Singularity Avoidance for Cart-Mounted Hand-Guided Collaborative Robots: A Variational Approach

Most collaborative robots (cobots) can be taught by hand guiding: essentially, by manually jogging the robot, an operator teaches some configurations to be employed as via points. Based on those via points, Cartesian end-effector trajectories such as straight lines, circular arcs or splines are then constructed. Such methods can, in principle, be employed for cart-mounted cobots (i.e., when the jogging involves one or two linear axes, besides the cobot axes). However, in some applications, the sole imposition of via points in Cartesian space is not sufficient. On the contrary, albeit the overall system is redundant, (i) the via points must be reached at the taught joint configurations, and (ii) the undesirable singularity (and near-singularity) conditions must be avoided. The naive approach, consisting of setting the cart trajectory beforehand (for instance, by imposing a linear-in-time motion law that crosses the taught cart configurations), satisfies the first need, but does not guarantee the satisfaction of the second. Here, we propose an approach consisting of (i) a novel strategy for decoupling the planning of the cart trajectory and that of the robot joints, and (ii) a novel variational technique for computing the former in a singularity-aware fashion, ensuring the avoidance of a class of workspace singularity and near-singularity configurations.