Highly articulated systems are capable of executing a variety of behaviors by coordinating their many internal degrees of freedom to help them move more effectively in complex terrains. However, this inherent variety poses significant challenges that have been the subject of a great deal of previous work: What are the most effective or most efficient methods for achieving the intrinsic coordination necessary to produce desired global objectives? This work takes these questions one step further, asking how different levels of coordination, which we quantify in terms of kinematic coupling, affect articulated locomotion in environments with different degrees of underlying structure. We introduce shape functions as the analytical basis for specifying kinematic coupling relationships that constrain the relative motion among the internal degrees of freedom for a given system during its nominal locomotion. Furthermore, we show how shape functions are used to derive shape-based controllers (SBCs) that manage the compliant interaction between articulated bodies and the environment while explicitly preserving the inter-joint coupling defined by shape functions. Initial experimental evidence provides a comparison of the benefits of different levels of coordination for two separate platforms in environments with different degrees of inherent structure. The experimental results show that decentralized implementations, where there is relatively little inter-joint coupling, perform well across a spectrum of different terrains but that there are potential benefits to higher degrees of coupling in structured terrains. We discuss how this observation has implications related to future planning and control approaches that actively "tune" their underlying structure by dynamically varying the assumed level of coupling as a function of task specification and local environmental conditions.
Kinematic motion planning using geometric mechanics tends to prescribe a trajectory in a parameterization of a shape space and determine its displacement in a position space. Often this trajectory is called a gait. Previous works assumed that the shape space is Euclidean when often it is not, either because the robotic joints can spin around forever (i.e., has an S 1 configuration space component, or its parameterization has an S 1 dimension). Consider a shape space that is a torus; gaits that "wrap" around the full range of a shape variable and return to its starting configuration are valid gaits in the shape space yet appear as line segments in the parameterization. Since such a gait does not form a closed loop in the parameterization, existing geometric mechanics methods cannot properly consider them. By explicitly analyzing the topology of the underlying shape space, we derive geometric tools to consider systems with toroidal and cylindrical shape spaces.
To make a modular robotic system both capable and scalable, the controller must be equally as modular as the mechanism. Given the large number of designs that can be generated from even a small set of modules, it becomes impractical to create a new system-wide controller for each design. Instead, we construct a modular control policy that handles a broad class of designs. We take the view that a module is both form and function, i.e. both mechanism and controller. As the modules are physically re-configured, the policy automatically re-configures to match the kinematic structure. This novel policy is trained with a new model-based reinforcement learning algorithm, which interleaves model learning and trajectory optimization to guide policy learning for multiple designs simultaneously. Training the policy on a varied set of designs teaches it how to adapt its behavior to the design. We show that the policy can then generalize to a larger set of designs not seen during training. We demonstrate one policy controlling many designs with different combinations of legs and wheels to locomote both in simulation and on real robots.
Modular robots hold the promise of versatility in that their components can be re-arranged to adapt the robot design to a task at deployment time. Even for the simplest designs, determining the optimal design is exponentially complex due to the number of permutations of ways the modules can be connected. Further, when selecting the design for a given task, there is an additional computational burden in evaluating the capability of each robot, e.g., whether it can reach certain points in the workspace. This work uses deep reinforcement learning to create a search heuristic that allows us to efficiently search the space of modular serial manipulator designs. We show that our algorithm is more computationally efficient in determining robot designs for given tasks in comparison to the current state-of-the-art.
Abstract-Having many degrees of freedom is both a blessing and a curse. A mechanism with a large number of degrees of freedom can better comply to and therefore better move in complex environments. Yet, possessing many degrees of freedom is only an advantage if the system is capable of coordinating them to achieve desired goals in realtime. This work supports the belief that a middle layer of abstraction between conventional planning and control is needed to enable robust locomotion of articulated systems in complex terrains. The basis for this abstraction is the notion that a system's shape can be used to capture jointto-joint coupling and provide an intuitive set of controllable parameters that adapt the system to the environment in real time. This paper presents a generalizable framework that specifies desired shapes in terms of shape functions. We show how shape functions can be used to link low-level controllers to high-level planners in a compliant control framework that directly controls shape parameters. The resultant shape-based controllers produce behaviors that enable robots to robustly feel their way through unknown environments. This framework is applied to the control of two separate mechanisms, a snake-like and a hexapod robot.
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