Obstacle Avoidance Constraints Research Articles

Trajectory optimization with obstacles avoidance via strong duality equivalent and hp‐pseudospectral sequential convex programming

AbstractA trajectory optimization algorithm is developed in this article to compute a trajectory that avoids obstacles for an unmanned aerial vehicle and minimize the load factor. Quadratic and polyhedron obstacles are both considered in this article. To satisfy the safety distance requirements in engineering practice, a distance‐based obstacle avoidance constraint is formulated, which restricts the minimum distance that a vehicle can approach the obstacle. Strong duality equivalent converts the constraints into equivalent forms without introducing binary variables. Subsequently, the trajectory optimization problem is numerically solved via a hp‐pseudospectral sequential convex programming method, which iteratively solves a sequence of second‐order cone programming subproblems until convergence is attained. Furthermore, a modified trust‐region constraint and a customized nominal trajectory update rule are proposed to accelerate the convergence of the algorithm. A group of simulations are performed to demonstrate that the algorithm is computationally efficient and capable of generating a trajectory that satisfies safety distance requirements, preventing conservativeness in the trajectory, reducing the incidence of intersample constraints violation.

Multi-Target Coordinated Search Algorithm for Swarm Robotics Considering Practical Constraints.

In order to deal with the multi-target search problems for swarm robots in unknown complex environments, a multi-target coordinated search algorithm for swarm robots considering practical constraints is proposed in this paper. Firstly, according to the target detection situation of swarm robots, an ideal search algorithm framework combining the strategy of roaming search and coordinated search is established. Secondly, based on the framework of the multi-target search algorithm, a simplified virtual force model is combined, which effectively overcomes the real-time obstacle avoidance problem in the target search of swarm robots. Finally, in order to solve the distributed communication problem in the multi-target search of swarm robots, a distributed neighborhood communication mechanism based on a time-varying characteristic swarm with a restricted random line of sight is proposed, and which is combined with the multi-target search framework. For the swarm robot kinematics, obstacle avoidance, and communication constraints of swarm robots, the proposed multi-target search strategy is more stable, efficient, and practical than the previous methods. The effectiveness of this proposed method is verified by numerical simulations.

Event‐triggered model predictive control for multi‐vehicle systems with collision avoidance and obstacle avoidance

AbstractIn this article, event‐triggered model predictive control is used for simultaneous tracking and formation of a multi‐vehicle system with collision avoidance and obstacle avoidance. An event‐triggered mechanism is established to reduce computational burden in the model predictive control strategy. A compatibility constraint is proposed to guarantee collision avoidance and convergence for the multi‐vehicle system by limiting an uncertainty deviation of each vehicle. Between each vehicle and obstacles, a safe distance is ensured by a robust obstacle avoidance constraint. Finally, effectiveness and advantages of the proposed strategy are shown by two simulation examples.

Fastest motion planning for an unmanned vehicle in the presence of accelerating obstacles

Estimating the fastest trajectory is one of the main challenges in autonomous vehicle research. It is fundamental that the vehicle determines its path not only to minimize travel time, but to arrive at the destination safely by avoiding any obstacles that may be in collision route. In this paper, we consider estimating the trajectory and acceleration functions of the trip simultaneously with an optimization objective function. By approximating the trajectory and acceleration function with B-splines, we transform an infinite-dimensional problem into a finite-dimensional one. Obstacle avoidance and kinematic constraints are carried out with the addition of a penalization function that penalizes trajectories and acceleration functions that do not satisfy the vehicles’ constraints or that are in a collision route with other obstacles. Our approach is designed to model observations of the obstacles that contain measurement errors, which incorporates the realistic stochasticity of radars and sensors. We show that, as the number of observations increases, the estimated optimization function converges to the optimal one where the obstacles’ positions are known. Moreover, we show that the estimated optimization function has a minimizer and that its minimizers converge to the minimizers of the optimization function involving the true threat zones.

