Motion Planning Approach Research Articles

An Energy Efficient Jumping Drone - A Simple Projectile Motion Approach

Jumping robots are interesting devices that offer several advantages in terms of navigation about cluttered environments. However, they present unique challenges with respect to their design and control. In this paper, we propose a design that uses four planar thrusters/propellers on a jumping robot. Such a system provides better maneuverability due to agility provided by the propellers to guide the motion. From energy consumption perspective, we use the gravity for free fall and a spring mechanism to execute the jumping motion without loss of much energy on impact. The primary contribution of this paper is developing a novel navigation and control method for such jumping robots to go to the desired goal. In this paper, we present a projectile motion planning approach for the control of the proposed system. We propose proportional (P) and proportional-derivative (PD) controllers that compute the launch velocity required for the jumping drone after impact with the ground to follow a projectile motion in each jump to reach the goal position. The jumping drone bounces after impact with the ground, and the drone is then actuated for a certain time till it attains the required launch velocity after which it is made to move freely under the influence of gravity. Such a system shows significant reduction of energy consumption (by 81.35%) as compared to a normal drone navigating to the same goal location. Simulation results validate the effectiveness of the proposed approach.

A Versatile Continuum Gripping Robot with a Concealable Gripper.

Continuum robots with their inherent compliance provide the potential for crossing narrow unstructured workspace and safely grasping various objects. However, the display gripper increases the size of the robots, and therefore, it tends to get stuck in constrained environments. This paper proposes a versatile continuum grasping robot (CGR) with a concealable gripper. The CGR can capture large objects with respect to the robot's scale using the continuum manipulator and can grasp various objects using the end concealable gripper especially in narrow and unstructured workspaces. To perform the cooperative operation of the concealable gripper and the continuum manipulator, a global kinematic model based on screw theory and a motion planning approach referred to as "multi-node synergy method" for the CGR are presented. The simulation and experimental results show that objects of different shapes and sizes can be captured by the same CGR even in complex and narrow environments. Finally, in the future, the CGR is expected to serve for satellite capture in harsh space environments such as high vacuum, strong radiation, and extreme temperatures.

Equidistant Tool Path and Cartesian Trajectory Planning for Robotic Machining of Curved Freeform Surfaces

This article proposes an equidistant tool path planning strategy on curved freeform surfaces with the focus on robotic machining tasks. The strategy is based on the arc-length parameterization of the surface and can be considered as a variant of the iso-parametric path planning. This method allows us to directly consider a given Cartesian boundary in the parameter domain. Using an inverse interpolation scheme of the parameterization with cubic splines, the path planned in arc-length coordinates is mapped back in Cartesian coordinates. The equidistance property is also satisfied for larger path intervals and does not depend on the local curvature of the surface. The proposed trajectory planner ensures a constant velocity along the planned path on the freeform surface while limiting the maximum centripetal acceleration. However, general velocity profiles can be included depending on the actual machining application. Exploiting the differential geometric properties of the path and surface allows us to directly determine the orientation and angular velocity of the end-effector along the planned trajectory. The proposed methods are demonstrated with a robotic manipulator on a real curved freeform surface. Note to Practitioners—Robotic manipulators and five-axis computerized numerical control (CNC) machines provide high flexibility for machining processes on curved freeform surfaces, for example, polishing or grinding. For these applications, it is often desired that the distance between two subsequent machining paths is independent of the local geometry and surface curvature. This article proposes a novel method to plan equidistant coverage paths on a curved freeform surface. Therefore, we develop a transformation between the 3-D Cartesian coordinates and the 2-D parameters based on the arc-lengths along the surface. The geometry is given by CAD data or a 3-D scan of the part and is directly processed, making our approach particularly feasible for both large to small batch sizes and even individualized products. To cover an arbitrary area with parallel paths, its boundary—given in Cartesian coordinates—is transformed into arc-length parameters. The coverage path is planned in this parameter space, consisting of parallel, equidistant lines with interconnection paths. The path is transformed back in Cartesian coordinates using an inverse transformation. We plan the motion of the tool along this path, satisfying a desired feed rate depending on the actual machining application. The tool is slowed down when the maximum centripetal acceleration is reached. Considering the geometry of the path and the surface, we can also plan the tool’s orientation and its angular velocity during the manufacturing task. We demonstrate the path and motion planning approach on an experimental setup with a robotic manipulator.

