Trajectory Planning Approach Research Articles

Collision-free trajectory planning for robotic assembly of lightweight structures

This research presents a trajectory planning approach for robotic assembly of lightweight structures for COVID-19 healthcare facilities. The prefabricated building components of COVID-19 healthcare facilities have nonnegligible volume, where the crux of the scientific question lies in how to incorporate geometry-based collision checks in trajectory planning. This research developed an algorithm that refines the RRT* (Rapidly-exploring Random Tree-Star) algorithm to enable the detour of a planned trajectory based on the geometry of prefabricated components to prevent collisions. Testing of the approach reveals that it has satisfactory collision-avoiding and trajectory-smoothing performance, and is time- and labour-saving compared with the traditional human method. The satisfactory results highlight the practical implication of this research, where robots can replace human labour and contribute to the mitigation of COVID-19 spread on construction sites. The subsequent research will investigate the use of a collaborative robot to screw bolt connections after the components are assembled at locations.

Human-Machine Cooperative Trajectory Planning and Tracking for Safe Automated Driving

This paper investigates a human-machine cooperative trajectory planning and tracking control approach for automated vehicles. The proposed method is developed based on a novel algorithm of cooperative human-machine rapidly-exploring random (HM-RRT) for path planning, together with the risk assessment of driver behavior. First, the driver’s behaviour is assessed according to the information of the predicted vehicle trajectory, the identified safe driving area and the driving risks evaluated in both lateral and longitudinal directions. Based on the driver’s expected driving task, when driving risks are identified by real-time assessment, then the human-machine cooperation is activated during trajectory planning. By HM-RRT, the newly developed safety assurance mechanism for path planning, the cooperative trajectory is then generated, which incorporates the driver’s desire and actions and automation’s corrective actions, to ensure the safety, stability and smoothness of the human-vehicle system. The simulation and experimental results show that the proposed HM-RRT algorithm can effectively improve the convergence rate and reduce the computation load, comparing to the conventional method. Beyond this, the proposed human-machine cooperation approach is able to simultaneously ensure the safety, stability and smoothness of the vehicle and largely reduce human-machine conflicts in real-time applications, demonstrating its feasibility and effectiveness.

A Fast and Close-to-Optimal Receding Horizon Control for Trajectory Generation in Dynamic Environments

This paper presents a new approach for the optimal trajectory planning of nonlinear systems in a dynamic environment. Given the start and end goals with an objective function, the problem is to find an optimal trajectory from start to end that minimizes the objective while taking into account the changes in the environment. One of the main challenges here is that the optimal control sequence needs to be computed in a limited amount of time and needs to be adapted on-the-fly. The control method presented in this work has two stages: the first-order gradient algorithm is used at the beginning to compute an initial guess of the control sequence that satisfies the constraints but is not yet optimal; then, sequential action control is used to optimize only the portion of the control sequence that will be applied on the system in the next iteration. This helps to reduce the computational effort while still being optimal with regard to the objective; thus, the proposed approach is more applicable for online computation as well as dealing with dynamic environments. We also show that under mild conditions, the proposed controller is asymptotically stable. Different simulated results demonstrate the capability of the controller in terms of solving various tracking problems for different systems under the existence of dynamic obstacles. The proposed method is also compared to the related indirect optimal control approach and sequential action control in terms of cost and computation time to evaluate the improvement of the proposed method.

Toward a Data-Driven Template Model for Quadrupedal Locomotion

This work investigates a data-driven template model for trajectory planning of dynamic quadrupedal robots. Many state-of-the-art approaches involve using a reduced-order model, primarily due to computational tractability. The spirit of the trajectory planning approach in this work draws on recent advancements in the area of behavioral systems theory. Here, we aim to capitalize on the knowledge of well-known template models to construct a data-driven model, enabling us to obtain an information rich reduced-order model. In particular, this work considers input-output states similar to that of the single rigid body model and proceeds to develop a data-driven representation of the system, which is then used in a predictive control framework to plan a trajectory for quadrupeds. The optimal trajectory is passed to a low-level and nonlinear model-based controller to be tracked. Preliminary experimental results are provided to establish the efficacy of this hierarchical control approach for trotting and walking gaits of a high-dimensional quadrupedal robot on unknown terrains and in the presence of disturbances.

