Non-convex Collision Avoidance Constraints Research Articles

Energy- and time-optimal reconfiguration of spacecraft clusters with collision avoidance

Spacecraft cluster reconfiguration is one of the enabling technologies to ensure non-traditional attributes of distributed space systems. This work treats energy- and time-optimal reconfiguration problems for both circular and eccentric reference orbits. Furthermore, typical local and coupling constraints have been taken into account. Particularly, focus is given to two coupling constraints: final configuration constraints and collision avoidance constraints. For final configuration constraints, a parameterization method is applied to ensure that the reconfiguration problem can be solved as only one optimization problem, rather than a large number of optimization problems resulting from the traditional discretization method. A generalized formulation is proposed for non-convex collision avoidance constraints, which are then convexified via linearization and convex restriction technology. This method provides the affine approximation as a special case. After incorporating above constraints, the reconfiguration problem is formulated as an open-loop optimal control problem, which is solved via the Gauss pseudospectral method (GPM). By virtue of elegant features of GPM, those solutions can serve as a counterpart and stepping stone for a distributed implementation of reconfiguration algorithms. Various simulations demonstrate that minimum-energy/time cluster reconfiguration problems with collision avoidance for circular and eccentric reference orbits can be solved effectively and efficiently using GPM.

Computationally Efficient Collision-Free Trajectory Planning of Satellite Swarms Under Unmodeled Orbital Perturbations

This paper studies the problem of collision-free trajectory planning for a satellite swarm reconfiguration under perturbations and modeling uncertainties in a low Earth orbit (LEO). Determining exact trajectory planning solutions is computationally heavy as they require solving a mixed-integer nonlinear program owing to i) nonlinear relative dynamic models of satellites, ii) fuel-optimal assignment of satellites on the final formation, and iii) nonconvex collision avoidance constraints. To address these, first, a suitable linear model for trajectory planning is identified by quantifying modeling accuracy associated with various models capturing LEO perturbations. The effects of any residual modeling errors in the path prediction are mitigated by shrinking-horizon model-predictive feedback control, which updates the control command based on the latest satellite measurements. Secondly, an optimal swarm configuration is efficiently computed by decoupling the target-assignment algorithm from the trajectory optimization problem. Based on the estimated fuel expenditure for each satellite–target pairing, the target-assignment algorithm selects a configuration with minimal fuel consumption. Lastly, to determine collision-free, fuel-optimal maneuvers, two novel trajectory planning approaches, namely, distributed and decentralized trajectory optimization, are presented. While the former iteratively searches for collision-free feasible paths to optimal terminal configuration, the latter computes a near-optimal configuration with collision-free paths.

RDA: An Accelerated Collision Free Motion Planner for Autonomous Navigation in Cluttered Environments

Autonomous motion planning is challenging in multi-obstacle environments due to nonconvex collision avoidance constraints. Directly applying numerical solvers to these nonconvex formulations fails to exploit the constraint structures, resulting in excessive computation time. In this paper, we present an accelerated collision-free motion planner, namely regularized dual alternating direction method of multipliers (RDADMM or RDA for short), for the model predictive control (MPC) based motion planning problem. The proposed RDA addresses nonconvex motion planning via solving a smooth biconvex reformulation via duality and allows the collision avoidance constraints to be computed in parallel for each obstacle to reduce computation time significantly. We validate the performance of the RDA planner through path-tracking experiments with car-like robots in both simulation and real-world settings. Experimental results show that the proposed method generates smooth collision-free trajectories with less computation time compared with other benchmarks and performs robustly in cluttered environments. The source code is available at https://github.com/hanruihua/RDA_planner.

