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With the development of robotics, there are growing needs for real time motion planning. However, due to obstacles in the environment, the planning problem is highly non-convex, which makes it difficult to achieve real time computation using existing non-convex optimization algorithms. This paper introduces the convex feasible set algorithm (CFS) w...
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... As shown in Figure 5, the safe region that satisfies the CAV's safety requirements is nonconvex. Therefore, we project the non-convex state feasibility region onto a convex control input set using the attractive domain principle [36]. To be safe at all times, the driving safe states set X ( (t )) must keep the same characteristic with respect to time, that is, R(t ) ⩽ max , ∀t ⩾ t 0 . ...
The rapid development of vehicle‐to‐everything (V2X) communication technologies significantly promotes the revolution of intelligent transportation systems. V2X communication is expected to play a critical role in enhancing the safety and efficiency of connected and automated vehicles (CAVs), especially for mixed traffic scenarios. Additionally, the computational and storage capabilities of roadside units (RSUs) will be harnessed to effectively enhance the motion planning and control performance of CAVs within the constraints of limited on‐board computational resources. Thus, a V2X assisted co‐design of motion planning and control algorithm for CAVs to improve their situational awareness and computational efficiency is proposed. Under this architecture, a pre‐planning algorithm is proposed first to utilize the computational and storage capabilities of RSUs and generate feasible trajectories for different driving tasks. By analysing the relationship between driving risk index and motion planning performance, an online‐planning algorithm is derived to modify the pre‐planned trajectories in real‐time with static or dynamic obstacles. Furthermore, the lateral and longitudinal control of the vehicle using the Frenet coordinate system is decoupled. The lateral control employs an offline linear quadratic regulator (LQR) from RSUs to control the steering angle of the vehicle. The longitudinal control employs a dual‐loop PID to control the throttle opening of the vehicle. The performance of the proposed framework is evaluated and demonstrated by a Carsim‐Prescan simulation study in different mixed traffic scenarios. Compared with conventional methods, the proposed method improves the computational efficiency by 23% and reduces the collision rate by 13%.
... Motion planning for AVs is a typical nonconvex three-dimensional (3D, station, lateral, and time) optimization with complex constraints. There are two types of methods for solving the optimization problem: direct 3D optimization methods (e.g., SQP algorithm [26], CFS algorithm [27], constrained iterative LQR algorithm [28]) and path-speed decoupled methods (e.g., [29]). Direct methods perform optimization in spatiotemporal state space, while decoupled methods transform the original 3D optimization problem into two 2D optimization problems (path optimization and speed optimization) and solve them successively. ...
Humanlike driving is significant in improving the safety and comfort of automated vehicles. This paper proposes a personalized motion planning method with driver characteristics in longitudinal and lateral directions for highway automated driving. The motion planning is decoupled into path optimization and speed optimization under the framework of the Baidu Apollo EM motion planner. For modeling driver behavior in the longitudinal direction, a car-following model is developed and integrated into the speed optimizer based on a weight ratio hypothesis model of the objective functional, whose parameters are obtained by Bayesian optimization and leave-one-out cross validation using the driving data. For modeling driver behavior in the lateral direction, a Bayesian network (BN), which maps the physical states of the ego vehicle and surrounding vehicles and the lateral intentions of the surrounding vehicles to the driver’s lateral intentions, is built in an efficient and lightweight way using driving data. Further, a personalized reference trajectory decider is developed based on the BN, considering traffic regulations, the driver’s preference, and the costs of the trajectories. According to the actual traffic scenarios in the driving data, a simulation is constructed, and the results validate the human likeness of the proposed motion planning method.
... On the other hand, Chen et al. [26] introduced a safe corridor algorithm, designed to generate collision-free trajectories for autonomous quadrotor flight in cluttered environments. Another noteworthy contribution comes from Liu et al., who proposed the convex feasible set algorithm (CFS) [27], capable of solving nonconvex optimization problems with convex costs and nonconvex constraints, with a primary focus on achieving real-time computation in motion planning for robotics. In addition, Li et al. introduced safe travel corridors (STCs) [28] to simplify collision avoidance constraints in automatic parking maneuver planning, thereby enhancing efficiency and robustness in complex environments. ...
Due to the limitation of space rover onboard computing resources and energy, there is an urgent need for high-quality drive trajectories in complex environments, which can be provided by delicately designed motion optimization methods. The nonconvexity of the collision avoidance constraints poses a significant challenge to the optimization-based motion planning of nonholonomic vehicles, especially in unstructured cluttered environments. In this paper, a novel obstacle decomposition approach, which swiftly decomposes nonconvex obstacles into their constituent convex substructures while concurrently minimizing the proliferation of resultant subobstacles, is proposed. A safe convex corridor construction method is introduced to formulate the collision avoidance constraints. The numerical approximation methods are applied to transfer the resulting continuous motion optimization problem to a nonlinear programming problem (NLP). Simulation experiments are conducted to illustrate the feasibility and superiority of the proposed methods over the rectangle safe corridor method and the area method.