Smooth and proximate time-optimal trajectory planning of robotic manipulators

The simultaneous achievement of high accuracy and productivity in robotics has been extensively investigated using the trajectory planning approach. We propose a smooth and proximate time-optimal trajectory planning method. First, we generated the velocity limit curve by expressing joint torque and joint velocity constraints as a function of the path coordinate. Then, we calculated the time-optimal trajectory using a dynamic programming technique and fitted the smooth cubic spline. The smoothing factor of the cubic spline curve was optimized by applying a binary recursive. The proposed method can guarantee the continuity and smoothness of joint torque. The simulation results showed that the proposed method can reduce joint-jerk and improve the tracking accuracy of the controller.

Optimal Model-Based Trajectory Planning With Static Polygonal Constraints

The main contribution of this paper is a novel method for planning globally optimal trajectories for dynamical systems subject to polygonal constraints. The proposed method is a hybrid trajectory planning approach, which combines graph search, i.e. a discrete roadmap method, with convex optimization, i.e. a complete path method. Contrary to past approaches, which have focused on using simple obstacle approximations, or sub-optimal spatial discretizations, our approach is able to use the exact geometry of polygonal constraints in order to plan optimal trajectories. The performance and flexibility of the proposed method is evaluated via simulations by planning distance-optimal trajectories for a Dubins car model, as well as time-, distance- and energy-optimal trajectories for a marine vehicle.

Predictive-ECMS based degradation protective control strategy for a fuel cell hybrid electric vehicle considering uphill condition

The fuel economy and powertrain durability of fuel cell hybrid electrical vehicles (FCHEV) are sensitively affected by the load changing brought by the traffic, and most of the current power management strategies (PMS) are devoted to reducing the cost of hydrogen consumption and degradation. However, the variation in terrain information brings more severe load fluctuation, which is scarcely considered among the currently studied PMS. Since the terrain information tends to be predictable with the development of the intelligent transportation system, this paper develops a hierarchical PMS which integrates the terrain information. Firstly, a predictive equivalent consumption minimizes strategy of the inner layer is developed for providing power distribution decisions. Then, a fuel cell longevity-conscious strategy which devises a dynamic constraint on reference fuel cell output power is devised in the external layer. Finally, a heuristic battery SoC trajectory planning approach is used to guide the operation mode of the powertrain on the ramp, and the influence of the signal error is fully discussed. The effectiveness of this study is validated by the hardware-in-loop experiment, validation results show the strategy can improve 4.3% fuel economy, the erosion of the durability of the powertrain can be mitigated while the uphill condition.

Time-optimal trajectory generation in joint space for 6R industrial serial robots using Cuckoo search algorithm

The trajectory planning problem in industrial robotic applications has recently attracted the great attention of many researchers. In this paper, an optimal trajectory planning approach is proposed based on optimal time by utilizing the interpolation spline method. The method including a combination of cubic spline and 7th order polynomial is used for generating the trajectory in joint space for robot manipulators. Cuckoo Search (CS) optimization algorithm is chosen to optimize the joint trajectories based on objective, including minimizing total traveling time along the whole trajectory. The spline method has been applied to the PUMA robot for optimizing the joint trajectories with the CS algorithm based on the objective. With the trajectory planning method, the joint velocities, accelerations, and jerks along the whole trajectory optimized by CS meet the requirements of the kinematic constraints in the case of the objective. Simulation results validated that the used trajectory planning method based on the proposed algorithm is very effective in comparison with the same methods based on the algorithms proposed by earlier authors. Keywords: CS; industrial robots; interpolation; spline methods; trajectory planning.

