This paper focuses on the motion planning problem for serial articulated robots with revolute joints under kinematic constraints. Many motion planners leverage iterative local optimization methods but are often trapped in local minima due to non-convexity of the problem. A key reason for the non-convexity is the trigonometric term when parameterizing the kinematics using joint angles. Recent distance-based formulations can eliminate these trigonometric terms by formulating the kinematics based on distances, and has shown superior performance against classic joint angle based formulations in domains like inverse kinematics (IK). However, distance-based kinematics formulations have not yet been studied for motion planning, and naively applying them for motion planning may lead to poor computational efficiency. In particular, IK seeks one configuration while motion planning seeks a sequence of configurations, which greatly increases the scale of the underlying optimization problem. This paper proposes Propagative Distance Optimization for Motion Planning (PDOMP), which addresses the challenge by (i) introducing a new compact representation that reduces the number of variables in the distance-based formulation, and (ii) leveraging the chain structure to efficiently compute forward kinematics and Jacobians of the robot among waypoints along a path. Test results show that PDOMP runs up to 10 times faster than the sampling-based and angle-based-optimization baseline methods.

The Orienteering Problem (OP) seeks a path on a graph to maximize total rewards collected subject to a path length budget. Typically, a reward is achieved by visiting a vertex in the graph, and such a reward is constant for all time. This paper considers a variant of OP where the reward of each vertex is an arbitrary time-dependent function, and hence the name time-varying reward OP (TR-OP). To solve this problem, we develop a novel heuristic search algorithm called Reward Maximization A* (RMA*), which is guaranteed to find an optimal solution to TR-OP. We also develop a fast method to compute an admissible heuristic for RMA* that can effectively direct the search to save computational effort. Furthermore, we introduce a hyper-parameter in RMA* that trades off between solution quality and runtime efficiency for RMA*. We benchmark RMA* against a recent dynamic programming (DP) approach, which runs fast in practice, but has no guarantee of the solution optimality. In our tests, RMA* reduces the runtime by up to 70% compared to DP. By adjusting the hyper-parameter, RMA* is able to find solutions with up to 30% more rewards than those found by DP.