Path-Tree Optimization in Discrete Partially Observable Environments Using Rapidly-Exploring Belief-Space Graphs

Robots often need to solve path planning problems where essential and discrete aspects of the environment are partially observable. This introduces a multi-modality, where the robot must be able to observe and infer the state of its environment. To tackle this problem, we introduce the Path-Tree Optimization (PTO) algorithm which plans a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">path-tree</i> in belief-space. A path-tree is a tree-like motion with branching points where the robot receives an observation leading to a belief-state update. The robot takes different branches depending on the observation received. The algorithm assumes a deterministic observation model and is composed of three main steps. First, a rapidly-exploring random graph (RRG) on the state space is grown. Second, the RRG is expanded to a belief-space graph by querying the observation model. In a third step, dynamic programming is performed on the belief-space graph to extract a path-tree. The resulting path-tree combines exploration with exploitation i.e. it balances the need for gaining knowledge about the environment with the need for reaching the goal. We demonstrate the algorithm capabilities on navigation and mobile manipulation tasks, and show its advantage over a baseline using a task and motion planning approach (TAMP) both in terms of optimality and runtime.

E 3 MoP: Efficient Motion Planning Based on Heuristic-Guided Motion Primitives Pruning and Path Optimization With Sparse-Banded Structure

To solve the autonomous navigation problem in complex environments, an efficient motion planning approach is newly presented in this paper. Considering the challenges from large-scale, partially unknown complex environments, a three-layer motion planning framework is elaborately designed, including global path planning, local path optimization, and time-optimal velocity planning. Compared with existing approaches, the novelty of this work is twofold: 1) a novel heuristic-guided pruning strategy of motion primitives is proposed and fully integrated into the state lattice-based global path planner to further improve the computational efficiency of graph search, and 2) a new soft-constrained local path optimization approach is proposed, wherein the sparse-banded system structure of the underlying optimization problem is fully exploited to efficiently solve the problem. We validate the safety, smoothness, flexibility, and efficiency of our approach in various complex simulation scenarios and challenging real-world tasks. It is shown that the computational efficiency is improved by 66.21% in the global planning stage and the motion efficiency of the robot is improved by 22.87% compared with the recent quintic Bézier curve-based state space sampling approach. We name the proposed motion planning framework E <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathbf {^{3}} $ </tex-math></inline-formula> MoP, where the number 3 not only means our approach is a three-layer framework but also means the proposed approach is efficient in three stages. Note to Practitioners—This paper is motivated by the challenges of motion planning problems of mobile robots. A three-layer motion planning framework is proposed by combining global path planning, local path optimization, and time-optimal velocity planning. For mobile robot navigation applications in semi-structured environments, optimization-based local planners are recommended. Extensive simulation and experimental results show the effectiveness of the proposed motion planning framework. However, due to the non-convexity of the path optimization formulation, the proposed local planner may get stuck in local optima. In future research, we will concentrate on extending the proposed local path optimization approach with the theory of homology classes to maintain several homotopically distinct local paths and seek global optima.

Motion planning for unmanned surface vehicle based on a maneuverability mathematical model

To address the issue that the path generated by the conventional path planning methods cannot match the maneuverability of an unmanned surface vehicle (USV), a motion planning approach has been proposed based on the maneuverability mathematical model of the USV (MA* algorithm). This method predicts the USV's motion trajectories using a maneuverability mathematical model of the USV. The state of the search space can be formed in accordance with the positions and directions that the projected trajectories can reach. In conjunction with the improved collision avoidance rules and cost function, the USV can plan a practical motion route that matches its actual maneuverability. The experimental results demonstrate that the path planned by the MA* algorithm not only entirely avoids obstacles, but also meets the maneuverability requirements of USV. This method combines the discrete search space with the hydrodynamic model to assure the continuity of the motion states during path planning for USV.

Walking is like slithering: A unifying, data-driven view of locomotion

Legged movement is ubiquitous in nature and of increasing interest for robotics. Most legged animals routinely encounter foot slipping, yet detailed modeling of multiple contacts with slipping exceeds current simulation capacity. Here we present a principle that unifies multilegged walking (including that involving slipping) with slithering and Stokesian (low Reynolds number) swimming. We generated data-driven principally kinematic models of locomotion for walking in low-slip animals (Argentine ant, 4.7% slip ratio of slipping to total motion) and for high-slip robotic systems (BigANT hexapod, slip ratio 12 to 22%; Multipod robots ranging from 6 to 12 legs, slip ratio 40 to 100%). We found that principally kinematic models could explain much of the variability in body velocity and turning rate using body shape and could predict walking behaviors outside the training data. Most remarkably, walking was principally kinematic irrespective of leg number, foot slipping, and turning rate. We find that grounded walking, with or without slipping, is governed by principally kinematic equations of motion, functionally similar to frictional swimming and slithering. Geometric mechanics thus leads to a unified model for swimming, slithering, and walking. Such commonality may shed light on the evolutionary origins of animal locomotion control and offer new approaches for robotic locomotion and motion planning.