Trajectory Planning for Hybrid Unmanned Aerial Underwater Vehicles with Smooth Media Transition

In the last decade, a great effort has been employed in the study of Hybrid Unmanned Aerial Underwater Vehicles, robots that can easily fly and dive into the water with different levels of mechanical adaptation. However, most of this literature is concentrated on physical design, practical issues of construction, and, more recently, low-level control strategies. Little has been done in the context of high-level intelligence, such as motion planning and interactions with the real world. Therefore, we proposed in this paper a trajectory planning approach that allows collision avoidance against unknown obstacles and smooth transitions between aerial and aquatic media. Our method is based on a variant of the classic Rapidly-exploring Random Tree, whose main advantages are the capability to deal with obstacles, complex nonlinear dynamics, model uncertainties, and external disturbances. The approach uses the dynamic model of the HyDrone, a hybrid vehicle proposed with high underwater performance, but we believe it can be easily generalized to other types of aerial/aquatic platforms. In the experimental section, we present simulated results in environments filled with obstacles, where the robot is commanded to perform different media movements, demonstrating the applicability of our strategy.

Multi-objective Trajectory Planning Method based on the Improved Elitist Non-dominated Sorting Genetic Algorithm

Robot manipulators perform a point-point task under kinematic and dynamic constraints. Due to multi-degree-of-freedom coupling characteristics, it is difficult to find a better desired trajectory. In this paper, a multi-objective trajectory planning approach based on an improved elitist non-dominated sorting genetic algorithm (INSGA-II) is proposed. Trajectory function is planned with a new composite polynomial that by combining of quintic polynomials with cubic Bezier curves. Then, an INSGA-II, by introducing three genetic operators: ranking group selection (RGS), direction-based crossover (DBX) and adaptive precision-controllable mutation (APCM), is developed to optimize travelling time and torque fluctuation. Inverted generational distance, hypervolume and optimizer overhead are selected to evaluate the convergence, diversity and computational effort of algorithms. The optimal solution is determined via fuzzy comprehensive evaluation to obtain the optimal trajectory. Taking a serial-parallel hybrid manipulator as instance, the velocity and acceleration profiles obtained using this composite polynomial are compared with those obtained using a quintic B-spline method. The effectiveness and practicability of the proposed method are verified by simulation results. This research proposes a trajectory optimization method which can offer a better solution with efficiency and stability for a point-to-point task of robot manipulators.

Integrating Algorithmic Sampling-Based Motion Planning with Learning in Autonomous Driving

Sampling-based motion planning (SBMP) is a major algorithmic trajectory planning approach in autonomous driving given its high efficiency and outstanding performance in practice. However, driving safety still calls for further refinement of SBMP. In this article we organically integrate algorithmic motion planning with learning models to improve SBMP in highway traffic scenarios from the following two perspectives. First, given the number of points to be sampled, we develop a new model to sample “important” points for SBMP by predicting the intention of surrounding vehicles and learning the distribution of human drivers’ trajectory. Second, we empirically study the relationship between the number of sample points and the environment, which is largely ignored in conventional SBMP. Then, we provide a guideline to select the appropriate number of points to be sampled under different scenarios to guarantee efficiency. The simulation experiments are conducted based on the vehicle trajectory dataset NGSIM. The results show that the proposed sampling strategy outperforms existing sampling strategies in terms of the computing time, traveling time, and smoothness of the trajectory.

Eco-driving Trajectory Planning of a Heterogeneous Platoon in Urban Environments⋆

Given the increasing popularity and demand for connected and autonomous vehicles (CAVs), Eco-driving and platooning in highways and urban areas to increase the efficiency of the traffic system is becoming a possibility. This paper presents an Eco-driving trajectory planning approach for a platoon of heterogeneous electric vehicles (EVs) in urban environments. The proposed control strategy for the platoon considers energy consumption, mobility and passenger comfort, with which vehicles may pass signalized intersections with no stops. For a given urban route, first, the platoon's leader vehicle employs dynamic programming (DP) to plan a trajectory for the anticipated path with the aim of balancing energy consumption, mobility and passenger comfort. Then, other following CAVs in the platoon either follow the preceding vehicles, using a PID-based cooperative adaptive cruise control, or plan their own trajectory by checking whether they can pass the next intersection without stopping. Furthermore, a heavy vehicle that cannot efficiently follow a light-weight vehicle would instead employ the DP-based trajectory planner. The results of simulation studies demonstrate the efficacy of the proposed control strategy with which the platoon's energy consumption is shown to reduce while the mobility is not compromised.

