Category Archives: Robot Motion Planning

Motion planning with uncertain obstacles is NP-hard

Shimanuki L, Axelrod B., Hardness of Motion Planning with Obstacle Uncertainty in Two Dimensions, . The International Journal of Robotics Research. 2021;40(10-11):1151-1166 DOI: 10.1177/0278364921992787.

We consider the problem of motion planning in the presence of uncertain obstacles, modeled as polytopes with Gaussian-distributed faces (PGDFs). A number of practical algorithms exist for motion planning in the presence of known obstacles by constructing a graph in configuration space, then efficiently searching the graph to find a collision-free path. We show that such an exact algorithm is unlikely to be practical in the domain with uncertain obstacles. In particular, we show that safe 2D motion planning among PGDF obstacles is NP-hard with respect to the number of obstacles, and remains NP-hard after being restricted to a graph. Our reduction is based on a path encoding of MAXQHORNSAT and uses the risk of collision with an obstacle to encode variable assignments and literal satisfactions. This implies that, unlike in the known case, planning under uncertainty is hard, even when given a graph containing the solution. We further show by reduction from 3-SAT that both safe 3D motion planning among PGDF obstacles and the related minimum constraint removal problem remain NP-hard even when restricted to cases where each obstacle overlaps with at most a constant number of other obstacles.

Learning the parameters of a robot navigator through Q-learning

Chang, L., Shan, L., Jiang, C. et al, Reinforcement based mobile robot path planning with improved dynamic window approach in unknown environment, . Auton Robot 45, 51–76 (2021) DOI: 10.1007/s10514-020-09947-4.

Mobile robot path planning in an unknown environment is a fundamental and challenging problem in the field of robotics. Dynamic window approach (DWA) is an effective method of local path planning, however some of its evaluation functions are inadequate and the algorithm for choosing the weights of these functions is lacking, which makes it highly dependent on the global reference and prone to fail in an unknown environment. In this paper, an improved DWA based on Q-learning is proposed. First, the original evaluation functions are modified and extended by adding two new evaluation functions to enhance the performance of global navigation. Then, considering the balance of effectiveness and speed, we define the state space, action space and reward function of the adopted Q-learning algorithm for the robot motion planning. After that, the parameters of the proposed DWA are adaptively learned by Q-learning and a trained agent is obtained to adapt to the unknown environment. At last, by a series of comparative simulations, the proposed method shows higher navigation efficiency and successful rate in the complex unknown environment. The proposed method is also validated in experiments based on XQ-4 Pro robot to verify its navigation capability in both static and dynamic environment.

Qualitative modelling of quadcopters that is claimed to be better than reinforcement learning

Šoberl, D., Bratko, I. & Žabkar, Learning to Control a Quadcopter Qualitatively., . J Intell Robot Syst 100, 1097–1110 (2020) DOI: 10.1007/s10846-020-01228-7.

Qualitative modeling allows autonomous agents to learn comprehensible control models, formulated in a way that is close to human intuition. By abstracting away certain numerical information, qualitative models can provide better insights into operating principles of a dynamic system in comparison to traditional numerical models. We show that qualitative models, learned from numerical traces, contain enough information to allow motion planning and path following. We demonstrate our methods on the task of flying a quadcopter. A qualitative control model is learned through motor babbling. Training is significantly faster than training times reported in papers using reinforcement learning with similar quadcopter experiments. A qualitative collision-free trajectory is computed by means of qualitative simulation, and executed reactively while dynamically adapting to numerical characteristics of the system. Experiments have been conducted and assessed in the V-REP robotic simulator.

Using abstraction of dimensions in RRT motion planning

Xanthidis, M., Esposito, J.M., Rekleitis, I. et al., Motion Planning by Sampling in Subspaces of Progressively Increasing Dimension, . J Intell Robot Syst 100, 777–789 (2020) DOI: 10.1007/s10846-020-01217-w.

This paper introduces an enhancement to traditional sampling-based planners, resulting in efficiency increases for high-dimensional holonomic systems such as hyper-redundant manipulators, snake-like robots, and humanoids. Despite the performance advantages of modern sampling-based motion planners, solving high dimensional planning problems in near real-time remains a considerable challenge. The proposed enhancement to popular sampling-based planning algorithms is aimed at circumventing the exponential dependence on dimensionality, by progressively exploring lower dimensional volumes of the configuration space. Extensive experiments comparing the enhanced and traditional version of RRT, RRT-Connect, and Bidirectional T-RRT on both a planar hyper-redundant manipulator and the Baxter humanoid robot show significant acceleration, up to two orders of magnitude, on computing a solution. We also explore important implementation issues in the sampling process and discuss the limitations of this method.

