Category Archives: Robot Motion Planning

A novel method of mathematical compression of the value function for polynomial (in the state) time complexity of value iteration / policy iteration

March 27, 2018 09:01 ,

Alex Gorodetsky, Sertac Karaman, and Youssef Marzouk, High-dimensional stochastic optimal control using continuous tensor decompositions, The International Journal of Robotics Research Vol 37, Issue 2-3, pp. 340 – 377, DOI: 10.1177/0278364917753994.

Motion planning and control problems are embedded and essential in almost all robotics applications. These problems are often formulated as stochastic optimal control problems and solved using dynamic programming algorithms. Unfortunately, most existing algorithms that guarantee convergence to optimal solutions suffer from the curse of dimensionality: the run time of the algorithm grows exponentially with the dimension of the state space of the system. We propose novel dynamic programming algorithms that alleviate the curse of dimensionality in problems that exhibit certain low-rank structure. The proposed algorithms are based on continuous tensor decompositions recently developed by the authors. Essentially, the algorithms represent high-dimensional functions (e.g. the value function) in a compressed format, and directly perform dynamic programming computations (e.g. value iteration, policy iteration) in this format. Under certain technical assumptions, the new algorithms guarantee convergence towards optimal solutions with arbitrary precision. Furthermore, the run times of the new algorithms scale polynomially with the state dimension and polynomially with the ranks of the value function. This approach realizes substantial computational savings in “compressible” problem instances, where value functions admit low-rank approximations. We demonstrate the new algorithms in a wide range of problems, including a simulated six-dimensional agile quadcopter maneuvering example and a seven-dimensional aircraft perching example. In some of these examples, we estimate computational savings of up to 10 orders of magnitude over standard value iteration algorithms. We further demonstrate the algorithms running in real time on board a quadcopter during a flight experiment under motion capture.

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using fuzzy Petri nets for mobile robot navigation

February 28, 2018 08:35 ,

Seung-yun Kim, Yilin Yang, A self-navigating robot using Fuzzy Petri nets, Robotics and Autonomous Systems, Volume 101, 2018, Pages 153-165, DOI: 10.1016/j.robot.2017.11.008.

Petri nets (PNs) are capable of modeling nearly any conceivable system and can provide a better understanding of the idealized action sequence in which to most effectively describe or execute said system through their powerful analytical capabilities. However, because real world instances are rarely as consistent and ideal as simulated models, basic PN modeling and simulation properties may be insufficient in practical application. We remedy this through specialization in Fuzzy Petri nets (FPNs). Fuzzy logic is incorporated to better model a self-navigating robot algorithm, thanks to its versatile multi-valued logic reasoning. By using FPNs, it is possible to simulate, assess, and communicate the process and reasoning of the navigational algorithm and apply it to real world programming. In this paper, we propose a series of specific fuzzy algorithms intended to be implemented in concert on a mobile robot platform in order to optimize the sequence of actions needed for a given task, primarily the navigation of an unknown maze. A set of varied maze configurations were developed and simulated as PN and FPN models, providing a testing environment to examine the efficiency of several methodologies. Five methods, including an original proposal in this paper, were compared across 30,000 simulations, evaluating in particular performance in processing cost in time. Our experiments concluded with results suggesting a very competitive task completion time at a considerable fraction in processing cost compared to the closest performing alternatives.

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Hybridizing RRT with deliberative path planning to improve performance

February 13, 2018 07:54 ,

Dong, Y., Camci, E. & Kayacan, Faster RRT-based Nonholonomic Path Planning in 2D Building Environments Using Skeleton-constrained Path Biasing, J Intell Robot Syst (2018) 89: 387, DOI: 10.1007/s10846-017-0567-9.