Fault diagnosis for linear heterodirectional hyperbolic ODE–PDE systems using backstepping-based trajectory planning

This paper is concerned with the fault diagnosis problem for general linear heterodirectional hyperbolic ODE–PDE systems. A systematic solution is presented for additive time-varying actuator, process and sensor faults in the presence of disturbances. The faults and disturbances are represented by the solutions of finite-dimensional ODEs, which allow to take a large class of signals into account. For disturbances, that are only bounded, a threshold for secured fault diagnosis is derived. By applying integral transformations to the system an algebraic fault detection equation to detect faults in finite time is obtained. The corresponding integral kernels result from the realization of a finite-time transition between a non-equilibrium initial state and a vanishing final state of a hyperbolic ODE–PDE system. For this new challenging problem, a systematic trajectory planning approach is presented. In particular, this problem is facilitated by mapping the kernel equations into backstepping coordinates and tracing the solution of the transition problem back to a simple trajectory planning. The fault diagnosis for a 4 × 4 heterodirectional hyperbolic system coupled with a second order ODE demonstrates the results of the paper.

Optimization of tool orientation for improving the cleaning efficiency of offshore jacket-cleaning systems

Marine organisms grow on the jackets of an offshore oil platform, thereby affecting its service life and safety. Therefore, these marine organisms need to be cleaned regularly. Correspondingly, an underwater pipe cleaning system is urgently needed because the conventional manual cleaning is severely limited in underwater missions in terms of duration, depth, and safety. Autonomous underwater intervention robots can provide a longer duration or deeper working depth and allow fast deployment and operation in adverse environments. Hence, an underwater cleaning robot equipped with a six degrees of freedom electric manipulator is developed for marine biofouling stripping tasks. An automatic trajectory planning approach based on the hierarchical task control framework is proposed for efficient and delicate manipulation. In this control approach, we transformed the jet pistol orientation relative to the target surface into an optimization problem on the basis of uncomplicated constraints. Simulations and experimental trials are successively presented to show that the developed robot system provides a solution for a less execution time and robotize pipe-cleaning process.

Human-Machine Cooperative Trajectory Planning for Semi-Autonomous Driving Based on the Understanding of Behavioral Semantics

This paper presents a novel cooperative trajectory planning approach for semi-autonomous driving. The machine interacts with the driver at the decision level and the trajectory generation level. To minimize conflicts between the machine and the human, the trajectory planning problem is decomposed into a high-level behavior decision-making problem and a low-level trajectory planning problem. The approach infers the driver’s behavioral semantics according to the driving context and the driver’s input. The trajectories are generated based on the behavioral semantics and driver’s input. The feasibility of the proposed approach is validated by real vehicle experiments. The results prove that the proposed human–machine cooperative trajectory planning approach can successfully help the driver to avoid collisions while respecting the driver’s behavior.

An improved dynamic window approach for local trajectory planning in the environment with dense objects

The Dynamic Window Approach (DWA) has been one of the most popular solutions in local trajectory planning due to the advantages of movement fluency. However, the traditional DWA faces the challenge of low-efficiency in the case of local trajectory planning since the robot cannot perceive the density of the obstacle. In this paper, we propose an improved DWA to solve this problem. First, we use multi-sensor technology and new evaluation algorithms to enable the capability of density perception for the disorderly environment. Second, the evaluation factor related to the density change is introduced into the path evaluation function, which will facilitate the robot to perceive the distribution of dense objects in advance. Computer simulation and field experiments show that the efficiency of the improved DWA is increased by 25%. The improved DWA not only considers the original factors such as heading angle, but also introduces a density factor to evaluate the next path, so as to avoid entering dense areas in advance. It can be seen that the improved DWA has relatively stable speed and acceleration, and can avoid dense areas in advance, which can be widely used in robots running in dense environments.

