Real-Time Motion Planning for Collaborative Robot Arms

Human-robot interactions have been recognized to be a key element of future robots in many application domains such as manufacturing, transportation, and service. For example, various collaborative robots are cooperating with human workers in factories. It is challenging to design the behavior of those co-robots. The design objective is to ensure their behavior is both efficient and safe. In a well-defined, deterministic environment, these requirements have already been achieved by state-of-the-art systems. However, interactions with other intelligent entities bring large uncertainties to such systems. Moreover, onboard computation power is usually limited to account for all possible scenarios. These represent the major challenges faced by co-robots. The problem that this talk is trying to address is how to design the behavior of those robots in dynamic, uncertain environments under limited computation capacity in order to maximize efficiency while guaranteeing safety.

This talk mainly addresses the problem from a motion planning perspective. In order for the robot to be responsive to environmental changes, it is critical that the motion planning algorithms run in real time. Moreover, the planned trajectory needs to be both collision-free and time-optimal. However, the nonconvexity of the motion planning problem makes computation expensive. Liu et al. developed the convex feasible set algorithm (CFS), which is an efficient nonconvex optimization solver that can be applied to both the trajectory planning problem and the temporal optimization problem. Experiments on different problems show that the CFS algorithm is more efficient than other state-of-the-art nonconvex optimization algorithms such as sequential quadratic programming and interior point method. With the CFS algorithm, the collaborative robots can generate trajectories in real time, and are thus more responsive, safe, and efficient.

The CFS algorithm transforms a nonconvex optimization problem into a sequence of convex sub-problems by constraining the original problem in a sequence of convex feasible sets. It is efficient because the unique geometric structure of the problem is efficiently exploited by relaxation and convexification. One consequence was that the step size of the algorithm was unconstrained, hence the number of iterations was greatly reduced. Another consequence was that line search in CFS was not needed, hence the computation time during each iteration also decreased. Most importantly, as the feasible set was directly searched, the solution was good enough even before convergence. “Good enough” meant feasible and safe. Hence, the iteration was safely stopped before convergence and the suboptimal trajectory was executed.