Control of Complex Objects: Challenges of Linear Internal Dynamics

Physical interaction with an object that has internal dynamics can be challenging, both for humans and robots. An example is carrying a cup of coffee, where the nonlinear dynamics between the cup and the liquid can be chaotic and unpredictable. This study examined how nonlinearity of an object’s dynamics contributed to the difficulty of a task and if linearization of the object dynamics facilitated performance. Human subjects did a task in a virtual set-up with a haptic interface using a robotic manipulandum. The task of transporting a cup of coffee was reduced to a 2D cart-and-pendulum model; subjects moved the cart and felt the dynamics of the pendulum representing sloshing coffee. Performance with the nonlinear system was compared to a linearized mass-spring version of the system. Subjects (n=16) executed continuous rhythmic, self-paced movements. In the linearized system subjects chose to move at frequencies close to the resonant frequencies and clearly avoided the anti-resonance frequency. In the nonlinear system subjects did not avoid the anti-resonance frequency. To evaluate performance, mutual information quantified predictability between the interaction force and the cup and object dynamics. Mutual information was lower in trials when the cup moved close to the anti-resonance frequency in both linear and nonlinear systems. The magnitudes of the interaction forces were higher in the linear system, especially at frequencies slightly below the anti-resonance. These results run counter to the expectation that linearization would simplify this task. These findings may be useful as design considerations for robot control and human-robot interaction: if humans interact with robots that exhibit complex dynamics in the frequency range of human actions, linearizing a nonlinear system may potentially disturb intuitive and low-effort cooperation.