Computational Design Synthesis of Passive Dynamic Systems

Abstract

Passive dynamic systems have the advantage over conventional robotic systems in that they do not require actuators and control. Such systems are usually designed manually by engineers who draw inspiration from biology. However, a computational design synthesis (CDS) approach has the capability to search vast design spaces and find solutions that go beyond those possible by manual design. This dissertation addresses the CDS of passive dynamic systems by introducing a method that breaks the task down into different design stages. Robot topologies, which define the number of bodies and joints as well as how they are connected, are generated using a graph grammar based method. From each robot topology, a dynamic multi-body simulation model is derived, which still depends on a number of optimization variables, such as masses and distances between joints. For each dynamic simulation model, a parametric optimization is performed, where evaluation is based on system trajectories. The resulting multi-body systems are optimized to perform the given robotic task. At this stage, bodies are defined only by their inertia properties, i.e. mass, moment of inertia and center of gravity, lacking a shape embodiment. Therefore, a subsequent embodiment design stage is needed to find a shape for each body that matches the given inertia properties while connecting all given joints of the body. It is discussed how this new type of topology optimization problem leads to the problem of disconnected material distributions, which is not common in the field of topology optimization. A rule based topology optimization method is presented that guarantees that the topology is manifold. The problem is extended to include collision avoidance for given trajectories. A static collision matrix is introduced, which needs to be calculated only once prior to starting the optimization and contains all information of the trajectories necessary for collision detection. The separation of simulation-driven and embodiment design optimization reduces the representation complexity and thus computational burden of the simulation-driven optimization, while allowing large shape freedom in the finite element based embodiment design optimization. Additive manufacturing is chosen as a fabrication method to exploit the possible shape complexity. It also requires little post-processing, making it a suitable part of an automated process. Combining all of the design stages, namely robot topology design, simulation-driven parametric optimization, embodiment design optimization and fabrication, the CDS and fabrication of passive dynamic systems becomes possible in a largely automated fashion. The CDS method is shown to find different, new solutions to the problem of the design of two-dimensional passive dynamic, continuous contact, brachiating robots. Brachiating is the swinging motion of certain apes from one tree branch to the next. The presented graph grammar rules preserve symmetry among robot topologies. The results show that multiple solutions with varying complexity are found, which trade-off cyclic motion and the space required for the system. The concept of passive dynamic pick and place is introduced, which moves objects repetitively from an original location to a destination lower in the gravity field. The difference in potential energy of the object can be used to overcome friction. This is similar to passive dynamic walking robots moving on a downwards slope using the loss of potential energy with each step to compensate friction and impact losses. Besides compensating friction, the available potential energy can also be used to power a gripper for the pick and place task. Such pick and place mechanisms are synthesized using the CDS method described above and selected designs are fabricated and successfully tested. In this dissertation, the CDS of passive dynamic systems, which includes robot topology design, is approached for the first time in literature. The main contribution is a complete method from robot topology to embodiment design and fabrication. Further contributions include a structural topology optimization method that can avoid collision between bodies for given trajectories and the idea of separating simulation-driven and embodiment design. The concept of repetitive passive dynamic pick and place is presented for the first time and working prototypes are fabricated. Several novel ideas are introduced in the individual design stages, e.g. graph grammar rules, which preserve symmetry for brachiating mechanisms and a static collision matrix, which can be used to check for collision between bodies for given trajectories very efficiently by only two vector-matrix multiplications. The presented work expands the range of possible applications of passive dynamic systems by exploring new design methods. In future work, passive dynamic systems designed with CDS can be extended with small actuators and control in order to increase the robustness and flexibility of the systems, while keeping them energy-efficient.