An optimization-based approach for elasticity-aware trajectory planning of link-elastic manipulators

Elastic manipulators often result from lightweight construction or safety requirements in human–robot-collaboration scenarios. In many cases, vibration-damping becomes necessary to enable stable and precise operation, which imposes high demands on controllers. A fundamental challenge for link-elastic manipulators with general kinematics and no dedicated damping actuators is the potential inability of a joint to control the vibration of a link depending on the manipulator’s configuration. Numerous control concepts assume a sufficiently high ability to control vibrations by, for example, dedicated actuators or special kinematic structures. This work presents an online, optimization-based motion planning approach with three methods for maximizing this ability for link-elastic manipulators. The planning algorithm utilizes modified cost functions to incorporate the controllability of vibrations by prioritization and adaptive activation of competing objectives. The effectiveness of the approach is demonstrated on a real manipulator with 3 actuated DoFs and two elastic links in different disturbance scenarios. The results show that the amplitudes of vibrations caused by disturbances decay noticeably faster than with conventional motion planning.

Robust Tube-Based Model Predictive Control for Lane Change Maneuver of Tractor-Trailer Vehicles Based on a Polynomial Trajectory

This paper reports an effective quintic polynomial-based trajectory planning approach and a robust tube-based model predictive control (RTMPC) method for an underactuated tractor-trailer vehicle system during lane change maneuver. To begin with, a time-based quintic polynomial function is introduced for implementation of trajectory planning, which takes vehicle system safety, comfort, and traffic efficiency into account. After that, an RTMPC scheme, consisting of a nominal system-oriented model predictive controller and an ancillary feedback control law, is proposed to construct posture controller, such that favorable transient performances can be achieved for the trajectory tracking process. Lastly, the simulation results confirm that the proposed lane change trajectory planning and tracking control methods can effectively perform the lane change behaviors for tractor-trailer vehicles.

Social Trajectory Planning for Urban Autonomous Surface Vessels

In this article, we propose a trajectory planning algorithm that enables autonomous surface vessels to perform socially compliant navigation in a city's canal. The key idea behind the proposed algorithm is to adopt an optimal control formulation in which the deviation of movements of the autonomous vessel from nominal movements of human-operated vessels is penalized. Consequently, given a pair of origin and destination points, it finds vessel trajectories that resemble those of human-operated vessels. To formulate this, we adopt kernel density estimation (KDE) to build a nominal movement model of human-operated vessels from a prerecorded trajectory dataset, and use a Kullback-Leibler control cost to measure the deviation of the autonomous vessel's movements from the model. We establish an analogy between our trajectory planning approach and the maximum entropy inverse reinforcement learning (MaxEntIRL) approach to explain how our approach can learn the navigation behavior of human-operated vessels. On the other hand, we distinguish our approach from the MaxEntIRL approach in that it does not require well-defined bases, often referred to as features, to construct its cost function as required in many of inverse reinforcement learning approaches in the trajectory planning context. Through experiments using a dataset of vessel trajectories collected from the automatic identification system, we demonstrate that the trajectories generated by our approach resemble those of human-operated vessels and that using them for canal navigation is beneficial in reducing head-on encounters between vessels and improving navigation safety.

Optimum time-energy-jerk trajectory planning for serial robotic manipulators by reparameterized quintic NURBS curves

This paper deals with the trajectory planning for serial robotic manipulators passing through key points by minimizing execution time, energy consumption and joint jerks. Quintic NURBS curves are adopted to fit the trajectory, of which the trajectory is reparameterized with respect to time for generation of geometric path and motion laws, aiming at continuity of the robot velocity, acceleration and jerk. A trajectory planning approach for optimum robot performance is proposed by solving a multi-objective optimization problem to attain optimal curve parameters and distributed execution time along curve segments simultaneously. The proposed technique of trajectory planning is numerically illustrated with a robotic arm and evaluated by experimental measurements. The comparison of total execution time and joint dynamics with/without variables optimization shows the effectiveness of the proposed approach.