Geometry Yields

Geometry Yields is a contact improvisation light performance in which a performer interacts directly with a force-controlled robot arm holding a light tube and planar lasers. The arm is set to resist or permit movement according to geometric constraints. Push it, and it follows only where the current geometry allows. The resulting motion is symbiotic between human and a machine. The work was developed at the Stanford Robotics Center in summer 2026.

The starting point is Oskar Schlemmer's stage work at the Bauhaus in the 1920s. His Triadic Ballet wraps dancers in rigid costumes constraining their movement, so that the geometry of the costume defines the choreographic form. In the Stäbetanz, long slats strapped to the limbs extend each joint into the space around the body, turning a person into an abstract mechanism. Schlemmer was asking what industrialization would do to the performing body. 100 years later robots can execute complex tasks that look increasingly natural. Geometry Yields attempts to bring human emotion to the shape of the movement, within the constraints defined by an industrial robot.

The arm runs in different spatial modes. In the first, the constraint lives in the robot's own joints: individual axes are locked or freed. In the second, the constraint is defined in the global coordinate system, so the light beam at the end of the robot can be moved along a plane or a line regardless of how the joints have to rearrange themselves to get there. In the third, the arm pivots around the light itself, so that its tip stays fixed while the body of the robot swings around it. None of these spaces is visible. They become apparent only when someone pushes against them, and the visitor is free to grab any part of the arm, not just the end effector, and to bring their own sense of movement to what the robot will accept.

The symbiotic movement is possible through force control, the paradigm at the core of Oussama Khatib's research at Stanford and the direct inspiration for this piece. Rather than commanding a position, the controller senses the external force applied to the arm and lets it yield within the active constraint. The visitor and the controller are negotiating the motion together.

A generative soundscape follows the movement of the arm, so that the small shifts in force become audible to people watching as well as to the person touching the robot. In a second stage, planes of laser light visualize the folding spatial planes, as the robot retraces the movement from the interaction.

The project began as a plan for a choreographed stage piece in front of an audience. That changed during an early session when Elle McCue, a dancer and roboticist at the center, remarked that working with the arm felt like contact improvisation. The work reorganized itself around that observation. The idea of a finished choreography gave way to the act of moving with the robot inside abstract geometries, and how the motion is produced became the subject rather than what the motion looks like.