This paper presents a faster RRT-based path planning approach for regular 2-dimensional (2D) building environments. To minimize the planning time, we adopt the idea of biasing the RRT tree-growth in more focused ways. We propose to calculate the skeleton of the 2D environment first, then connect a geometrical path on the skeleton, and grow the RRT tree via the seeds generated locally along this path. We conduct batched simulations to find the universal parameters in manipulating the seeds generation. We show that the proposed skeleton-biased locally-seeded RRT (skilled-RRT) is faster than the other baseline planners (RRT, RRT*, A*-RRT, Theta*-RRT, and MARRT) through experimental tests using different vehicles in different 2D building environments. Given mild assumptions of the 2D environments, we prove that the proposed approach is probabilistically complete. We also present an application of the skilled-RRT for unmanned ground vehicle. Compared to the other baseline algorithms (Theta*-RRT and MARRT), we show the applicability and fast planning of the skilled-RRT in real environment.

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Achieving smooth motion in robotic manipulators on-line through their controller, and a nice state-of-the-art of the problem of smooth motion

February 7, 2018 08:52 ,

Yu-Sheng Lu, Yi-Yi Lin, Smooth motion control of rigid robotic manipulators with constraints on high-order kinematic variables, Mechatronics,
Volume 49, 2018, Pages 11-25, DOI: 10.1016/j.mechatronics.2017.11.003.

This paper presents a design for a jerk-constrained, time-optimal controller (JCTOC) that allows the smooth control of rigid robotic manipulators, in which time-optimal output responses are attained with confined jerk. A snap-constrained, time-optimal control (SCTOC) scheme is also proposed to produce even smoother output responses that are time-optimal, with a constraint on the maximum admissible snap. In contrast to conventional path-planning approaches that involve a bounded jerk/snap, the proposed JCTOC and SCTOC practically limit the corresponding high-order kinematic variables in real time. Using the structure of the computed torque control, the PD control, the JCTOC and the SCTOC are experimentally compared in terms of specific performance indices, including a chatter index, which is used to measure the unevenness of a signal.

Posted in: Control Engineering, Robot motion planning , Tagged:

On the drawbacks of RRT and how including deterministic sampling can help

January 31, 2018 08:05 ,

Lucas Janson, Brian Ichter, and Marco Pavone, Deterministic sampling-based motion planning: Optimality, complexity, and performance , The International Journal of Robotics Research Vol 37, Issue 1, pp. 46 – 61, DOI: 10.1177/0278364917714338.

Probabilistic sampling-based algorithms, such as the probabilistic roadmap (PRM) and the rapidly exploring random tree (RRT) algorithms, represent one of the most successful approaches to robotic motion planning, due to their strong theoretical properties (in terms of probabilistic completeness or even asymptotic optimality) and remarkable practical performance. Such algorithms are probabilistic in that they compute a path by connecting independently and identically distributed (i.i.d.) random points in the configuration space. Their randomization aspect, however, makes several tasks challenging, including certification for safety-critical applications and use of offline computation to improve real-time execution. Hence, an important open question is whether similar (or better) theoretical guarantees and practical performance could be obtained by considering deterministic, as opposed to random, sampling sequences. The objective of this paper is to provide a rigorous answer to this question. Specifically, we first show that PRM, for a certain selection of tuning parameters and deterministic low-dispersion sampling sequences, is deterministically asymptotically optimal, in other words, it returns a path whose cost converges deterministically to the optimal one as the number of points goes to infinity. Second, we characterize the convergence rate, and we find that the factor of sub-optimality can be very explicitly upper-bounded in terms of theℓ2 -dispersion of the sampling sequence and the connection radius of PRM. Third, we show that an asymptotically optimal version of PRM exists with computational and space complexity arbitrarily close to O(n) (the theoretical lower bound), where n is the number of points in the sequence. This is in contrast to the O(nlogn) complexity results for existing asymptotically optimal probabilistic planners. Fourth, we discuss extending our theoretical results and insights to other batch-processing algorithms such as FMT*, to non-uniform sampling strategies, to k-nearest-neighbor implementations, and to differentially constrained problems. Importantly, our main theoretical tool is the ℓ2-dispersion, an interesting consequence of which is that all our theoretical results also hold for low-ℓ2-dispersion random sampling (which i.i.d. sampling does not satisfy). In other words, achieving deterministic guarantees is really a matter of i.i.d. sampling versus non-i.i.d. low-dispersion sampling (with deterministic sampling as a prominent case), as opposed to random versus deterministic. Finally, through numerical experiments, we show that planning with deterministic (or random) low-dispersion sampling generally provides superior performance in terms of path cost and success rate.

