Apparatus and method for computing operational-space physical quantity

An operational space physical quantity calculation method for computing a physical quantity in an operational space describing a relationship between a force and acceleration acting on a link structure including a plurality of linked rigid bodies, comprising the steps of:

• (a) computing an inverse operational space inertia matrix by performing a forward dynamics calculation using a kinetic model of the link structure and force information acting on the link structure in order to obtain accelerations occurring at certain points of the link structure;
• and
• (b) computing an operational space bias acceleration by performing the forward dynamics calculation.

A kinetic simulation method for reconstructing a physical interaction including a collision and a contact between virtual objects in a virtual environment in which a plurality of the virtual objects coexist, comprising the steps of:

• (a) computing an inverse operational space inertia matrix and an operational space bias acceleration by performing a forward dynamics calculation on the basis of a kinetic model of the virtual objects on which physical interactions act and an external force caused by the physical interactions in order to obtain accelerations occurring at the virtual objects;
• and
• (b) computing, by using the inverse operational space inertia matrix and the operational space bias acceleration computed in step (a), an acceleration and a force that satisfy a linear complementarity problem including a relational expression of an acceleration and a force in an operational space described using an inverse operational space inertia matrix and an operational space bias acceleration and constraint conditions imposed when the physical interactions act and determining an external force acting on the virtual object on the basis of the obtained force.

A computer-readable program for causing a computer system to compute a physical quantity in an operational space describing a relationship between a force acting on a link structure in which a plurality of rigid bodies are linked and an acceleration, comprising the steps of:

• (a) computing an inverse operational space inertia matrix by causing the computer system to perform a forward dynamics calculation on the basis of a kinetic model of the link structure and information about a force acting on the link structure in order to obtain accelerations occurring at certain points of the link structure;
• and
• (b) computing an operational space bias acceleration by causing the computer system to perform the forward dynamics calculation.

A computer-readable program for causing a computer system to execute a kinetic simulation method for reconstructing a physical interaction including a collision and a contact between virtual objects in a virtual environment in the computer system, comprising the steps of:

• (a) computing an inverse operational space inertia matrix and an operational space bias acceleration by causing the computer system to perform a forward dynamics calculation on the basis of a kinetic model of virtual objects on which physical interactions act and an external force caused by the physical interactions in order to obtain accelerations occurring at the virtual objects;
• and
• (b) computing, by using the inverse operational space inertia matrix and the operational space bias acceleration computed in step (a), an acceleration and a force that satisfy a linear complementarity problem including a relational expression of an acceleration and a force in an operational space described using an inverse operational space inertia matrix and an operational space bias acceleration and constraint conditions imposed when the physical interactions act and determining an external force acting on the virtual object on the basis of the obtained force.

An operational space physical quantity calculation apparatus for computing a physical quantity in an operational space describing a relationship between a force and acceleration acting on a link structure including a plurality of linked rigid bodies, comprising:

• a forward dynamics calculating unit configured to perform a forward dynamics calculation on the basis of force information about a force acting on the link structure in order to obtain accelerations occurring at certain points of the link structure;
• and
• an operational space physical quantity computing unit configured to compute an inverse operational space inertia matrix and an operational space bias acceleration by causing the forward dynamics calculating unit to perform the forward dynamics calculation using a kinetic model of the link structure.