Ambarish Goswami

Real-Time Inverse Kinematics Techniques for Anthropomorphic Limbs

In this paper we develop a set of inverse kinematics algorithms suitable for an anthropomorphic arm or leg. We use a combination of analytical and numerical methods to solve generalized inverse kinematics problems including position, orientation, and aiming constraints. Our combination of analytical and numerical methods results in faster and more reliable algorithms than conventional inverse Jacobian and optimization-based techniques. Additionally, unlike conventional numerical algorithms, our methods allow the user to interactively explore all possible solutions using an intuitive set of parameters that define the redundancy of the system.

Capture Point: A Step toward Humanoid Push Recovery

It is known that for a large magnitude push a human or a humanoid robot must take a step to avoid a fall. Despite some scattered results, a principled approach towards when and where to take a step has not yet emerged. Towards this goal, we present methods for computing capture points and the capture region, the region on the ground where a humanoid must step to in order to come to a complete stop. The intersection between the capture region and the base of support determines which strategy the robot should adopt to successfully stop in a given situation. Computing the capture region for a humanoid, in general, is very difficult. However, with simple models of walking, computation of the capture region is simplified. We extend the well-known linear inverted pendulum model to include a flywheel body and show how to compute exact solutions of the capture region for this model. Adding rotational inertia enables the humanoid to control its centroidal angular momentum, much like the way human beings do, significantly enlarging the capture region. We present simulations of a simple planar biped that can recover balance after a push by stepping to the capture region and using internal angular momentum. Ongoing work involves applying the solution from the simple model as an approximate solution to more complex simulations of bipedal walking, including a 3D biped with distributed mass.

Postural stability of biped robots and the foot-rotation indicator (FRI) point

The focus of this paper is the problem of foot rotation in biped robots during the single-support phase. Foot rotation is an indication of postural instability, which should be carefully treated in a dynamically stable walk and avoided altogether in a statically stable walk. We introduce the foot-rotation indicator (FRI) point, which is a point on the foot/ground-contact surface where the net ground-reaction force would have to act to keep the foot stationary. To ensure no foot rotation, the FRI point must remain within the convex hull of the foot-support area. In contrast with the ground projection of the center of mass (GCoM), which is a static criterion, the FRI point incorporates robot dynamics. As opposed to the center of pressure (CoP)—better known as the zero-moment point (ZMP) in the robotics literature—which may not leave the support area, the FRI point may leave the area. In fact, the position of the FRI point outside the footprint indicates the direction of the impending rotation and the magnitude of rotational moment acting on the foot. Owing to these important properties, the FRI point helps not only to monitor the state of postural stability of a biped robot during the entire gait cycle, but indicates the severity of instability of the gait as well. In response to a recent need, the paper also resolves the misconceptions surrounding the CoP/ZMP equivalence.

Ground Reference Points in Legged Locomotion: Definitions, Biological Trajectories and Control Implications

The zero moment point (ZMP), foot rotation indicator (FRI) and centroidal moment pivot (CMP) are important ground reference points used for motion identification and control in biomechanics and legged robotics. In this paper, we study these reference points for normal human walking, and discuss their applicability in legged machine control. Since the FRI was proposed as an indicator of foot rotation, we hypothesize that the FRI will closely track the ZMP in early single support when the foot remains flat on the ground, but will then significantly diverge from the ZMP in late single support as the foot rolls during heel-off. Additionally, since spin angular momentum has been shown to remain small throughout the walking cycle, we hypothesize that the CMP will never leave the ground support base throughout the entire gait cycle, closely tracking the ZMP. We test these hypotheses using a morphologically realistic human model and kinetic and kinematic gait data measured from ten human subjects walking at self-selected speeds. We find that the mean separation distance between the FRI and ZMP during heel-off is within the accuracy of their measurement (0.1% of foot length). Thus, the FRI point is determined not to be an adequate measure of foot rotational acceleration and a modified FRI point is proposed. Finally, we find that the CMP never leaves the ground support base, and the mean separation distance between the CMP and ZMP is small (14% of foot length), highlighting how closely the human body regulates spin angular momentum in level ground walking.

Foot rotation indicator (FRI) point: a new gait planning tool to evaluate postural stability of biped robots

The focus of the paper is the problem of foot rotation in biped robots during the single support phase. Foot rotation is an indication of postural instability and should be carefully treated in a dynamically stable walk and avoided altogether in a statically stable walk. We introduce the foot rotation indicator (FRI) point which is a point on the foot/ground contact surface where the net ground reaction force would have to act to keep the foot stationary. To ensure no foot rotation, the FRI point must remain within the convex hull of the foot support area. In contrast with the ground projection of the center of mass (GCoM), which is a static criterion, the FRI point incorporates the robot dynamics. As opposed to the center of pressure (CoP)-better known as the zero moment point (ZMP) in the robotics literature-which may not leave the support area, the FRI point may. Due to these important properties the FRI point helps not only to monitor the state of static stability of a biped robot during the entire gait cycle, but indicates the stability robustness or the severity of instability of the gait as well. In response to a recent need the paper also resolves the misconceptions surrounding the CoP/ZMP equivalence.