Receding-Horizon Reinforcement Learning Approach for Kinodynamic Motion Planning of Autonomous Vehicles

Kinodynamic motion planning is critical for autonomous vehicles with high maneuverability in dynamic environments. However, obtaining near-optimal motion planning solutions with low computational costs and inaccurate prior model information is challenging. To address this issue, this paper proposes a receding-horizon reinforcement learning approach for kinodynamic motion planning (RHRL-KDP) of autonomous vehicles in the presence of inaccurate dynamics information and moving obstacles. Specifically, a receding-horizon actor-critic reinforcement learning algorithm is presented, resulting in a neural network-based planning strategy that can be learned both offline and online. A neural network-based model is built and learned online to approximate the modeling uncertainty of the prior nominal model in order to improve planning performance. Furthermore, active collision avoidance in dynamic environments is realized by constructing safety-related terms in actor and critic networks using potential fields. In theory, the uniformly ultimate boundedness property of the modeling uncertainty’s approximation error is proven, and the convergence of the proposed RHRL-KDP is analyzed. Simulation tests show that our approach outperforms the previously developed motion planners based on model predictive control (MPC), safe RL, and RRT <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${^\star }$</tex-math></inline-formula> in terms of planning performance. Furthermore, in both online and offline learning scenarios, RHRL-KDP outperforms MPC and RRT <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^{\star }$</tex-math></inline-formula> in terms of computational efficiency.

Appointed-Time and Attack-Free Bipartite Synchronization of Generic Linear Multiagent Systems Over Directed Switching Networks

This article derives a solution to the appointed-time and attack-free bipartite synchronization problem for generic linear multiagent systems over directed switching networks accommodating cooperative and antagonistic interactions. Herein, appointed-time means that the settling time is independent of any parameters and is preappointed in advance. Attack-free requires that the communication channel is protected, which means that no state and observer information exchange is allowed, and only measured relative output information is available when designing protocols. Firstly, by virtue of Pontryagin’s maximum principle, a distributed appointed-time state-feedback protocol is developed for directed switching networks, which tackles the appointed-time bipartite synchronization problem from a motion-planning approach based on sampling measurements, but takes the risk of facing cyber attacks on information exchange channels. Then, to be free of network attacks, a sampling-based attack-free observer using relative output information is designed to observe bipartite synchronization errors at an appointed time. By combining the appointed-time state-feedback protocol with the sampling-based attack-free observer, an attack-free output-feedback protocol is developed without requiring the state or control input information. The attack-free appointed-time bipartite synchronization problem is thus resolved. Both the state-feedback and attack-free protocols show the ability of disturbance rejection to the nonidentical bounded disturbances. To our knowledge, it is the first time to solve the appointed-time and attack-free bipartite synchronization problem for generic linear multiagents based on state- and output-feedback information, respectively. Finally, simulations verify the effectiveness of the two protocols.

A circle grid-based approach for obstacle avoidance motion planning of unmanned surface vehicles

Aiming at an obstacle avoidance problem with dynamic constraints for Unmanned Surface Vehicle (USV), a method based on Circle Grid Trajectory Cell (CGTC) is proposed. Firstly, the ship model and standardization rules are constructed to develop and constrain the trajectory, respectively. Secondly, by analyzing the properties of the circle grid, the circle grid tree is produced to guide the motion of the USV. Then, the kinematics and dynamics of the USV are considered through the on-line trajectory generator by designing a relational function that links the rudder angle, the heading angle, and the central angle of the circle grid. Finally, obstacle avoidance is achieved by utilizing the on-line trajectory generator to choose a safe, smooth, and efficient path for the USV. The experimental results indicate that the proposed method can avoid both static and dynamic obstacles, showing better performance in terms of distance cost and steering cost comparing with the related methods, and our method only takes 50% steering cost of the grid-based method; the collision avoidance path not only conforms to the USV dynamic characteristics but also provides a reference of steering command.

Specified-time group consensus for general linear systems over directed graphs

This paper studies the distributed specified-time group consensus control with hard settling-time constraint and milder communication topology constraint. To this end, we propose two distributed control schemes by employing a motion planning approach for the single- and double-integrator systems. Compared with the most existing works over undirected communication topologies, the underlying topology of each group is required to be directed graphs in our proposed distributed controllers. Furthermore, the root vertex of one group is allowed to belong to the other group. The convergence analysis is performed via the algebraic graph theory and matrix theory. The results show that the agents in the same group can reach consensus within any prespecified settling-time instead of a conservative upper bound of the settling-time. Moreover, the designed specified-time group consensus protocols do not require continuous information exchange. Finally, simulation results are provided to illustrate the effectiveness of the proposed methods.