Hierarchical Control of Trajectory Planning and Trajectory Tracking for Autonomous Parallel Parking

For the parallel parking problem in narrow space, this paper proposes a trajectory tracking control method with a novel trajectory planning layer for autonomous parallel parking based on a numerical optimization algorithm and model predictive control. In the trajectory planning layer, the vehicle kinematics model suitable for the low-velocity parking scene is established. Considering the vehicle physical constraints, boundary condition constraints, and obstacle avoidance constraints during the parking process, the parking trajectory planning task is described as an optimal control problem, further transformed into a nonlinear programming problem by Gauss pseudo-spectral method. Taking the shortest parking completion time as the optimization objective function, the parking trajectories of the large, medium and small parking spaces are obtained, respectively. A parking trajectory tracking controller based on the model predictive control algorithm is designed in the trajectory tracking control layer. The linear error model is used as the prediction model, and the quadratic programming is adopted as the rolling optimization algorithm in the tracking controller. The velocity and front-wheel swing angle are obtained as control signals for parking trajectory tracking. Through CarSim and Simulink's co-simulation, the feasibility and effectiveness of the proposed parallel parking trajectory planning and tracking control method are verified. The co-simulation results show that the maximum tracking errors of horizontal and longitudinal positions are less than 0.15m. The maximum tracking errors of heading angle are less than 2° under three different parking spaces. Real vehicle tests are carried out to verify the effectiveness of the proposed hierarchical control method. The test results show that the vehicle can park in the parking space safely, quickly and accurately when the actual parking space is detected. The proposed method can plan the parking trajectory with the constraints and the shortest time and control the vehicle to complete the parking operation accurately along the planned trajectory.

Proposal of Model Predictive Trajectory Planning Method for Autonomous Parking Considering Obstacle Avoidance Constraint with Coordinate Transformation

Proposal of Model Predictive Trajectory Planning Method for Autonomous Parking Considering Obstacle Avoidance Constraint with Coordinate Transformation

Model Predictive Control for a Mecanum-wheeled Robot Navigating among Obstacles

Abstract Mecanum-wheeled robots have been thoroughly used to automate tasks in many different applications. However, they are usually controlled by neglecting their dynamics and relying only on their kinematic model. In this paper, we model the behaviour of such robots by taking into account both their equations of motion and the electrodynamic response of their actuators, including dry and viscous friction at their shafts. This allows us to design a model predictive controller aimed to minimise the energy consumed by the robot. The controller also satisfies a number of non-linear inequalities modelling motor voltage limits and obstacle avoidance constraints. The result is an agile controller that can quickly adapt to changes in the environment, while generating fast and energy-efficient manoeuvres towards the goal.

Task Planning of Manipulator Based on Dynamic Space Constraint and Torque Sensor

It is a main direction of industrial application that manipulator performs grasping task in task space and combines obstacle avoidance planning. This paper presents an improved RRTConnect path planning algorithm IRRTC based on dynamic constrained space and admittance control. The sliding constraints on the Cartesian position space is used to search for the reachable path of the traction robot by the algorithm. For orientation control, a priori path is formed by artificially given constraint interval, and then the dynamic admittance control is modified by using the end grasping load moment estimated by the joint torque sensor of the manipulator as the constraint. At the same time, the algorithm designs a local escape algorithm based on the current state and target state of the robotic arm, which overcomes the problem that the traditional RRTConnect and RRT cannot escape the local minimum. The simulation and experimental results of the Xmate3 redundant manipulator show that a feasible path can be quickly searched based on constraints and local escape strategies, and a relatively optimal trajectory can be planned based on the original path by the optimized path and also meet the constraints. Within 3S, the average planning success rate is increased to over 90%, and without time constraint, the success rate is 100%, the efficiency is higher than other algorithms. Because the admittance control is used in conjunction with the joint torque feedback to maintain the dynamic correction of the end orientation, which improves the stability of the manipulator. The algorithm can be artificially designed to solve the obstacle avoidance and task constraints in disorderly grasping.

