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We propose a locomotion framework for bipedal robots consisting of a new motion planning method, dubbed trajectory optimization for walking robots plus (TOWR+), and a new whole-body control method, dubbed implicit hierarchical whole-body controller (IHWBC). For versatility, we consider the use of a composite rigid body (CRB) model to optimize the robot’s walking behavior. The proposed CRB model considers the floating base dynamics while accounting for the effects of the heavy distal mass of humanoids using a pre-trained centroidal inertia network. TOWR+ leverages the phase-based parameterization of its precursor, TOWR, and optimizes for base and end-effectors motions, feet contact wrenches, as well as contact timing and locations without the need to solve a complementary problem or integer program. The use of IHWBC enforces unilateral contact constraints (i.e., non-slip and non-penetration constraints) and a task hierarchy through the cost function, relaxing contact constraints and providing an implicit hierarchy between tasks. This controller provides additional flexibility and smooth task and contact transitions as applied to our 10 degree-of-freedom, line-feet biped robot DRACO. In addition, we introduce a new open-source and light-weight software architecture, dubbed planning and control (PnC), that implements and combines TOWR+ and IHWBC. PnC provides modularity, versatility, and scalability so that the provided modules can be interchanged with other motion planners and whole-body controllers and tested in an end-to-end manner. In the experimental section, we first analyze the performance of TOWR+ using various bipeds. We then demonstrate balancing behaviors on the DRACO hardware using the proposed IHWBC method. Finally, we integrate TOWR+ and IHWBC and demonstrate step-and-stop behaviors on the DRACO hardware. 

We present a method that finds locomanipulation plans that perform simultaneous locomotion and manipulation of objects for a desired end-effector trajectory. Key to our approach is to consider an injective locomotion constraint manifold that defines the locomotion scheme of the robot and then using this constraint manifold to search for admissible manipulation trajectories. The problem is formulated as a weighted-A* graph search whose planner output is a sequence of contact transitions and a path progression trajectory to construct the whole-body kinodynamic locomanipulation plan. We also provide a method for computing, visualizing, and learning the locomanipulability region, which is used to efficiently evaluate the edge transition feasibility during the graph search. Numerical simulations are performed with the NASA Valkyrie robot platform that utilizes a dynamic locomotion approach, called the divergent-component-of-motion (DCM), on two example locomanipulation scenarios. 

Fine-scale evolutionary dynamics can be challenging to tease out when focused on broad brush strokes of whole populations over long time spans. We propose a suite of diagnostic metrics that operate on lineages and phylogenies in digital evolution experiments with the aim of improving our capacity to quantitatively explore the nuances of evolutionary histories in digital evolution experiments. We present three types of lineage measurements: lineage length, mutation accumulation, and phenotypic volatility. Additionally, we suggest the adoption of four phylogeny measurements from biology: depth of the most-recent common ancestor, phylogenetic richness, phylogenetic divergence, and phylogenetic regularity. We demonstrate the use of each metric on a set of two-dimensional, real-valued optimization problems under a range of mutation rates and selection strengths, confirming our intuitions about what they can tell us about evolutionary dynamics. 

Fine-scale evolutionary dynamics can be challenging to tease out when focused on the broad brush strokes of whole populations over long time spans. We propose a suite of diagnostic analysis techniques that operate on lineages and phylogenies in digital evolution experiments, with the aim of improving our capacity to quantitatively explore the nuances of evolutionary histories in digital evolution experiments. We present three types of lineage measurements: lineage length, mutation accumulation, and phenotypic volatility. Additionally, we suggest the adoption of four phylogeny measurements from biology: phylogenetic richness, phylogenetic divergence, phylogenetic regularity, and depth of the most-recent common ancestor. In addition to quantitative metrics, we also discuss several existing data visualizations that are useful for understanding lineages and phylogenies: state sequence visualizations, fitness landscape overlays, phylogenetic trees, and Muller plots. We examine the behavior of these metrics (with the aid of data visualizations) in two well-studied computational contexts: (1) a set of two-dimensional, real-valued optimization problems under a range of mutation rates and selection strengths, and (2) a set of qualitatively different environments in the Avida digital evolution platform. These results confirm our intuition about how these metrics respond to various evolutionary conditions and indicate their broad value.