Conflict-Directed Diverse Planning for Logic-Geometric Programming

Robots operating in the real world must combine task planning for reasoning about what to do with motion planning for reasoning about how to do it -- this is known as task and motion planning. One promising approach for task and motion planning is Logic Geometric Programming (LGP) which integrates a logical layer and a geometric layer in an optimization formulation. The logical layer describes feasible high-level actions at an abstract symbolic level, while the geometric layer uses continuous optimization methods to reason about motion trajectories with geometric constraints. In this paper we propose a new approach for solving task and motion planning problems in the LGP formulation, that leverages state-of-the-art diverse planning at the logical layer to explore the space of feasible logical plans, and minimizes the number of optimization problems to be solved on the continuous geometric layer. To this end, geometric infeasibility is fed back into planning by identifying prefix conflicts and incorporating this back into the planner through a novel multi-prefix forbidding compilation. We further leverage diverse planning with a new novelty criteria for selecting candidate plans based on the prefix novelty, and a metareasoning approach which attempts to extract only useful conflicts by leveraging the information that is gathered in the course of solving the given problem.

Sine Resistance Network-Based Motion Planning Approach for Autonomous Electric Vehicles in Dynamic Environments

This article proposes a motion planning approach for autonomous electric vehicles to generate an appropriate planned path according to the time-varying surrounding information. This approach utilizes the proposed novel sine resistance network to mesh the road with the aim of improving the planned path smoothness, which has the capability of generating a continuous-curvature planned path that contributes to tracking and reducing the jerkiness. Meanwhile, considering that the classical artificial potential field (APF) method is only suitable for the static scenarios, a bias oval APF is constructed to predict the change of relative distance between the ego vehicle and each obstacle by taking the speed information into account. The proposed planning approach can ensure that the planned path is collision-free in dynamic environments and the generated path is smooth simultaneously. Cosimulation results in CarSim and MATLAB/Simulink are provided to prove the advantage and feasibility of the proposed motion planning approach for autonomous electric vehicles.

Constrained Motion Planning of 7-DOF Space Manipulator via Deep Reinforcement Learning Combined with Artificial Potential Field

During the on-orbit operation task of the space manipulator, some specific scenarios require strict constraints on both the position and orientation of the end-effector, such as refueling and auxiliary docking. To this end, a novel motion planning approach for a space manipulator is proposed in this paper. Firstly, a kinematic model of the 7-DOF free-floating space manipulator is established by introducing the generalized Jacobian matrix. On this basis, a planning approach is proposed to realize the motion planning of the 7-DOF free-floating space manipulator. Considering that the on-orbit environment is dynamical, the robustness of the motion planning approach is required, thus the deep reinforcement learning algorithm is introduced to design the motion planning approach. Meanwhile, the deep reinforcement learning algorithm is combined with artificial potential field to improve the convergence. Besides, the self-collision avoidance constraint is considered during planning to ensure the operational security. Finally, comparative simulations are conducted to demonstrate the performance of the proposed planning method.

Using Spherical Harmonics for Navigating in Dynamic and Uncertain Environments

In this paper, we present a novel approach for local motion planning in an unknown environment populated by static and dynamic obstacles. A key component of our planner is the use of harmonic basis functions defined over the unit sphere, known as spherical harmonics (SH), to represent a collision-free space near an agent. In contrast with our previous approach, which only applies to unknown static environments, the approach proposed herein handles dynamic obstacles as well. It is done by efficiently calculating the coefficients of a spherical harmonics approximation of the local collision-free space for each step of a given planning horizon. Our method for approximating the collision-free space with spherical harmonics allows us to plan trajectories in challenging environments (e.g., planning through narrow passages) where other methods for generating search-spaces fail. To accurately approximate the collision-free space for future time steps along a planning horizon, we use a Kalman Filter (KF) to propagate the measured point cloud through time. Our use of the KF allows us to better approximate obstacles moving in space in comparison to inaccurate constant obstacle velocity assumptions used by other methods. Finally, we show the effectiveness of our proposed trajectory planner using two different non-trivial scenarios.

