The control of robot manipulators with bounded input

The problem of tracking a desired trajectory in the state space of an
n
-link robotic manipulator with bounds on the allowable input torque is considered. Using a so-called optimal decision strategy (ODS), a pointwise optimal control law is derived which, at each time
t
, minimizes the deviation between the vector of joint accelerations and a desired joint acceleration vector, subject to the input constraints. The design of the optimal control law is reduced to the solution of a quadratic programming problem which is solved using the primal-dual method. The solution gives an on-line feedback control scheme for trajectory following in the presence of input constraints. In addition, we extend the above optimal decision strategy to the case where the controller design is based on a simplified model or where the plant itself is imprecisely known. The resulting torque optimization scheme may be incorporated into any existing control scheme to account for input bounds. This has important implications for the problem of deriving robust control schemes that take into account parameter uncertainty and model simplification. Simulations are presented for the case of a three-link manipulator with bounded torque, and our results are compared to the computed torque method. Our simulations show that by optimally adjusting the input torque to each joint when one or more of them saturates, significant improvement in tracking performance can result.