Andreas G. Hofmann

Angular momentum regulation during human walking: biomechanics and control

Motivated by biomechanical studies on human walking, we present a control strategy for biologically realistic walking based on the principle of spin angular momentum regulation. Using a morphologically realistic human model and kinematic gait data, we compute the total spin angular momentum at a self-selected walking speed for one human test subject. We find that dimensionless spin angular momentum remains small (S/sub 1//(mass height velocity) < 0.02) throughout the gait cycle, and maximum whole body angular excursions within sagittal (<1/spl deg/), coronal (<0.2/spl deg/), and transverse (<2/spl deg/) planes are negligible. These data support the hypothesis that spin angular momentum in human walking is highly regulated by the central nervous system, and that there exists a nonlinear coupling between ground reaction force, F~, center of mass position, r~/sub CM/ , and center of pressure location, r~/sub CP/, or F~ = (FZ/sub ///Z/sub CM/)(r~/sub CM/ -r~/sub CP/). We employ this relationship to rapidly generate biologically realistic CP and CM reference trajectories. Using an open loop optimization strategy, we show that biologically realistic leg joint kinematics emerge through the minimization of spin angular momentum and the total sum of joint torque squared, suggesting that both angular momentum and energetic factors are important considerations for biomimetic controllers.

A sliding controller for bipedal balancing using integrated movement of contact and non-contact limbs

We present an algorithm that provides enhanced flexibility and robustness in the control of single-leg humanoid standing through the coordination of stance leg ankle torques and stabilizing movements of non-contact limbs. Current control approaches generally assume the presence of explicitly specified joint reference trajectories or desired virtual force calculations that ignore system dynamics. Here we describe a practical controller that 1) simplifies control of abstract variables such as the center of mass location using a two-stage model-based plant linearization; 2) determines motion of non-contact limbs useful for achieving control targets while satisfying dynamic balance constraints; and 3) provides robustness to modeling error using a sliding controller. The controller is tested with a morphologically realistic, 3-dimensional, 18 degree-of-freedom humanoid model serving as the plant. It is demonstrated that the controller can use less detailed control targets, and reject stronger disturbances, than previously implemented controllers that employ desired virtual forces and static body calculations.

Zero spin angular momentum control: definition and applicability

In this paper, we seek control strategies for legged robots that produce resulting kinetics and kinematics that are both stable and biologically realistic. Recent biomechanical investigations have found that spin angular momentum is highly regulated in human standing, walking and running. Motivated by these biomechanical findings, we argue that biomimetic control schemes should explicitly control spin angular momentum, minimizing spin and CM torque contributions not only local in time but throughout movement tasks. Assuming a constant and zero spin angular momentum, we define the zero spin center of pressure (ZSCP) point. For human standing control, we show experimentally and by way of numerical simulation that as the ZSCP point moves across the edge of the foot support polygon, spin angular momentum control changes from regulation to non-regulation. However, even when the ZSCP moves beyond the foot support polygon, stability can be achieved through the generation of restoring CM forces that reestablish the CM position over the foot support polygon. These results are interesting because they suggest that different control strategies are utilized depending on the location of the ZSCP point relative to the foot support polygon.

Search-based Foot Placement for Quadrupedal Traversal of Challenging Terrain

A primary motivation for employing quadrupedal robots is that their morphology allows them to traverse difficult terrain. For example, a mountain goat, by carefully choosing its foot placements, is able to scale steep cliff sides. In contrast, wheeled robots have difficulty traveling over non-level terrain, and bipedal robots face stability challenges on rough terrain, even at low velocities. In order for quadrupeds to perform traversals over rough terrain in a stable manner, robust navigation strategies are needed that allow the robots to take full advantage of their physical capabilities. Foot placement and body pose planning is one of the most challenging problems associated with such navigation. We approach this problem as a combinatoric search over candidate foot placements and body poses. The search returns the sequence of kinematically feasible steps with the lowest cost as determined by their deviation from the terrain-independent nominal steps. Due to the large search domain in this problem and the speed required by real time robots, searching for the true optimal solution is computationally intractable. Therefore, we use a limited-horizon best-first search that quickly finds a near-optimal feasible solution. We show, through a series of tests, that this algorithm is sufficient for traversing challenging terrain, with obstacle heights approaching the leg length of the quadruped.

Temporally and spatially flexible plan execution for dynamic hybrid systems

Abstract Planners developed in the Artificial Intelligence community assume that tasks in the task plans they generate will be executed predictably and reliably. This assumption provides a useful abstraction in that it lets the task planners focus on what tasks should be done, while lower-level motion planners and controllers take care of the details of how the task should be performed. While this assumption is useful in many domains, it becomes problematic when controlling physically embedded systems, where there are often delays, disturbances, and failures. The task plans do not provide enough information about allowed flexibility in task duration and hybrid state evolution. Such flexibility could be useful when deciding how to react to disturbances. An important domain where this gap has caused problems is robotics, particularly, the operation of robots in unstructured, uncertain environments. Due to the complexity of this domain, the demands of tasks to be performed, and the actuation limits of robots, knowledge about permitted flexibility in execution of a task is crucial. We address this gap through two key innovations. First, we specify a Qualitative State Plan (QSP), which supports representation of spatial and temporal flexibility with respect to tasks. Second, we extend compilation approaches developed for temporally flexible execution of discrete activity plans to work with hybrid discrete/continuous systems using a recently developed Linear Quadratic Regulator synthesis algorithm, which performs a state reachability analysis to prune infeasible trajectories, and which determines optimal control policies for feasible state regions. The resulting Model-based Executive is able to take advantage of spatial and temporal flexibility in a QSP to improve handling of disturbances. Note that in this work, we focus on execution of QSPs, and defer the problem of how they are generated. We believe the latter could be accomplished through extensions to existing task planners.

Dynamic Balancing and Flexible Task Execution for Dynamic Bipedal Walking Machines

Effective use of robots in unstructured environments requires that they have sufficient autonomy and agility to execute task-level commands with temporal constraints successfully. A challenging example of such a robot is a bipedal walking machine, particularly one of humanoid form. Key features of the human morphology include a variable base of support and a high center of mass. The high center of mass supports the ability to support a high “sensor package”; when standing erect, the head can see over obstacles. The variable base of support allows both for operation in tight spaces, by keeping the feet close together, and stability against disturbances, by keeping the feet further apart to widen the support base. The feet can also be placed in specific locations when there are constraints due to challenging terrain. Thus, the human morphology supports a range of capabilities, and is important for operating in unstructured environments as humans do. A bipedal robot with human morphology should be able to walk to a particular location within a particular time, while observing foot placement constraints, and avoiding a fall, if this is physically possible. This is a challenging problem because a biped is highly nonlinear and has limited actuation due to its limited base of support. This chapter describes a novel approach to solving this problem that incorporates three key components: (1) a robust controller that is able to use angular momentum to enhance controllability beyond the limits imposed by the support base; (2) a plan specification where task requirements are expressed in a qualitative form that provides for spatial and temporal execution flexibility; and (3) a task executive that compiles the plan into a form that makes the dynamic limitations explicit, and then executes the compiled form using the robust controller.