2.3 Manipulation control
Figure 2.3: Hierarchical control method structure .
first one is the grasp controller, which generates torques to avoid the slippage; the
second module is the manipulation controller, which generates torques to manip-
ulate the object according to the desired trajectory of the object; finally, the third
one is the suppresser module which has the duty to suppress the grasp controller
when the manipulation torques become high. Hence, the suppresser is a sort of
supervisor managing possible conflicts between manipulation and grasp torques.
Figure 2.3 shows the control scheme corresponding to this method.
There is a difference between the hybrid postion/force control law and an hybrid
model of a robotic hand: in the former case, the model is written in the contin-
uous state space and the control law is said to be hybrid since it is the sum of
two different spaces, namely the position space and the force space; in the latter
case, the system "hand plus object" is modeled with an hybrid combination of
continuous and discrete or logical variables.
This last case is widely studied in the works [106, 107, 108, 109]. In these, the
whole dynamics of the system "hand plus object" is recast in a framework subject
to complementary and slackness conditions to create a DC (dynamic complemen-
tary) model of the system, which includes both continuous and logical variables.
This DC model can be represented in a mixed logical dynamical form (MLD model)
which allows a unified approach for mathematical, numerical and control investi-
gations. In a MLD model, it is possible to specify actuators limits, joint ranges,
and to model the impact of a finger with the surface of the object. The main ad-
vantage of MLD models is the possibility to use model predictive control (MPC)
schemes that are based on the receding horizon control approach. Moreover, mixed
integer quadric problem (MIPQ) solvers can be useful from the numerical analysis
point of view, in order to reach an optimal solution for the manipulation control
problem. The optimal sequence of both continuous and logical variables is simul-
taneously found and it corresponds to the optimal motion as to realize dexterous
2.3.5 Predictive control There is a difference between the hybrid postion/force control law and an hybrid model of a robotic hand: in the former case, the model is written in the contin- uous state space and the control law is said to be hybrid since it is the sum of two different spaces, namely the position space and the force space;