Fig. 5: Constraints and MR connector considerations integrated into the optimization framework.
From: Optimized user-guided motion control of modular robots
a Collision avoidance (Eq. (6)) demonstrated on two Roombot modules. b Legged morphologies made of Mori3 and corresponding visualization of the CoM constraint elements (Eq. (8)). c Module to module connection modeled as bilateral contact. The contact is associated with a wrench \({{{{\bf{f}}}}}_{{{{{\rm{c}}}}}_{j}}\) (QP decision variable) consisting of moments \({m}_{{{{{\rm{c}}}}}_{j}}^{{{{\rm{X}}}}},{m}_{{{{{\rm{c}}}}}_{j}}^{{{{\rm{Y}}}}},{m}_{{{{{\rm{c}}}}}_{j}}^{{{{\rm{Z}}}}}\) and tension-compression forces \({f}_{{{{{\rm{c}}}}}_{j}}^{X},{f}_{{{{{\rm{c}}}}}_{j}}^{{{{\rm{Y}}}}},{f}_{{{{{\rm{c}}}}}_{j}}^{{{{\rm{Z}}}}}\). The moment around the motor axis \({m}_{{{{{\rm{c}}}}}_{j}}^{{{{\rm{Y}}}}}\) can be bounded as part of joint torque constraints. d Increasing structure inclination introduces more stress in the form of higher wrenches applied to connector links. A bilateral contact constraint is defined between MR and the ground. Constraining these wrenches prevents users from driving the MR system to violate connector strength constraints (illustrated in red).