A Data-Driven Method Towards Minimizing Collision Severity for Highly Automated Vehicles

The deployment of autonomous vehicles on public roads calls for the development of methods that are reliably able to mitigate injury severity in case of unavoidable collisions. This study proposes a data-driven motion planning method capable of minimizing injury severity for vehicle occupants in unavoidable collisions. The method is based on establishing a metric that models the relationship between impact location and injury severity using real accident data, and subsequently including it in the cost function of a motion planning framework. The vehicle dynamics and associated constraints are considered through a precomputed trajectory library, which is generated by solving an optimal control problem. This allows for efficient computation as well as an accurate representation of the vehicle. The proposed motion planning approach is evaluated by simulation, and it is shown that the trajectory associated with the minimum cost mitigates the collision severity for occupants of passenger vehicles involved in the collision.

An efficient motion planning based on grid map: Predicted Trajectory Approach with global path guiding

This paper presents a Predicted Trajectory Approach (PTA) for global motion planning of an underactuated unmanned surface vehicle (USV). Different from the conventional path planning algorithms which mostly focus on the shortest, safest or smoothest paths, PTA takes all the dynamic constraints of the USV into account, and finds the global trajectory that can be traced precisely via its own maneuvering system. In present strategy, the predicted trajectories produced by the mathematical model of the USV are decomposed into a series of waypoints on grid map. Then an efficient trajectory can be found for the USV by performing the A* search method. To improve the search efficiency and accuracy, the PTA is enhanced with global path guiding (GPTA). When searching for feasible trajectories, GPTA can employ the global path obtained by Theta* to accurately estimate the heuristic cost of the objective function, rather than using the Euclidean distance directly as PTA does. Numerical simulations in various scenarios are conducted to compare the performance of the PTA, GPTA, Trajectory Units (TUs) and hybrid path planning algorithm combining global and local path planning (HGL). The results demonstrate that GPTA has higher safety and navigation efficiency for motion planning of the underactuated USV.

E-Graphs: Bootstrapping Planning with Experience Graphs

In this paper, we develop an online motion planning approach which learns from its planning episodes (experiences) a graph, an Experience Graph. On the theoretical side, we show that planning with Experience graphs is complete and provides bounds on suboptimality with respect to the graph that represents the original planning problem. Experimentally, we show in simulations and on a physical robot that our approach is particularly suitable for higher-dimensional motion planning tasks such as planning for two armed mobile manipulation.

Optimal Motion Planning in GPS-Denied Environments Using Nonlinear Model Predictive Horizon.

Navigating robotic systems autonomously through unknown, dynamic and GPS-denied environments is a challenging task. One requirement of this is a path planner which provides safe trajectories in real-world conditions such as nonlinear vehicle dynamics, real-time computation requirements, complex 3D environments, and moving obstacles. This paper presents a methodological motion planning approach which integrates a novel local path planning approach with a graph-based planner to enable an autonomous vehicle (here a drone) to navigate through GPS-denied subterranean environments. The local path planning approach is based on a recently proposed method by the authors called Nonlinear Model Predictive Horizon (NMPH). The NMPH formulation employs a copy of the plant dynamics model (here a nonlinear system model of the drone) plus a feedback linearization control law to generate feasible, optimal, smooth and collision-free paths while respecting the dynamics of the vehicle, supporting dynamic obstacles and operating in real time. This design is augmented with computationally efficient algorithms for global path planning and dynamic obstacle mapping and avoidance. The overall design is tested in several simulations and a preliminary real flight test in unexplored GPS-denied environments to demonstrate its capabilities and evaluate its performance.

Enhancing kinematic accuracy of redundant wheeled mobile manipulators via adaptive motion planning

An increasing demand for wheeled mobile manipulators (WMMs) in fields that require high precision tasks has introduced new requirements as far as their kinematic accuracy. A WMM consists of a manipulator mounted on a mobile base. This configuration usually makes the WMM a redundant robotic system. One limiting factor is that the kinematic accuracy of the mobile base is often lower than that of the manipulator because of modeling errors and disturbances such as slippage. Thus, it makes sense to distribute more of a given set of motion requirements for the entire mobile manipulator to the manipulator when possible — this is usually done using a weighting matrix that sums the mobile base motion and the manipulator motion. In this paper, considering a redundant WMM, a novel adaptive motion planning method is proposed as a secondary objective in the null space of the primary objective (improvement of the WMM’s kinematic accuracy) for the WMM. Also, a tertiary objective to move the manipulator away from its singularity is proposed. This objective is activated if the secondary objective is feasible and the WMM still has remaining redundant degrees of freedom. The proposed method is implemented at the acceleration level to circumvent the discontinuity of the commanded joint velocity due to the adaptive motion planning algorithm. The advantages and effectiveness of the proposed approach are demonstrated with a traditional motion planning approach through experiments.