... Model predictive control (MPC) algorithms generate trajectories by solving optimal control problems under collision constraints [3]- [5]. Since MPC methods rely on an accurate model, uncertain vehicle dynamics could lead to performance degradation in planning and control. ...
... When dealing with polygonal obstacles, the third module, reference heading angle calculation, employs a consistent strategy described in [5]. The established constraint at the i-th 1 , a i,2 ] ⊤ ∈ R 2 and −a i,1 /a i,2 is the slope of a straight line, b i ∈ R is the intercept, and p i = (X i , Y i ) ⊤ ∈ R 2 is the position of the vehicle. ...
... The performance of GP-SKRL was tested through comparisons with kinodynamic RRT ⋆ (Kd-RRT ⋆ ) [2], model predictive control with control barrier function (MPC-CBF) [3], local model predictive contouring control (LMPCC) [4] and convex feasible set algorithm (CFS) [5] under specific metrics. Their characteristics and differences are shown in TABLE I. Then we compared the tracking-control performance of GP-SKRL with and without model learning, abbreviated as GP-SKRL (w/ ML) and GP-SKRL (w/o ML), to validate the capability of learning uncertainties. ...
Motion planning has been an important research topic in achieving safe and flexible maneuvers for intelligent vehicles. However, it remains challenging to realize efficient and optimal planning in the presence of uncertain model dynamics. In this paper, a sparse kernel-based reinforcement learning (RL) algorithm with Gaussian Process (GP) Regression (called GP-SKRL) is proposed to achieve online adaption and near-optimal motion planning performance. In this algorithm, we design an efficient sparse GP regression method to learn the uncertain dynamics. Based on the updated model, a sparse kernel-based policy iteration algorithm with an exponential barrier function is designed to learn the near-optimal planning policies with the capability to avoid dynamic obstacles. Thereby, batch-mode GP-SKRL with online adaption capability can estimate the changing system dynamics. The converged RL policies are then deployed on vehicles efficiently under a safety-aware module. As a result, the produced driving actions are safe and less conservative, and the planning performance has been noticeably improved. Extensive simulation results show that GP-SKRL outperforms several advanced motion planning methods in terms of average cumulative cost, trajectory length, and task completion time. In particular, experiments on a Hongqi E-HS3 vehicle demonstrate that superior GP-SKRL provides a practical planning solution.
... 1) Obstacle Avoidance in Planning and Control: In the last two decades, a majority of obstacle avoidance problems have been considered using optimization-based trajectory planning algorithms through dynamic programming-related approaches [5], such as trajectory parametrization [6], [7], convex optimizations [8], [9], sequential optimization [10]- [12], LQR/LQG [13]- [15], and model predictive control [16]- [18]. All the above approaches and their variants are related to optimization techniques that use the gradient of the discretetime system dynamics. ...
... Consider the minimum distance optimization problem (8) written as ...
... Define C ij (x) = (C i (x i ), C j (x j )), which is lower and upper semi-continuous, non-empty, and compact-valued by assumption. Then (38) is equivalent to (8) and C * ij (x) = {(z * i (x), z * j (x))}, which is a singleton set in a neighbourhood of x by Lem. 2 and continuity of h. Since all conditions for the maximum theorem are satisfied, C * ij is upper semi-continuous and thus (z * i , z * j ) is a continuous function of x ∈ S. ...
In this paper, we focus on non-conservative obstacle avoidance between robots with control affine dynamics with strictly convex and polytopic shapes. The core challenge for this obstacle avoidance problem is that the minimum distance between strictly convex regions or polytopes is generally implicit and non-smooth, such that distance constraints cannot be enforced directly in the optimization problem. To handle this challenge, we employ non-smooth control barrier functions to reformulate the avoidance problem in the dual space, with the positivity of the minimum distance between robots equivalently expressed using a quadratic program. Our approach is proven to guarantee system safety. We theoretically analyze the smoothness properties of the minimum distance quadratic program and its KKT conditions. We validate our approach by demonstrating computationally-efficient obstacle avoidance for multi-agent robotic systems with strictly convex and polytopic shapes. To our best knowledge, this is the first time a real-time QP problem can be formulated for general non-conservative avoidance between strictly convex shapes and polytopes.