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A new spatial transformation for planning mobile robot trajectories that guarantees a solution and also time requirement satisfaction

December 6, 2017 09:04 ,

S. G. Loizou, The Navigation Transformation, IEEE Transactions on Robotics, vol. 33, no. 6, pp. 1516-1523, DOI: 10.1109/TRO.2017.2725323.

This work introduces a novel approach to the solution of the navigation problem by mapping an obstacle-cluttered environment to a trivial domain called the point world, where the navigation task is reduced to connecting the images of the initial and destination configurations by a straight line. Due to this effect, the underlying transformation is termed the “navigation transformation.” The properties of the navigation transformation are studied in this work as well as its capability to provide-through the proposed feedback controller designs-solutions to the motion- and path-planning problems. Notably, the proposed approach enables the construction of temporal stabilization controllers as detailed herein, which provide a time abstraction to the navigation problem. The proposed solutions are correct by construction and, given a diffeomorphism from the workspace to a sphere world, tuning free. A candidate construction for the navigation transformation on sphere worlds is proposed. The provided theoretical results are backed by analytical proofs. The efficiency, robustness, and applicability of the proposed solutions are supported by a series of experimental case studies.

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A theoretical framework based on hybrid models and logical verification to prove the guarantees for obstacle avoidance in mobile robot navigation

October 28, 2017 08:40 ,

Stefan Mitsch, Khalil Ghorbal, David Vogelbacher, and André Platzer, Formal verification of obstacle avoidance and navigation of ground robots, The International Journal of Robotics Research Vol 36, Issue 12, pp. 1312 – 1340, DOI: 0.1177/0278364917733549.

This article answers fundamental safety questions for ground robot navigation: under which circumstances does which control decision make a ground robot safely avoid obstacles? Unsurprisingly, the answer depends on the exact formulation of the safety objective, as well as the physical capabilities and limitations of the robot and the obstacles. Because uncertainties about the exact future behavior of a robot’s environment make this a challenging problem, we formally verify corresponding controllers and provide rigorous safety proofs justifying why the robots can never collide with the obstacle in the respective physical model. To account for ground robots in which different physical phenomena are important, we analyze a series of increasingly strong properties of controllers for increasingly rich dynamics and identify the impact that the additional model parameters have on the required safety margins. We analyze and formally verify: (i) static safety, which ensures that no collisions can happen with stationary obstacles; (ii) passive safety, which ensures that no collisions can happen with stationary or moving obstacles while the robot moves; (iii) the stronger passive-friendly safety, in which the robot further maintains sufficient maneuvering distance for obstacles to avoid collision as well; and (iv) passive orientation safety, which allows for imperfect sensor coverage of the robot, i.e., the robot is aware that not everything in its environment will be visible. We formally prove that safety can be guaranteed despite sensor uncertainty and actuator perturbation. We complement these provably correct safety properties with liveness properties: we prove that provably safe motion is flexible enough to let the robot navigate waypoints and pass intersections. To account for the mixed influence of discrete control decisions and the continuous physical motion of the ground robot, we develop corresponding hybrid system models and use differential dynamic logic theorem-proving techniques to formally verify their correctness. Since these models identify a broad range of conditions under which control decisions are provably safe, our results apply to any control algorithm for ground robots with the same dynamics. As a demonstration, we also synthesize provably correct runtime monitor conditions that check the compliance of any control algorithm with the verified control decisions.

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Real-time modification of user inputs in the teleoperation of an UAV in order to avoid obstacles with a reactive algorithm, transparently from the user control

July 26, 2017 08:55 ,

Daman Bareiss, Joseph R. Bourne & Kam K. Leang, On-board model-based automatic collision avoidance: application in remotely-piloted unmanned aerial vehicles, Auton Robot (2017) 41:1539–1554, DOI: 10.1007/s10514-017-9614-4.