Early Termination of Convex QP Solvers in Mixed-Integer Programming for Real-Time Decision Making

The branch-and-bound optimization algorithm for mixed-integer model predictive control (MI-MPC) solves several convex quadratic program relaxations, but often the solutions are discarded based on already known integer feasible solutions. This letter presents a projection and early termination strategy for infeasible interior point methods to reduce the computational effort of finding a globally optimal solution for MI-MPC. The method is shown to be also effective for infeasibility detection of the convex relaxations. We present numerical simulation results with a reduction of the total number of solver iterations by 42% for an MI-MPC example of decision making for automated driving with obstacle avoidance constraints.

A Trajectory Planning Method for Autonomous Valet Parking via Solving an Optimal Control Problem.

In the last decade, research studies on parking planning mainly focused on path planning rather than trajectory planning. The results of trajectory planning are more instructive for a practical parking process. Therefore, this paper proposes a trajectory planning method in which the optimal autonomous valet parking (AVP) trajectory is obtained by solving an optimal control problem. Additionally, a vehicle kinematics model is established with the consideration of dynamic obstacle avoidance and terminal constraints. Then the parking trajectory planning problem is modeled as an optimal control problem, while the parking time and driving distance are set as the cost function. The homotopic method is used for the expansion of obstacle boundaries, and the Gauss pseudospectral method (GPM) is utilized to discretize this optimal control problem into a nonlinear programming (NLP) problem. In order to solve this NLP problem, sequential quadratic programming is applied. Considering that the GPM is insensitive to the initial guess, an online calculation method of vertical parking trajectory is proposed. In this approach, the offline vertical parking trajectory, which is calculated and stored in advance, is taken as the initial guess of the online calculation. The selection of an appropriate initial guess is based on the actual starting position of parking. A small parking lot is selected as the verification scenario of the AVP. In the validation of the algorithm, the parking trajectory planning is divided into two phases, which are simulated and analyzed. Simulation results show that the proposed algorithm is efficient in solving a parking trajectory planning problem. The online calculation time of the vertical parking trajectory is less than 2 s, which meets the real-time requirement.

Distributed synchronous cooperative tracking algorithm for ground moving target in urban by UAVs

ABSTRACT In this paper, a cooperative path planning method is proposed to track the unknown ground moving target by multiple unmanned aerial vehicles (UAVs). The kinematic UAV model with dual-input including commanded speed and heading rate is adopted, and the unknown target state is forecasted by the Extended Kalman Filter (EKF) with probability estimate. The cooperative path planning with multiple objectives and priorities is designed, where the infrastructure occlusion to line of detection sight and energy consumption are considered. Three optimisation objectives are fuzzified, and the priority is modelled by the relaxed order of satisfactory degrees. With the synchronous communication, the collision avoidance constraints and compatibility constraints under communication delay are designed. Moreover, the obstacle avoidance constraints with high buildings are addressed. Based on the distributed receding horizon control (RHC), the fuzzy multi-objective synchronous cooperative tracking model is built, and the optimal path of UAVs can be obtained by regulating the parameter. The algorithm to find the bound of regulation parameter is developed based on Karush–Kuhn–Tucker (KKT) condition. Finally, simulation results verify that the proposed method is effective and reliable.

Lateral obstacle avoidance control based on driving behavior recognition of the preceding vehicles in adjacent lanes

Abstract This paper proposes a lateral lane change obstacle avoidance constraint control simulation algorithm based on the driving behavior recognition of the preceding vehicles in adjacent lanes. Firstly, the driving behavior of the preceding vehicles is recognized based on the Hidden Markov Model, this research uses longitudinal velocity, lateral displacement and lateral velocity as the optimal observation signals to recognize the driving behaviors including lane-keeping, left-lane-changing or right-lane-changing; Secondly, through the simulation of the dangerous cutting-in behavior of the preceding vehicles in adjacent lanes, this paper calculates the ideal front wheel steering angle according to the designed lateral acceleration in the process of obstacle avoidance, designs the vehicle lateral motion controller by combining the backstepping and Dynamic Surface Control, and the safety boundary of the lateral motion is constrained based on the Barrier Lyapunov Function; Finally, simulation model is built, and the simulation results show that the designed controller has good performance. This active safety technology effectively reduces the impact on the autonomous vehicle safety when the preceding vehicle suddenly cuts into the lane.