... Fig. 2 illustrates the architecture of the proposed framework. Existing motion planners [20], [21] can solve q in Eq. (1) efficiently. To achieve safe and efficient human-robot co-assembly, we need to ensure that 1) with data scarcity, H intention can be robustly predicted for different humans in different environments, and 2) q can be safely executed, subject to C safety , in real-time under uncertainty. ...
Human-robot collaboration (HRC) is one key component to achieving flexible manufacturing to meet the different needs of customers. However, it is difficult to build intelligent robots that can proactively assist humans in a safe and efficient way due to several challenges.First, it is challenging to achieve efficient collaboration due to diverse human behaviors and data scarcity. Second, it is difficult to ensure interactive safety due to uncertainty in human behaviors. This paper presents an integrated framework for proactive HRC. A robust intention prediction module, which leverages prior task information and human-in-the-loop training, is learned to guide the robot for efficient collaboration. The proposed framework also uses robust safe control to ensure interactive safety under uncertainty. The developed framework is applied to a co-assembly task using a Kinova Gen3 robot. The experiment demonstrates that our solution is robust to environmental changes as well as different human preferences and behaviors. In addition, it improves task efficiency by approximately 15-20%. Moreover, the experiment demonstrates that our solution can guarantee interactive safety during proactive collaboration.
... Convex Feasible Set Algorithm We use CFS (Liu et al. (2018)) to efficiently handle the nonlinear inequality constraint (2) for safety in confined environments. CFS solves a sequence of convex optimizations constrained in the convex feasible sets to search the non-convex feasible space for solutions. ...
... For each constraint Λ i , We will find a convex feasible set F i and construct the convex feasible set around a reference point as F(x r ) = ∩ i F i (x r ). The complete rules of finding F i are summarized in (Liu et al. (2018)), here we approximate F i for each constraint Λ i via: (8) with the understanding that the approximation error will be minimized when approaching the optimal solution. This approach works successfully in practice to find optimal solutions that are strictly feasible, as demonstrated in the results section. ...
Trajectory generation in confined environment is crucial for wide adoption of intelligent robot manipulators. In this paper, we propose a novel motion planning approach for redundant robot arms that uses a hybrid optimization framework to search for optimal trajectories in both the configuration space and null space, generating high-quality trajectories that satisfy task constraints and collision avoidance constraints, while also avoiding local optima for incremental planners. Our approach is evaluated in an onsite polishing scenario with various robot and workpiece configurations, demonstrating significant improvements in trajectory quality compared to existing methods. The proposed approach has the potential for broad applications in industrial tasks involving redundant robot arms.
... To this end, several OGM-based approaches [13]- [16] have been proposed. However, considering the requirements of down-stream motion planning [17], [18], OGM has disadvantages of having large memory footprints and increasing the computational cost [19]. On this basis, there are two major challenges for AGVs: How to reliably detect all kind of unknown obstacles and how to compactly represent them? ...
This article proposes a compact vectorized representation approach to realize reliable obstacle detection for autonomous ground vehicles. Bridging the gap between the advantage of occupancy grid map in general obstacle detection and its shortcomings in memory-consuming and computational cost, a novel obstacle representation by multiple convex polygons is first proposed. Specially, to overcome the computational challenge brought by many 3-D point cloud, based on ground plane extraction and nearest obstacle selection, 3-D obstacle points are transformed into 2-D obstacle points. In addition, the maintenance process of grid map with a fixed range is proposed to further improve efficiency. More importantly, the compact obstacle representation is realized via multiple convex polygons through double threshold-based boundary simplification and convex polygon segmentation. The compact vectorized representation is the main contribution, which achieves the goal of compactness and accuracy on the premise of ensuring effective and reliable obstacle detection. The proposed approach has been applied in a practical autonomous driving project because of its superior performance on general obstacles detection. In addition, the quantitative evaluation shows the superior performance on making use of fewer number of points (decreased by about 50%) to represent local static environments.
... An autonomous vehicle is principally composed of a sensing system, a decision-making system and a motion control system [4][5][6]. The decision-making system can be viewed as the brain of an intelligent vehicle and is essential for high-level autonomous driving, and it mainly includes risk assessment module, trajectory planning module and behavior decision-making module [7][8][9]. Many studies have published the progress made on overall framework and the feasibility of intelligent driving technology [10][11][12][13]. ...
... The criterion according to which the sub-region is selected involves evaluating the feasibility of the resulting QP problem, and thus ensures that a solution will be found if it exists. Differently from related approaches (e.g., [17]) the proposed method does not require solving multiple optimization problems at a given time-step, thanks to the fact that the feasibility region can be evaluated in closed-form. ...
