Computational Models satisfying relative angle constraints for 2-dimensional segmented bodies

Planar hinged segmented bodies have been used to represent models of biomechanical systems. One characteristic of a segmented body moving under gravitational acceleration and torques between segments is the possibility that the body's segments spin through more than a revolution or past a natural limit, and a computational mechanism to stop such behaviour should be provided. This could be done by introducing angle constraints between segments, and computational models utilising optimal control are studied here. Three models to maintain angle constraints between segments are proposed and compared. These models are: all-time angle constraints, a restoring torque in the state equations and an exponential penalty model. The models are applied to a 2-D three-segment body to test the behaviour of each model when optimising torques to minimise an objective. The optimisation is run to find torques so that the end effector of the body follows the trajectory of a half-circle. The result shows the behaviour of each model in maintaining the angle constraints. The all-time constraints case exhibits a behaviour of not allowing torques (at a solution) which makes segments move past the constraints, while the other two show a flexibility in handling the angle constraints which is more similar to what occurs in a real biomechanical system.