Efficient Multi-Agent Motion Planning in Continuous Workspaces Using Medial-Axis-Based Swap Graphs

We present an algorithm for homogeneous, labeled, and disk-shaped multi-agent motion planning in continuous workspaces with arbitrarily-shaped obstacles. Our method consists of two steps. First, we convert the continuous free space into a discrete graph where agents are placed on vertices and move along edges. On the graph, a set of swap operations are defined and we ensure that performing these swap operations will not lead to collisions between agents or with obstacles. Second, we prove that it is possible for agents' locations to be arbitrarily permuted on graph vertices using our swap operations, as long as these graph vertices are not fully occupied. In other words, a multi-agent motion planning problem on our graph is always solvable. Finally, we show that such continuous-to-discrete conversion can be performed efficiently with the help of a medial axis analysis and can be performed robustly for workspaces with arbitrarily-shaped obstacles. Moreover, the resulting graph has many vertices and can accommodate a large number of densely packed agents (up to $69\%$ of the volume of free space), and motion plans can be computed $10\times$ faster using our swap operations compared to state-of-the-art methods

Custom optimization algorithms for efficient hardware implementation

The focus is on real-time optimal decision making with application in advanced control systems. These computationally intensive schemes, which involve the repeated solution of (convex) optimization problems within a sampling interval, require more efficient computational methods than currently available for extending their application to highly dynamical systems and setups with resource-constrained embedded computing platforms. A range of techniques are proposed to exploit synergies between digital hardware, numerical analysis and algorithm design. These techniques build on top of parameterisable hardware code generation tools that generate VHDL code describing custom computing architectures for interior-point methods and a range of first-order constrained optimization methods. Since memory limitations are often important in embedded implementations we develop a custom storage scheme for KKT matrices arising in interior-point methods for control, which reduces memory requirements significantly and prevents I/O bandwidth limitations from affecting the performance in our implementations. To take advantage of the trend towards parallel computing architectures and to exploit the special characteristics of our custom architectures we propose several high-level parallel optimal control schemes that can reduce computation time. A novel optimization formulation was devised for reducing the computational effort in solving certain problems independent of the computing platform used. In order to be able to solve optimization problems in fixed-point arithmetic, which is significantly more resource-efficient than floating-point, tailored linear algebra algorithms were developed for solving the linear systems that form the computational bottleneck in many optimization methods. These methods come with guarantees for reliable operation. We also provide finite-precision error analysis for fixed-point implementations of first-order methods that can be used to minimize the use of resources while meeting accuracy specifications. The suggested techniques are demonstrated on several practical examples, including a hardware-in-the-loop setup for optimization-based control of a large airliner.Open Acces

LIPIcs, Volume 248, ISAAC 2022, Complete Volume

LIPIcs, Volume 248, ISAAC 2022, Complete Volum