Optimal Concurrent Control for Space Manipulators Rendezvous and Capturing Targets Under Actuator Saturation

This article proposes a control method for space manipulators rendezvousing with and capturing a target, involving concurrent operation of an optimal and a coordinated controller. The optimal controller drives the whole system to rendezvous with the target, which saves onboard fuel and satisfies obstacle avoidance constraint and base spacecraft thrust limits. The optimal control problem is solved using calculus of variations method, with state inequality constraints transformed into extended dynamical subsystems and thrust limits formulated as saturation functions. The coordinated controller is designed based on the dynamic equations of the space manipulator on a noninertial frame attached to the system center of mass, which drives the end-effector to approach the target along a desired trajectory while making the base attitude follow a desired profile. It also generates proper reaction moments on base through manipulator motions to ensure controlling the base attitude when base attitude actuators reach their torque limits. The solution optimality of the optimal controller and the stability of the coordinated controller are demonstrated. Numerical simulations verify the performance of the proposed concurrent control method.

A Non-Convex Optimization Approach to Dynamic Coverage Problem of Multi-agent Systems in an Environment with Obstacles

In this paper, a cooperative region reconnaissance problem is investigated where a group of agents are required to fly across and detect events occur in an environment with static obstacles until an effective coverage is achieved. First, the region reconnaissance is formulated as a non-convex optimization problem. A coverage performance index with additional collision and obstacle avoidance constraints is given. Since the optimization index is an implicit function of state variables and cannot be used to compute gradients on state variables directly, an approximate optimization index is selected. Then, a non-convex optimization-based coverage algorithm is proposed to find the optimal reconnaissance location for each agent and guarantee no collisions trajectories among agents and obstacles. Finally, simulation experiments are performed to verify the effectiveness of the proposed approach.

Differential Flatness Based Path Planning With Direct Collocation on Hybrid Modes for a Quadrotor With a Cable-Suspended Payload

Generating agile maneuvers for a quadrotor with a cable-suspended load is a challenging problem. State-of-the-art approaches often need significant computation time and complex parameter tuning. We use a coordinate-free geometric formulation and exploit a differential flatness based hybrid model of a quadrotor with a cable-suspended payload. We perform direct collocation on the differentially-flat hybrid system, and use complementarity constraints to avoid specifying hybrid mode sequences. The non-differentiable obstacle avoidance constraints are reformulated using dual variables, resulting in smooth constraints. We show that our approach has lower computational time than the state-of-the-art and guarantees feasibility of the trajectory with respect to both the system dynamics and input constraints without the need to tune lots of parameters. We validate our approach on a variety of tasks in both simulations and experiments, including navigation through waypoints and obstacle avoidance.

Multiaircraft Optimal 4D Trajectory Planning Using Logical Constraints

This paper studies the trajectory planning problem for multiple aircraft with logical constraints in disjunctive form which arise in modeling passage through waypoints, distance-based and time-based separation constraints, decision-making processes, conflict resolution policies, no-fly zones, or obstacle or storm avoidance. Enforcing separation between aircraft, passage through waypoints, and obstacle avoidance is especially demanding in terms of modeling efforts. Indeed, in general, separation constraints require the introduction of auxiliary integer variables in the model; for passage constraints, a multiphase optimal control approach is used, and for obstacle avoidance constraints, geometric approximations of the obstacles are introduced. Multiple phases increase model complexity, and the presence of integer variables in the model has the drawback of combinatorial complexity of the corresponding mixed-integer optimal control problem. In this paper, an embedding approach is employed to transform logical constraints in disjunctive form into inequality and equality constraints which involve only continuous auxiliary variables. In this way, the optimal control problem with logical constraints is converted into a smooth optimal control problem which is solved using traditional techniques, thereby reducing the computational complexity of finding the solution. The effectiveness of the approach is demonstrated through several numerical experiments by computing the optimal trajectories of multiple aircraft in converging and intersecting arrival routes with time-based separation constraints, distance-based separation constraints, and operational constraints.

