Extending iTaSC to support inequality constraints and non-instantaneous task specification

Constraints Compliant Control: Constraints compatibility and the displaced configuration approach

“…As shown in [6], in case of constant accelerationq m , the position evolution in s iteration is q(k + s) = q(k) + sq(k)δt + 1 2 (s 2 − s)q m δt 2 .…”

“…Since the n DOFs of a robot can only instantaneously comply with n equality conditions, the latter approach is doomed to fail given, for example, the 2n constraints associated to joint limits. To deal with this strong limitation, the most general approaches consist in formulating the control problem as a convex optimization one where constraints are naturally expressed both through equalities and inequalities ( [4], [5] and [6]). This type of approach induces, in the case of complex systems with multiple hierarchical levels, computation times which may not be suitable for a real-time implementation (even though some very recent work described in [7] exhibits a rather low computational complexity).…”

“…In [6], a framework is introduced to include any type of inequality and equality constraints. The presented results involve an incompatibility between acceleration and position constraints which is locally treated.…”

“…While this formalization is general enough to be used by any constraint compliant control law such as the one proposed in [6], our second contribution is to propose an intuitive and more direct constraint compliant control law including joint accelerations limits (section III). The obtained performances are exposed and discussed in section IV.…”

Synthesis of complex humanoid whole-body behavior: A focus on sequencing and tasks transitions

“…The same kind of approach is being used in the work of Escande et al ([8]) at the inverse velocity kinematics level with efficient implementation on a humanoid robot in mind and allowing to enforce priorities both at the tasks and constraints levels. Finally, even though not applied to the humanoid case directly, the work of Decré et al ( [9]) makes use of cascading LQPs to formulate complex control problems with priorities between tasks as well as unilateral constraints.…”