Causal approximations to the inverse dynamics of structurally flexible robots
Thesis DisciplineMechanical Engineering
Degree GrantorUniversity of Canterbury
Degree NameDoctor of Philosophy
Robotic manipulators have been extensively used in industrial automation, hazardous environments and outer space. The requirement for increased speeds of operation and lightweight design has made structural flexibility the constraining factor in robot design. For current manipulators that exhibit significant link flexibility, the control methodology seems to be to drive them so slowly that link dynamics are not excited. To make significant gains in speed and efficiency, the deflections due to link deformation will have to be compensated. With the ready availability of powerful processors, the cost of implementing complex control methodologies is not excessive. Flexible-link robots provide significant challenges for the control engineer. With nonlinear configuration-dependent and nonminimum-phase dynamics, the control of the end-effector in task-space is one of the most difficult problems encountered. Fortunately, flexible-link robots exhibit one beneficial characteristic. The map from joint torques to joint rate is passive, allowing a strictly passive feedback controller to produce a stable system. The requirement then is to produce a reference joint trajectory that will result in the end-effector following its desired track. This thesis deals with the problem of inverting the nonlinear nonrninimum-phase dynamics to produce a feedforward torque and joint trajectory from a given end-effector trajectory. Generally the inverse dynamics will be noncasual, that is the output of the inverse system will depend on future inputs. In the linear case this noncasual inverse can be solved using Fourier transform methods on the complete trajectory. In this work we have assumed that the complete end-effector trajectory is not available. The input may come from an operator controlling the movement by sight or by a system that is updating the trajectory as it analyses its own sensors. Because of this restriction, the inverse dynamics are approximated by a casual system which only uses past inputs. Using a nonlinear inner-outer factorisation of the dynamics, inverting the outer factor and approximating the inverse of the inner factor with its static inverse, an approximate inverse-dynamics system was generated. Alternatively, by modifying the input of the dynamics to be all of the rigid contribution plus a fraction of the elastic contribution, a stable inverse was generated. Both of these approximate inverses have been implemented on a planar three-DOF system with the first two links flexible. Simulation and implementation on an experimental facility has shown that approximate end-effector tracking can be obtained. While an approximate inverse based feedforward cannot produce perfect tracking, it is a significant improvement over the current standard of generating a joint trajectory based on the inverse of the equivalent rigid robot.