Kinematic error correction for minimally invasive surgical robots

Robots are useful tools in minimally invasive surgery, providing benefits such as reduction in hand tremor, navigation, and workspace scaling. Unfortunately, minimally invasive configurations result in two likely sources of kinematic error: port displacement and instrument shaft flexion. For a quasistatic system, a measure is presented that relates the errors in the robot Jacobian to the angular difference between desired motions and actual motions. Simulations and experimental data demonstrate this measure for a laboratory system. One potential use for the presented measure is, for bounded errors, determining whether the system monotonically converges for all initial and desired positions in the workspace. In addition, the measure is useful for path planning, determining less error-prone paths.