Forward kinematics of redundantly actuated, tendon-based robots

The number of ropes for a fully constrained, tendon-based robot has to be larger than the actuated degrees of freedom since ropes only impose unidirectional constraints. This actuation redundancy implicates that more position information is available than would be required for the the determination of the end-effector pose. This leads to an optimization problem for the forward kinematics of the robot which has to be solved in real-time. Furthermore, the kinematics of tendon-based robots are often kept simple in existing systems by guiding the ropes through holes into the workspace. This facilitates the description of the rope vectors. However, this solution is not applicable for high-load applications, as friction would cause excessive non-linearities and wear. To solve the forward kinematics of tenon-based robots, we introduce a physics-based interpretation of the mentioned optimization problem. The robotic system is described as a damped oscillator whose resting position is equal to the optimal solution. As a major advantage over the known algorithms, this physics-based approach is quantifiable in terms of accuracy of the solution and number of iterations. Furthermore, the design and mathematical description of a deflection unit´s geometry is presented. This deflection unit guides the rope smoothly into the workspace and its relevant influence on the kinematic equations can be compensated. The physics-based approach is experimentally evaluated on a tendon-based haptic interface, the r³-system, and it is compared to the solutions using only the minimum set of sensor information.