Abstract
The first use of quadratic programming (QP) in robotics control dates back to the 1990s. It was an alternative to Jacobian null-space-projection-based methods to solve redundancies while accounting for unilateral constraints. Since then, QP control has become a suitable tool for combining and mediating several control objectives with a soft or strict hierarchy. Nevertheless, QP controllers still have some limitations and open issues. In this thesis, our goal is twofold: (i) address a number of the QP control open problems, and (ii) unify control and observation via multi-objective QP control.Kinematic constraints constitute a large class of unilateral constraints that cannot be directly included in QP. Several solutions exist to write these constraints in terms of QP decision variables. Yet, none of them performed well in closed-loop because of their specificity to joint limits, non-robustness against non-modeled dynamics, and lack of theoretical grounding. We address this topic by proposing a general formulation encompassing all kinematic constraints. Our solution is based on adaptive-gains ordinary differential inequality with formal proofs of constraints fulfillment forward in time.We also investigate the stability of the closed-loop QP control scheme for robots controlled in kinematics, i.e., robots with high-gain joint-controllers having the desired joint position or velocity as input commands. Although these robots are widely used, the stability topic has not been explored. Using a simple 1-degree of freedom system, we show how the closed-loop control scheme is prone to instability, especially if the task and/or constraint gains are set to high values. Then, we propose a robust task and constraint formulation based on integral feedback terms that yield robust stability of the tasks and robust asymptotic stability of the set defined by the kinematic constraint. Our solution applies to any kinematic-controlled robot under practical assumptions.Then, we address the topic of constraints compatibility. Constraints are incompatible if they are in conflict. For example, if the deceleration required to stop the robot arm before getting into the collision is higher than what is currently allowed because of other constraints. Dealing with potential conflicts is typically an anticipatory task that requires a look-ahead on motions. Our solution consists of implementing a model predictive controller (MPC) as a layer on top of whole-body QP, to which we delegate the task of constraints compatibility. MPC model is constructed based on the closed-loop tasks and kinematic constraints dynamics. By accounting for the hardware limits and kinematic constraints over a finite time horizon, MPC outputs a sequence of optimal task targets tracked by whole-body QP, yielding a motion that satisfies all the constraints.Finally, we exploit the multi-objective control paradigm to unify two tasks of different natures: observation (estimation) and control (tracking). We formulate this unification through the concept of the interdependent tasks: the state of the observation task is forwarded as a reference for the tracking task, still via one compact QP controller. This novel formulation enables the generation of a motion toward an observed target. Typically in human-robot handover scenarios.