Topology Optimization of Rigid-Body Systems Considering Collision Avoidance

Passive dynamic mechanisms can perform simple robotic tasks without requiring actuators and control. In previous research, a computational design method was introduced that integrates dynamic simulation to evaluate and evolve configurations of such mechanisms. It was shown to find multiple solutions of passive dynamic brachiating robots (Stöckli and Shea, 2017, “Automated Synthesis of Passive Dynamic Brachiating Robots Using a Simulation-Driven Graph Grammar Method,” J. Mech. Des. 139(9), p. 092301). However, these solutions are limited, since bodies are modeled only by their inertia properties and thus lack a shape embodiment. This paper presents a method to generate rigid-body topologies based on given inertia properties. The rule-based topology optimization method presented guarantees that the topology is manifold, meaning that it has no disconnected parts, while still connecting all joints that need to be part of the body. Furthermore, collisions with the environment, as well as with other bodies, during their predefined motion trajectories are avoided. A collision matrix enables efficient collision detection as well as the calculation of the swept area of one body in the design space of another body by only one matrix–vector multiplication. The presented collision avoidance method proves to be computationally efficient and can be adopted for other topology optimization problems. The method is shown to solve different tasks, including a reference problem as well as passive dynamic brachiating mechanisms. Combining the presented methods with the simulation-driven method from Stöckli and Shea (2017, “Automated Synthesis of Passive Dynamic Brachiating Robots Using a Simulation-Driven Graph Grammar Method,” J. Mech. Des. 139(9), p. 092301), the computational design-to-fabrication of passive dynamic systems is now possible and solutions are provided as STL files ready to be 3D-printed directly.