Optimal 3D trajectory planning for AUVs using ocean general circulation models

In this paper, we consider the autonomous underwater vehicle (AUV) trajectory planning problem under the influence of a realistic 3D current as simulated by an ocean general circulation model (OGCM). Attention is focused on the case of a deterministic steady OGCM field, which is used to specify data for both the ocean current and for ocean bathymetry. A general framework for optimal trajectory planning is developed for this setting, accounting for the 3D ocean current and for static obstacle avoidance constraints. A nonlinear programming approach is used for this purpose, which leads to a low complexity discrete-time model that can be efficiently solved. To demonstrate the efficiency of the model, we consider the optimal time trajectory planning of an AUV operating in the Red Sea and Gulf of Aden, with velocity, and bathymetric data provided by an eddy-resolving MITgcm. Different optimal-time trajectory planning scenarios are implemented to demonstrate the capabilities of the model to identify trajectories that adapt to favorable and adverse currents and to avoid obstacles corresponding to a complex bathymetry environment. The simulations are also used to evaluate the performance of the proposed approach, and to illustrate the application of advanced visualization tools to interpret the model predictions.

A Combinatorial Approach for Small and Strong Formulations of Disjunctive Constraints

A framework is presented for constructing strong mixed-integer programming formulations for logical disjunctive constraints. This approach is a generalization of the logarithmically sized formulations of Vielma and Nemhauser for special ordered sets of type 2 (SOS2) constraints, and a complete characterization of its expressive power is offered. The framework is applied to a variety of disjunctive constraints, producing novel small and strong formulations for outer approximations of multilinear terms, generalizations of special ordered sets, piecewise linear functions over a variety of domains, and obstacle avoidance constraints.

Tracking and Formation of Multi-agent Systems with Collision and Obstacle Avoidance Based on Distributed RHC

This paper proposes a distributed receding horizon control approach for the formation and tracking problems of multi-agent systems with collision and obstacle avoidance. We design an algorithm to enlarge the terminal position sets of the agents in sequential order. Since the proposed approach is based on the synchronous framework, each agent must utilize the assumed predictive information of its neighbors. A compatibility constraint is reformulated for the local optimization, which restricts the deviation between the assumed and true predictive states. To ensure the safety of each agent, the deviation-dependent collision-avoidance constraint and the obstacle-avoidance constraint are designed. Moreover, the closed-loop multi-agent systems are guaranteed to be exponentially stable, and the control performance is improved compared with the previous approaches. A simulation example is provided to illustrate the advantages of the proposed approach.

Collision prediction and avoidance for satellite ultra-close relative motion with zonotope-based reachable sets

Collision prediction and avoidance are critical for satellite proximity operations, and the key is the treatment of satellites' motion uncertainties and shapes, especially for ultra-close autonomous systems. In this paper, the zonotope-based reachable sets are utilized to propagate the uncertainties. For satellites with slender structures (such as solar panels), their shapes are simplified as cuboids which is a special class of zonotopes, instead of the classical sphere approach. The domains in position subspace influenced by the uncertainties and shapes are determined, and the relative distance is estimated to assess the safety of satellites. Moreover, with the approximation of the domains, the worst-case uncertainties for path constraints are determined, and a robust model predictive control method is proposed to deal with the line of sight and obstacle avoidance constraints. With zonotope representations of satellites, the proposed robust model predictive control is capable of handling the shapes of the satellite and obstacle simultaneously. Numerical simulations demonstrate the effectiveness of the proposed methods with an elliptic reference orbit. 1