Tackling Nonconvex Collision Avoidance Constraints for Optimal Trajectory Planning Using Saturation Functions

The problem of optimal trajectory planning with nonconvex collision avoidance constraints is discussed in this paper. The trajectory planning algorithm aims to generate a feasible trajectory with specified performance indexes to reduce collisions of aerospace vehicles in the presence of second-order smooth obstacles. The algorithm design that manages such mission scenarios is challenging because of the stringent avoidance constraints of various nonconvex types, especially considering the requirements of efficient computation. This problem is addressed within the sequential convex programming (SCP) framework by utilizing the characteristics of saturation functions. The introduction of the saturation function is found to significantly improve the convergence of the SCP algorithm by overcoming the drawbacks of potential interruptions from the iteration process and controlling the search directions for successive solutions. Theoretical analyses are performed to guarantee that the original constraints are satisfied and to ensure the iterative solution searches in the directions of the true optimal solution. Under multiple randomly generated test environments, the applications of the proposed approach in highly constrained aircraft path planning problems and spacecraft rendezvous operations are numerically simulated by comparing two representative conventional SCP-based methods to demonstrate the effectiveness, efficiency, and convergence of the proposed methodology.

A Successive Linearization in Feasible Set Algorithm for Vehicle Motion Planning in Unstructured and Low-Speed Scenarios

Motion planning in unstructured and low-speed environments is a fundamental and difficult task for all mobile robotics. If we view motion planning as an optimization problem, the non-convex collision avoidance constraints and the nonlinear vehicle dynamic constraints make motion planning challenging and time-consuming. In this paper, we propose a Successive Linearization in Feasible Set (SLiFS) algorithm to address these two difficulties. SLiFS consists of two steps. The first step is to iteratively construct convex feasible sets around the current trajectory to approximate non-convex collision avoidance constraints. The second step is to successively linearize the nonlinear dynamic constraints along the current trajectory and further penalize them into the objective function to avoid infeasible linearized constraints, so that the current trajectory can be reshaped within the obtained convex feasible sets by iteratively solving the linearized optimization problem. The main innovation of SLiFS algorithm is that we consider the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$L_{1}$ </tex-math></inline-formula> norm type penalty function in the second step. We find that the sparsity of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$L_{1}$ </tex-math></inline-formula> norm might help to satisfy the robotic dynamic constraints by numerical experiments. Numerical testing results show that our proposed SLiFS algorithm has a high success rate to find feasible trajectories and costs much less time than the classical interior-point method.

GPU Accelerated Convex Approximations for Fast Multi-Agent Trajectory Optimization

In this letter, we present a computationally efficient trajectory optimizer that can exploit GPUs to jointly compute trajectories of tens of agents in under a second. At the heart of our optimizer is a novel reformulation of the non-convex collision avoidance constraints that reduces the core computation in each iteration to a large scale, convex, unconstrained Quadratic Program (QP). Importantly, our QP structure requires us to compute the associated matrix factorization/inverse only once for a fixed number of agents. Moreover, we can do it offline and then use the same for different problem instances. This further simplifies the solution process, effectively reducing it to a few matrix-vector products. For a large number of agents, this computation can be trivially accelerated on GPUs using existing off-the-shelf libraries. We validate our optimizer's performance on challenging benchmarks and show substantial improvement over state of the art in computation time and trajectory quality.

Online Trajectory Planning for Multiple Quadrotors in Dynamic Environments Using Relative Safe Flight Corridor

This letter presents a new distributed multi-agent trajectory planning algorithm that generates safe, dynamically feasible trajectories considering the uncertainty of obstacles in dynamic environments. We extend the relative safe flight corridor (RSFC) presented in previous work to replace time-variant, non-convex collision avoidance constraints to convex ones, and we adopt a relaxation method based on reciprocal collision avoidance (RCA) to reduce the total flight time and distance without loss of success rate. The proposed algorithm can compute the trajectories for 50 agents on average 49.7 ms per agent with Intel i7 desktop and can generate safe trajectories for 16 agents with a success rate of more than 93% in simulation environments with four dynamic obstacles when the velocity of dynamic obstacles is below the maximum velocity of quadrotors. We validate the robustness of the proposed algorithm through a real flight test with four quadrotors and one moving human.

