- Authors:

- Publication Date:

- Research Org.:
- LESIA, Toulouse (FR)

- OSTI Identifier:
- 20001199

- Resource Type:
- Journal Article

- Journal Name:
- International Journal of Robotics Research

- Additional Journal Information:
- Journal Volume: 18; Journal Issue: 9; Other Information: PBD: Sep 1999; Journal ID: ISSN 0278-3649

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATION; ROBOTS; JOINTS; TRAJECTORIES; CALCULATION METHODS; ON-LINE CONTROL SYSTEMS

### Citation Formats

```
Tondu, B., and Bazaz, S.A.
```*The three-cubic method: An optional online robot joint trajectory generator under velocity, acceleration, and wandering constraints*. United States: N. p., 1999.
Web. doi:10.1177/02783649922066637.

```
Tondu, B., & Bazaz, S.A.
```*The three-cubic method: An optional online robot joint trajectory generator under velocity, acceleration, and wandering constraints*. United States. doi:10.1177/02783649922066637.

```
Tondu, B., and Bazaz, S.A. Wed .
"The three-cubic method: An optional online robot joint trajectory generator under velocity, acceleration, and wandering constraints". United States. doi:10.1177/02783649922066637.
```

```
@article{osti_20001199,
```

title = {The three-cubic method: An optional online robot joint trajectory generator under velocity, acceleration, and wandering constraints},

author = {Tondu, B. and Bazaz, S.A.},

abstractNote = {An original method called the three-cubic method is proposed to generate online robot joint trajectories interpolating given position points with associated velocities. The method is based on an acceleration profile composed of three cubic polynomial segments, which ensure a zero acceleration at each intermediate point. Velocity and acceleration continuity is obtained, and this three-cubics combination allows the analytical solution to the minimum time trajectory problem under maximum velocity and acceleration constraints. Possible wandering is detected and can be overcome. Furthermore, the analytical solution to the minimum time trajectory problem leads to an online trajectory computation.},

doi = {10.1177/02783649922066637},

journal = {International Journal of Robotics Research},

issn = {0278-3649},

number = 9,

volume = 18,

place = {United States},

year = {1999},

month = {9}

}

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