Globally Optimal Solution to Inverse Kinematics of 7DOF Serial Manipulator
This provides a certifiably globally optimal solution for inverse kinematics in robotics, addressing a critical challenge for precise robot control, though it is incremental as it builds on existing polynomial optimization methods.
The authors tackled the globally optimal inverse kinematics problem for a 7DOF serial manipulator by showing that kinematic constraints can be expressed as second-degree polynomials, enabling solution via Lasserre relaxations. They demonstrated the method on a KUKA LBR IIWA manipulator, achieving optimal solutions or infeasibility certification in 99% of tested poses.
The Inverse Kinematics (IK) problem is to nd robot control parameters to bring it into the desired position under the kinematics and collision constraints. We present a global solution to the optimal IK problem for a general serial 7DOF manipulator with revolute joints and a quadratic polynomial objective function. We show that the kinematic constraints due to rotations can all be generated by second-degree polynomials. This is important since it signicantly simplies further step where we nd the optimal solution by Lasserre relaxations of non-convex polynomial systems. We demonstrate that the second relaxation is sucient to solve the 7DOF IK problem. Our approach is certiably globally optimal. We demonstrate the method on the 7DOF KUKA LBR IIWA manipulator and show that we are able to compute the optimal IK or certify in-feasibility in 99 % tested poses.