Time optimal driving on curvilinear path with kinematic constraints

ABSTRACT

A time optimal driving algorithm is obtained for the moving on a curvilinear path in space. The algorithm takes velocity, acceleration and jerk as constraints. By imposing a jerk constraint, the acceleration time-derivative is limited and smooth driving is guaranteed. It is concluded that the moving object’s dynamics must be analyzed directly by using curvature and torsion of the path. It is also found that the given path must possess G² or higher continuity for applying a jerk constraint. For a given set of velocity, acceleration and jerk constraints, it is proved that the minimum driving time depends on path length, curvature, torsion and curvature’s path length derivative along the path. The resultant driving pattern guarantees minimum-time smooth driving.

GRAPHICAL ABSTRACT

KEYWORDS:

• Time optimal
• driving pattern
• curvilinear path
• jerk constraint
• curvature
• torsion
• G² continuity

Acknowledgment

We would like to express our deep gratitude to Hiroshi Makino, professor emeritus of Yamanashi University and Hirofumi Tamai, president of Muscle Co., Ltd. for their wise suggestions and advices.

ORCID

Fengli Lan http://orcid.org/0000-0002-0456-0916

Kenjiro T. Miura http://orcid.org/0000-0001-9326-3130