This paper delves into the fusion of quantum computing and robotics, focusing on motion planning in cluttered environments. Traditional algorithms struggle with complex problems where many constraints need to be satisfied. Hence, optimization-based approaches such as Constrained Quadratic Models (CQM) have become increasingly popular. Our work presents a 3D tracking algorithm based on CQM uniquely adapted for quantum computers to address computational challenges. With their parallel processing capabilities, Quantum computers offer a groundbreaking approach to optimizing complex problems. We formulate the CQM problem for efficient resolution on the D-Wave quantum computer, showcasing its superiority over classical counterparts. Our application centers on real-time planning in a target-chaser tracking scenario, highlighting the quantum advantage in handling the computation complexity of constrained problems. This paper bridges the quantum-robotics gap and sets the stage for future research in quantum-enhanced robotic motion planning.

This paper presents a real-time algorithm for computing the optimal sequence and motion plans for a fixed-base manipulator to pick and place a set of given objects. The optimality is defined in terms of the total execution time of the sequence or its proxy, the arc-length in the joint-space. The fundamental complexity stems from the fact that the optimality metric depends on the joint motion, but the task specification is in the end-effector space. Moreover, mapping between a pair of end-effector positions to the shortest arc-length joint trajectory is not analytic; instead, it entails solving a complex trajectory optimization problem. Existing works ignore this complex mapping and use the Euclidean distance in the end-effector space to compute the sequence. In this paper, we overcome the reliance on the Euclidean distance heuristic by introducing a novel data-driven technique to estimate the optimal arc-length cost in joint space (a.k.a the value function) between two given end-effector positions. We parametrize the value function as a Neural Network and motivate a niche choice for its architecture, inspired by the works on metric learning. The learned value function is then used as an edge cost in a capacitated vehicle routing problem (CVRP) set-up to compute the optimal visitation sequence. Finally, we optimize over the input space of the learnt value function network to propose a novel Inverse Kinematics (IK) algorithm that produces substantially shorter joint arc-length trajectories than existing approaches while executing the computed optimal sequence. We show that our sequence planner, in combination with our proposed IK, offers a substantial improvement in joint arc-length over existing state-of-the-art while maintaining scalability to a large number of objects.

Most commercially available fixed-wing aerial vehicles (FWV) can carry only small, lightweight computing hardware such as Jetson TX2 onboard. Solving non-linear trajectory optimization on these computing resources is computationally challenging even while considering only the kinematic motion model. Most importantly, the computation time increases sharply as the environment becomes more cluttered. In this paper, we take a step towards overcoming this bottleneck and propose a trajectory optimizer that achieves online performance on both conventional laptops/desktops and Jetson TX2 in a typical urban environment setting. Our optimizer builds on the novel insight that the seemingly non-linear trajectory optimization problem for FWV has an implicit multi-convex structure. Our optimizer exploits these computational structures by bringing together diverse concepts from Alternating Minimization, Bregman iteration, and Alternating Direction Method of Multipliers. We show that our optimizer outperforms the state-of-the-art implementation of sequential quadratic programming approach in optimal control solver ACADO in computation time and solution quality measured in terms of control and goal reaching cost.

Trajectory optimization problems under affine motion model and convex cost function are often solved through the convex-concave procedure (CCP), wherein the non-convex collision avoidance constraints are replaced with its affine approximation. Although mathematically rigorous, CCP has some critical limitations. First, it requires a collision-free initial guess of solution trajectory which is difficult to obtain, especially in dynamic environments. Second, at each iteration, CCP involves solving a convex constrained optimization problem which becomes prohibitive for real-time computation even with a moderate number of obstacles, if long planning horizons are used.In this paper, we propose a novel trajectory optimizer which like CCP involves solving convex optimization problems but can work with an arbitrary initial guess. Moreover, the proposed optimizer can be computationally upto a few orders of magnitude faster than CCP while achieving similar or better optimal cost. The reduced computation time, in turn, stems from some interesting mathematical structures in the optimizer which allows for distributed computation and obtaining solutions in symbolic form. We validate our claims on difficult benchmarks consisting of static and dynamic obstacles.