A Biomechanically Motivated Two-Phase Strategy for Biped Upright Balance Control

Balance maintenance and upright posture recovery under unexpected environmental forces are key requirements for safe and successful co-existence of humanoid robots in normal human environments. In this paper we present a two-phase control strategy for robust balance maintenance under a force disturbance. The first phase, called the reflex phase, is designed to withstand the immediate effect of the force. The second phase is the recovery phase where the system is steered back to a statically stable “home” posture. The reflex control law employs angular momentum and is characterized by its counter-intuitive quality of “yielding” to the disturbance. The recovery control employs a general scheme of seeking to maximize the potential energy and is robust to local ground surface feature. Biomechanics literature indicates a similar strategy in play during human balance maintenance.

Scalable nonlinear dynamical systems for agent steering and crowd simulation

Abstract We present a new methodology for agent modeling that is scalable and efficient. It is based on the integration of nonlinear dynamical systems and kinetic data structures. The method consists of three layers, which together model 3D agent steering, crowds and flocks among moving and static obstacles. The first layer, the local layer employs nonlinear dynamical systems theory to models low-level behaviors. It is fast and efficient, and it does not depend on the total number of agents in the environment. This dynamical systems-based approach also allows us to establish continuous numerical parameters for modifying each agents behavior. The second layer, a global environment layer consists of a specifically designed kinetic data structure to track efficiently the immediate environment of each agent and know which obstacles/agents are near or visible to the given agent. This layer reduces the complexity in the local layer. In the third layer, a global planning laye r, the problem of target tracking is generalized in a way that allows navigation in maze-like terrains, avoidance of local minima and cooperation between agents. We implement this layer based on two approaches that are suitable for different applications: One approach is to track the closest single moving or static target; the second is to use a pre-specified vector field, which may be generated automatically (with harmonic functions, for example) or based on user input to achieve the desired output. We also discuss how hybrid systems concepts for global planning can capitalize on both our layered approach and the continuous, reactive nature of our agent steering. We demonstrate the power of the approach through a series of experiments simulating single/multiple agents and crowds moving towards moving/static targets in complex environments.

Scalable dynamical systems for multi-agent steering and simulation

We present a methodology for agent modeling that is scalable and efficient. It is based on the integration of nonlinear dynamical systems and kinetic data structures. The method consists of three-layers that model steering, flocking, and crowding agent behaviors among moving and static obstacles in 2 and 3D. The first layer, the local layer is based on the the use of nonlinear dynamical systems theory and models low level behaviors, it is fast and efficient, and does not depend on the total number of agents in the environment. The use of dynamical systems allows the use of continuous numerical parameters with which we can modify the interaction of each agent with the environment. This creates controllable distinctive behaviors. The second layer, a global environment layer consists of a specifically designed kinetic data structure to track efficiently the immediate environment of each agent and know which obstacles/agents are near or visible to the given agent. This layer reduces the complexity in the local layer. In the third layer, a global planning layer, the problem of target tracking is generalized in a way that allows navigation in maze-like terrains, avoidance of local minima and cooperation between agents. We implement this layer based on two approaches that are suitable for different applications. One is to track the closest single moving or static target. The second is to use a pre-specified vector field. This vector can be generated automatically (with harmonic functions, for example) or based on user input to achieve the desired output. We demonstrate the power of the approach through a series of experiments simulating single/multiple agents and crowds moving towards moving/static targets in complex environments.

Mechanically implementable accommodation matrices for passive force control

Robot force control implemented by means of passive mechanical devices has inherent advantages over active implementations with regard to stability, response rapidity, and physical robustness. The class of devices considered in this paper consists of a Stewart platform-type mechanism interconnected with a network of adjustable mechanical elements such as springs and dampers. The control law repertoire of such a device, imagined as a robot wrist, is given by the range of admittance matrices that it may be programmed to possess. This paper focuses on wrists incorporating damper networks for which the admittance matrices reduce to accommodation or inverse-damping matrices. We show that a hydraulic network of fully adjustable damper elements may attain any diagonally dominant accommodation matrix. We describe the technique of selecting the individual damping coefficients to design a desired matrix. We identify the set of dominant matrices as a polyhedral convex cone in the space of matrix entries, and show that each dominant matrix can be composed of a positive linear combination of a fixed set of basis matrices. The overall wrist-accommodation matrix is obtained by projecting the accommodation matrix of the damper network through the wrist kinematics. The linear combination of the dominant basis matrices projected through the wrist kinematics generates the entire space of mechanically implementable force-control laws. We quantify the versatility of mechanically implementable force-control laws by comparing this space to the space of all matrices.