Combination of RL with human provided models for navigation

Amarildo Likmeta, Alberto Maria Metelli, Andrea Tirinzoni, Riccardo Giol, Marcello Restelli, Danilo Romano, Combining reinforcement learning with rule-based controllers for transparent and general decision-making in autonomous driving, . Robotics and Autonomous Systems, Volume 131, 2020 DOI: 10.1016/j.robot.2020.103568.

The design of high-level decision-making systems is a topical problem in the field of autonomous driving. In this paper, we combine traditional rule-based strategies and reinforcement learning (RL) with the goal of achieving transparency and robustness. On the one hand, the use of handcrafted rule-based controllers allows for transparency, i.e., it is always possible to determine why a given decision was made, but they struggle to scale to complex driving scenarios, in which several objectives need to be considered. On the other hand, black-box RL approaches enable us to deal with more complex scenarios, but they are usually hardly interpretable. In this paper, we combine the best properties of these two worlds by designing parametric rule-based controllers, in which interpretable rules can be provided by domain experts and their parameters are learned via RL. After illustrating how to apply parameter-based RL methods (PGPE) to this setting, we present extensive numerical simulations in the highway and in two urban scenarios: intersection and roundabout. For each scenario, we show the formalization as an RL problem and we discuss the results of our approach in comparison with handcrafted rule-based controllers and black-box RL techniques.

Towards the emergence of obstacle avoidance through collisions

Qian F, Koditschek DE., An obstacle disturbance selection framework: emergent robot steady states under repeated collisions, The International Journal of Robotics Research. 2020;39(13):1549-1566, DOI: 10.1177/0278364920935514.

Natural environments are often filled with obstacles and disturbances. Traditional navigation and planning approaches normally depend on finding a traversable “free space” for robots to avoid unexpected contact or collision. We hypothesize that with a better understanding of the robot–obstacle interactions, these collisions and disturbances can be exploited as opportunities to improve robot locomotion in complex environments. In this article, we propose a novel obstacle disturbance selection (ODS) framework with the aim of allowing robots to actively select disturbances to achieve environment-aided locomotion. Using an empirically characterized relationship between leg–obstacle contact position and robot trajectory deviation, we simplify the representation of the obstacle-filled physical environment to a horizontal-plane disturbance force field. We then treat each robot leg as a “disturbance force selector” for prediction of obstacle-modulated robot dynamics. Combining the two representations provides analytical insights into the effects of gaits on legged traversal in cluttered environments. We illustrate the predictive power of the ODS framework by studying the horizontal-plane dynamics of a quadrupedal robot traversing an array of evenly-spaced cylindrical obstacles with both bounding and trotting gaits. Experiments corroborate numerical simulations that reveal the emergence of a stable equilibrium orientation in the face of repeated obstacle disturbances. The ODS reduction yields closed-form analytical predictions of the equilibrium position for different robot body aspect ratios, gait patterns, and obstacle spacings. We conclude with speculative remarks bearing on the prospects for novel ODS-based gait control schemes for shaping robot navigation in perturbation-rich environments.

Path planning by merging random sampling (RRT) with informed heuristics (A*)

Jonathan D Gammell, Timothy D Barfoot, Siddhartha S Srinivasa, Batch Informed Trees (BIT*): Informed asymptotically optimal anytime search, The International Journal of Robotics Research. 2020;39(5):543-567, DOI: 10.1177/0278364919890396.

Path planning in robotics often requires finding high-quality solutions to continuously valued and/or high-dimensional problems. These problems are challenging and most planning algorithms instead solve simplified approximations. Popular approximations include graphs and random samples, as used by informed graph-based searches and anytime sampling-based planners, respectively.

Informed graph-based searches, such as A*, traditionally use heuristics to search a priori graphs in order of potential solution quality. This makes their search efficient, but leaves their performance dependent on the chosen approximation. If the resolution of the chosen approximation is too low, then they may not find a (suitable) solution, but if it is too high, then they may take a prohibitively long time to do so.

Anytime sampling-based planners, such as RRT*, traditionally use random sampling to approximate the problem domain incrementally. This allows them to increase resolution until a suitable solution is found, but makes their search dependent on the order of approximation. Arbitrary sequences of random samples approximate the problem domain in every direction simultaneously, but may be prohibitively inefficient at containing a solution.

This article unifies and extends these two approaches to develop Batch Informed Trees (BIT*), an informed, anytime sampling-based planner. BIT* solves continuous path planning problems efficiently by using sampling and heuristics to alternately approximate and search the problem domain. Its search is ordered by potential solution quality, as in A*, and its approximation improves indefinitely with additional computational time, as in RRT*. It is shown analytically to be almost-surely asymptotically optimal and experimentally to outperform existing sampling-based planners, especially on high-dimensional planning problems.