This paper focuses on real-world implementation and verification of a local, model-based stochastic automatic collision avoidance algorithm, with application in
remotely-piloted (tele-operated) unmanned aerial vehicles (UAVs). Automatic collision detection and avoidance for tele-operated UAVs can reduce the workload of pilots to allow them to focus on the task at hand, such as searching for victims in a search and rescue scenario following a natural disaster. The proposed algorithm takes the pilot’s input and exploits the robot’s dynamics to predict the robot’s trajectory for determining whether a collision will occur. Using on-board sensors for obstacle detection, if a collision is imminent, the algorithm modifies the pilot’s input to avoid the collision while attempting to maintain the pilot’s intent. The algorithm is implemented using a low-cost on-board computer, flight-control system, and a two-dimensional laser illuminated detection and ranging sensor for obstacle detection along the trajectory of the robot. The sensor data is processed using a split-and-merge segmentation algorithm and an approximate Minkowski difference. Results from flight tests demonstrate the algorithm’s capabilities for teleoperated collision-free control of an experimental UAV.

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A method to model trajectories that captures its essential parameters (for comparisons, clustering, etc.)

July 26, 2017 08:33 ,

W. Lin et al., “A Tube-and-Droplet-Based Approach for Representing and Analyzing Motion Trajectories,” in IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 39, no. 8, pp. 1489-1503, Aug. 1 2017.DOI: 10.1109/TPAMI.2016.2608884.

Trajectory analysis is essential in many applications. In this paper, we address the problem of representing motion trajectories in a highly informative way, and consequently utilize it for analyzing trajectories. Our approach first leverages the complete information from given trajectories to construct a thermal transfer field which provides a context-rich way to describe the global motion pattern in a scene. Then, a 3D tube is derived which depicts an input trajectory by integrating its surrounding motion patterns contained in the thermal transfer field. The 3D tube effectively: 1) maintains the movement information of a trajectory, 2) embeds the complete contextual motion pattern around a trajectory, 3) visualizes information about a trajectory in a clear and unified way. We further introduce a droplet-based process. It derives a droplet vector from a 3D tube, so as to characterize the high-dimensional 3D tube information in a simple but effective way. Finally, we apply our tube-and-droplet representation to trajectory analysis applications including trajectory clustering, trajectory classification & abnormality detection, and 3D action recognition. Experimental comparisons with state-of-the-art algorithms demonstrate the effectiveness of our approach.

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Several strategies for exploring unknown environments based on graphs extracted from Voronoi diagrams

July 26, 2017 08:30 ,

E. G. Tsardoulias, A. Iliakopoulou, A. Kargakos, L. Petrou, Cost-Based Target Selection Techniques Towards Full Space Exploration and Coverage for USAR applications in a Priori Unknown Environments, J Intell Robot Syst (2017) 87:313–340, DOI: 10.1007/s10846-016-0434-0.

Full coverage and exploration of an environment is essential in robot rescue operations where victim identification is required. Three methods of target selection towards full exploration and coverage of an unknown space oriented for Urban Search and Rescue (USAR) applications have been developed. These are the Selection of the closest topological node, the Selection of the minimum cost topological node and the Selection of the minimum cost sub-graph. All methods employ a topological graph extracted from the Generalized Voronoi Diagram (GVD), in order to select the next best target during exploration. The first method utilizes a distance metric for determining the next best target whereas the Selection of the minimum cost topological node method assigns four different weights on the graph’s nodes, based on certain environmental attributes. The Selection of the minimum cost sub-graph uses a similar technique, but instead of single nodes, sets of graph nodes are examined. In addition, a modification of A* algorithm for biased path creation towards uncovered areas, aiming at a faster spatial coverage, is introduced. The proposed methods’ performance is verified by experiments conducted in two heterogeneous simulated environments. Finally, the results are compared with two common exploration methods.

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