Towards Efficient Computation and Simplified Specification of Declaratively Specified Robot Motion Skills

This thesis contributes to the well established paradigm of declarative specification of robot tasks through (potentially conflicting) constraints and objectives, with a view towards industrial applications. A declarative specification separates task programming from the details of how it is achieved, which is solved by planners taking a world model into account, making this approach generalize better than hard-coded motion skills. The  relatively low level of uncertainty in controlled industrial environments and the desire for high performance, while satisfying system limits, motivates the selection of the optimal control framework at the continuous level to plan and control the robot motions.

Despite its clear potential to advance the industrial state-of-the-practice, wide adoption of optimal control and its reactive counterpart model predictive control (MPC) for planning/controlling industrial robots is hindered by their computationally intensive nature and the high level of engineering effort required. This thesis makes three main contributions addressing these specific challenges and presents an additional exploratory work.

Firstly, this thesis proposes a simple and practical exact-penalty function based formulation for solving task specifications with constraint prioritization. Our approach mitigates both the computational cost and the  implementation challenges of a lexicographic optimization solver. Our formulation is implemented using off-the-shelf solvers, can be readily adopted in other existing robot control architectures that use these off-the-shelf solvers, and is several times faster than the standard sequential method. For predictive control problems, our work reports computational timings that indicate the feasibility of deploying prioritized MPC for the first time, to the best of our knowledge.

Secondly, this thesis revisits the Popov Vereshchagin (PV) solver, a largely unknown (but efficient) constrained robot dynamics solver developed in the 1970s and provides an expository derivation. It further proposes major extensions contributing two original low-order complexity constrained dynamics algorithms and makes a new connection between the PV solver computations and the classic problem of computing the inverse operational space inertia matrix (OSIM) to obtain an efficient OSIM algorithm. For larger robots like humanoids, these contributions nearly halve the number of operations required to compute constrained robot dynamics algorithms, which forms a significant portion (up to 80%) of an optimal control problem’s computational cost.

Thirdly, this thesis mitigates the engineering effort of prototyping and deploying OCP-based robot motion skills by developing a Python toolbox Tasho. Tasho promotes an interesting design pattern of programming complex tasks by composing simpler tasks and provides a vertically integrated workflow from high-level task specification to an Orocos component motion skill that can be readily embedded in a larger control architecture.

Finally, this thesis presents an exploratory work, with futuristic outlook, on integrated task and motion planning (TAMP), where the OCP-based continuous motion skills are automatically sequenced by a long horizon planner to achieve high-level goals specified declaratively at the symbolic-level. TAMP resolves imperfect abstraction of the continuous level by the symbolic-level through bidirectional communication between the two levels to ensure that the sequence of motions are also feasible at the continuous level.