Modelling robot motion sequences through context-free grammars

Rudolf Lioutikov, Guilherme Maeda, Filipe Veiga, Kristian Kersting, Jan Peters, Learning attribute grammars for movement primitive sequencing, The International Journal of Robotics Research, Vol 39, Issue 1, 2020, DOI: 10.1177/0278364919868279.

Movement primitives are a well studied and widely applied concept in modern robotics. However, composing primitives out of an existing library has shown to be a challenging problem. We propose the use of probabilistic context-free grammars to sequence a series of primitives to generate complex robot policies from a given library of primitives. The rule-based nature of formal grammars allows an intuitive encoding of hierarchically structured tasks. This hierarchical concept strongly connects with the way robot policies can be learned, organized, and re-used. However, the induction of context-free grammars has proven to be a complicated and yet unsolved challenge. We exploit the physical nature of robot movement primitives to restrict and efficiently search the grammar space. The grammar is learned by applying a Markov chain Monte Carlo optimization over the posteriors of the grammars given the observations. The proposal distribution is defined as a mixture over the probabilities of the operators connecting the search space. Moreover, we present an approach for the categorization of probabilistic movement primitives and discuss how the connectibility of two primitives can be determined. These characteristics in combination with restrictions to the operators guarantee continuous sequences while reducing the grammar space. In addition, a set of attributes and conditions is introduced that augments probabilistic context-free grammars in order to solve primitive sequencing tasks with the capability to adapt single primitives within the sequence. The method was validated on tasks that require the generation of complex sequences consisting of simple movement primitives using a seven-degree-of-freedom lightweight robotic arm.

A comparison / evaluation of bug algorithms for mobile robots and their bad performance when relying in only one sensor

K.N. McGuire, G.C.H.E. de Croon, K. Tuyls, A comparative study of bug algorithms for robot navigation,. Robotics and Autonomous Systems, Volume 121, DOI: 10.1016/j.robot.2019.103261.

This paper presents a literature survey and a comparative study of Bug Algorithms, with the goal of investigating their potential for robotic navigation. At first sight, these methods seem to provide an efficient navigation paradigm, ideal for implementations on tiny robots with limited resources. Closer inspection, however, shows that many of these Bug Algorithms assume perfect global position estimate of the robot which in GPS-denied environments implies considerable expenses of computation and memory — relying on accurate Simultaneous Localization And Mapping (SLAM) or Visual Odometry (VO) methods. We compare a selection of Bug Algorithms in a simulated robot and environment where they endure different types noise and failure-cases of their on-board sensors. From the simulation results, we conclude that the implemented Bug Algorithms’ performances are sensitive to many types of sensor-noise, which was most noticeable for odometry-drift. This raises the question if Bug Algorithms are suitable for real-world, on-board, robotic navigation as is. Variations that use multiple sensors to keep track of their progress towards the goal, were more adept in completing their task in the presence of sensor-failures. This shows that Bug Algorithms must spread their risk, by relying on the readings of multiple sensors, to be suitable for real-world deployment.

Analyzing effects of loads and terrain on wheel shapes in order to reduce errors in position estimation of a mobile wheeled robot

Smieszek, M., Dobrzanska, M. & Dobrzanski, P. , The impact of load on the wheel rolling radius and slip in a small mobile platform. Auton Robot (2019) 43: 2095, DOI: 10.1007/s10514-019-09857-0.

Automated guided vehicles are used in a variety of applications. Their major purpose is to replace humans in onerous, monotonous and sometimes dangerous operations. Such vehicles are controlled and navigated by application-specific software. In the case of vehicles used in multiple environments and operating conditions, such as the vehicles which are the subject of this study, a reasonable approach is required when selecting the navigation system. The vehicle may travel around an enclosed hall and around an open yard. The pavement surface may be smooth or uneven. Vehicle wheels should be flexible and facilitate the isolation and absorption of vibrations in order to reduce the effect of surface unevenness to the load. Another important factor affecting the operating conditions are changes to vehicle load resulting from the distribution of the load and the weight carried. Considering all of the factors previously mentioned, the vehicle’s navigation and control system is required to meet two opposing criteria. One of them is low price and simplicity, the other is ensuring the required accuracy when following the preset route. In the course of this study, a methodology was developed and tested which aims to obtain a satisfactory compromise between those two conflicting criteria. During the study a vehicle made in Technical University of Rzeszow was used. The results of the experimental research have been analysed. The results of the analysis provided a foundation for the development of a methodology leading to a reduction in navigation errors. Movement simulations for the proposed vehicle system demonstrated the potential for a significant reduction in the number of positioning errors.