Tractor-Trailer Vehicle Trajectory Planning in Narrow Environments With a Progressively Constrained Optimal Control Approach

Trajectory planning for a tractor-trailer vehicle is challenging due to the non-convex collision avoidance constraints and the unstable kinematics. This article aims to plan precise and optimal trajectory for a car-like tractor that tows standard or general N-trailers in an environment with static obstacles. This trajectory planning scheme can be formulated as a unified optimal control problem, but numerically solving that problem is difficult. Two efforts are made to address the difficulty. First, an extended hybrid A* search algorithm is proposed to provide an initial guess for the numerical optimization. Second, the numerical optimization process is eased through adopting a progressively constrained optimization strategy, which is about sequentially handling the kinematics, collision avoidance constraints, and boundary conditions. Particularly in dealing with the collision avoidance constraints, an adaptively homotopic warm-starting algorithm is proposed, which defines a sequence of subproblems with the obstacle areas adaptively increase towards their nominal scales. Through solving these subproblems in a sequence, the whole collision avoidance difficulties are dispersed and gradually tackled. Comparative simulations are conducted to validate the efficacy of the proposed trajectory planner.

Trajectory Planning for Autonomous High-Speed Overtaking in Structured Environments Using Robust MPC

Automated vehicles are increasingly getting main-streamed and this has pushed development of systems for autonomous manoeuvring (e.g., lane-change, merge, and overtake) to the forefront. A novel framework for situational awareness and trajectory planning to perform autonomous overtaking in high-speed structured environments (e.g., highway and motorway) is presented in this paper. A combination of a potential field like function and reachability sets of a vehicle are used to identify safe zones on a road that the vehicle can navigate towards. These safe zones are provided to a tube-based robust model predictive controller as reference to generate feasible trajectories for combined lateral and longitudinal motion of a vehicle. The strengths of the proposed framework are: 1) it is free from non-convex collision avoidance constraints; 2) it ensures feasibility of trajectory even if decelerating or accelerating while performing lateral motion; and 3) it is real-time implementable. The ability of the proposed framework to plan feasible trajectories for high-speed overtaking is validated in a high-fidelity IPG CarMaker and Simulink co-simulation environment.

Autonomous Driving Motion Planning With Constrained Iterative LQR

Motion planning is a core technique for autonomous driving. Nowadays, there still exists a lot of challenges in motion planning for autonomous driving in complicated environments due to: 1) the need of both spatial and temporal planning in highly dynamic environments; 2) nonlinear vehicle dynamic models and non-convex collision avoidance constraints; and 3) the need of high computation efficiency for real-time implementation. Iterative linear quadratic regulator (ILQR) is an algorithm to solve the optimal control problem with nonlinear system very efficiently. However, it can not deal with constraints. In this paper, the constrained iterative LQR (CILQR) is proposed to efficiently solve the optimal control problem with nonlinear system dynamics and general form of constraints. An autonomous driving motion planning problem is then formulated and solved using CILQR. Simulation case studies show the capability of the CILQR algorithm to solve these kind of problems and the computation efficiency of CILQR is shown to be much higher than the standard SQP solver.

Predictive Control for Tight Group Formation of Multi-Agent Systems*

Abstract This paper addresses the real-time control problem of a group of agents in the presence of non-convex collision avoidance constraints. The goal is to guarantee the convergence towards a tight formation. Convex (polyhedral) regions will be used to define safety regions around each agent. Then, using the dynamics and constraints, an optimization-based control design can be adopted upon an appropriate receding horizon principle. A single optimal control problem is solved based on a prediction of the future evolution of the system and the resulting control law is implemented in a centralized way. At the supervision level, it is shown that the decision about which agents should take on what role in the desired tight formation is equivalent with a classical pairing (or task assignment) problem. An important contribution is the re-evaluation of the pairing at each iteration. Copyright © IFAC 2011