This paper proposes a bidirectional rapidly-exploring random trees (RRT) algorithm to solve the motion planning problem for hybrid systems. The proposed algorithm, called HyRRT-Connect, propagates in both forward and backward directions in hybrid time until an overlap between the forward and backward propagation results is detected. Then, HyRRT-Connect constructs a motion plan through the reversal and concatenation of functions defined on hybrid time domains, ensuring that the motion plan satisfies the given hybrid dynamics. To address the potential discontinuity along the flow caused by tolerating some distance between the forward and backward partial motion plans, we reconstruct the backward partial motion plan by a forward-in-hybrid-time simulation from the final state of the forward partial motion plan. effectively eliminating the discontinuity. The proposed algorithm is applied to an actuated bouncing ball system and a walking robot example to highlight its computational improvement.

This paper addresses the Dubins path planning problem for vehicles in 3D space. In particular, we consider the problem of computing CSC paths -- paths that consist of a circular arc (C) followed by a straight segment (S) followed by a circular arc (C). These paths are useful for vehicles such as fixed-wing aircraft and underwater submersibles that are subject to lower bounds on turn radius. We present a new parameterization that reduces the 3D CSC planning problem to a search over 2 variables, thus lowering search complexity, while also providing gradients that assist that search. We use these equations with a numerical solver to explore numbers and types of solutions computed for a variety of planar and 3D scenarios. Our method successfully computes CSC paths for the large majority of test cases, indicating that it could be useful for future generation of robust, efficient curvature-constrained trajectories.

This paper describes two C++/Open Motion Planning Library implementations of the recently developed motion planning algorithms HyRRT arXiv:2210.15082v1 [cs.RO] and HySST arXiv:2305.18649v1 [cs.RO]. Specifically, cHyRRT, an implementation of the HyRRT algorithm, is capable of generating a solution to a motion planning problem for hybrid systems with probabilistically completeness, while cHySST, an implementation of the asymptotically near-optimal HySST algorithm, is capable of computing a trajectory to solve the optimal motion planning problem for hybrid systems. cHyRRT is suitable for motion planning problems where an optimal solution is not required, whereas cHySST is suitable for such problems that prefer optimal solutions, within all feasible solutions. The structure, components, and usage of the two tools are described. Examples are included to illustrate the main capabilities of the toolbox.

This paper focuses on the motion planning problem for the systems exhibiting both continuous and discrete behaviors, which we refer to as hybrid dynamical systems. Firstly, the motion planning problem for hybrid systems is formulated using the hybrid equation framework, which is general to capture most hybrid systems. Secondly, a propagation algorithm template is proposed that describes a general framework to solve the motion planning problem for hybrid systems. Thirdly, a rapidly-exploring random trees (RRT) implementation of the proposed algorithm template is designed to solve the motion planning problem for hybrid systems. At each iteration, the proposed algorithm, called HyRRT, randomly picks a state sample and extends the search tree by flow or jump, which is also chosen randomly when both regimes are possible. Through a definition of concatenation of functions defined on hybrid time domains, we show that HyRRT is probabilistically complete, namely, the probability of failing to find a motion plan approaches zero as the number of iterations of the algorithm increases. This property is guaranteed under mild conditions on the data defining the motion plan, which include a relaxation of the usual positive clearance assumption imposed in the literature of classical systems. The motion plan is computed through the solution of two optimization problems, one associated with the flow and the other with the jumps of the system. The proposed algorithm is applied to an actuated bouncing ball system and a walking robot system so as to highlight its generality and computational features.

This paper proposes a bidirectional rapidly-exploring random trees (RRT) algorithm to solve the motion planning problem for hybrid systems. The proposed algorithm, called HyRRT-Connect, propagates in both forward and backward directions in hybrid time until an overlap between the forward and backward propagation results is detected. Then, HyRRT-Connect constructs a motion plan through the reversal and concatenation of functions defined on hybrid time domains, ensuring the motion plan thoroughly satisfies the given hybrid dynamics. To address the potential discontinuity along the flow caused by tolerating some distance between the forward and backward partial motion plans, we reconstruct the backward partial motion plan by a forward-in-hybrid-time simulation from the final state of the forward partial motion plan. By applying the reversed input of the backward partial motion plan, the reconstruction process effectively eliminates the discontinuity and ensures that as the tolerance distance decreases to zero, the distance between the endpoint of the reconstructed motion plan and the final state set approaches zero. The proposed algorithm is applied to an actuated bouncing ball example and a walking robot example so as to highlight its generality and computational improvement.

This paper proposes a stable sparse rapidly-exploring random trees (SST) algorithm to solve the optimal motion planning problem for hybrid systems. At each iteration, the proposed algorithm, called HySST, selects a vertex with the lowest cost among all the vertices within the neighborhood of a randomly selected sample and then extends the search tree by flow or jump, which is also chosen randomly when both regimes are possible. In addition, HySST maintains a static set of witness points such that all the vertices within the neighborhood of each witness are pruned except the vertex with the lowest cost. Through a definition of concatenation of functions defined on hybrid time domains, we show that HySST is asymptotically near optimal, namely, the probability of failing to find a motion plan such that its cost is close to the optimal cost approaches zero as the number of iterations of the algorithm increases to infinity. This property is guaranteed under mild conditions on the data defining the motion plan, which include a relaxation of the usual positive clearance assumption imposed in the literature of classical systems. The proposed algorithm is applied to an actuated bouncing ball system and a collision-resilient tensegrity multicopter system so as to highlight its generality and computational features.

This paper proposes a rapidly-exploring random trees (RRT) algorithm to solve the motion planning problem for hybrid systems. At each iteration, the proposed algorithm, called HyRRT, randomly picks a state sample and extends the search tree by flow or jump, which is also chosen randomly when both regimes are possible. Through a definition of concatenation of functions defined on hybrid time domains, we show that HyRRT is probabilistically complete, namely, the probability of failing to find a motion plan approaches zero as the number of iterations of the algorithm increases. This property is guaranteed under mild conditions on the data defining the motion plan, which include a relaxation of the usual positive clearance assumption imposed in the literature of classical systems. The motion plan is computed through the solution of two optimization problems, one associated with the flow and the other with the jumps of the system. The proposed algorithm is applied to a walking robot so as to highlight its generality and computational features.

Performing effective preference-based data retrieval requires detailed and preferentially meaningful structurized information about the current user as well as the items under consideration. A common problem is that representations of items often only consist of mere technical attributes, which do not resemble human perception. This is particularly true for integral items such as movies or songs. It is often claimed that meaningful item features could be extracted from collaborative rating data, which is becoming available through social networking services. However, there is only anecdotal evidence supporting this claim; but if it is true, the extracted information could very valuable for preference-based data retrieval. In this paper, we propose a methodology to systematically check this common claim. We performed a preliminary investigation on a large collection of movie ratings and present initial evidence.