Table 2.
Concise analysis of case studies under generative Gibsonian framework.
| Section | Emergent model | Basis model | Generative model | Gibsonian affordance | Agent-environment interaction | References |
|---|---|---|---|---|---|---|
| 2.1 | Energy-efficient locomotion on sand (Figure 5) | Direct-drive robot legs on dry granular media (Equation 1) | Virtual damping in leg triggered by decompression reduces work transferred to media (Figure 9) | Robot energy retention as a function of media sensitivity to policy-selected foot intrusion velocity (Sec. I.b.2) | Dissipated power (work exchange rate between robot and media) arising from virtually damped foot velocity | Roberts and Koditschek, 2018 |
| 2.2 | Energy-efficient standing on complex or broken ground (Equation 1) | Internal and external gravitational loading at joints of legged robot on fixed rigid substrate (Equations 22, 23) | Descent of jointspace energetic cost landscape by quasi-static feedback control (Equations 29, 31) | Efficient body pose as a function of descent-selected interaction between body morphology and local substrate geometry (Figure 1) | Landscape descent control computed from internal proprioceptive (actuator currents) sensing | Johnson et al., 2012 |
| 2.3 | Predictable steady state body heading from gait-obstacle interaction (Figure 11) | Gait mediated yaw mechanics (Equation 15) induced by obstacle disturbance field abstraction (Equation 11) | Locked heading calculated from basis model equilibrium (Equations 25, 26) | Body heading as a gait-selected function of interaction between body shape and periodic terrain geometry (Figure 3) | Body torque perturbations induced by gait-selected obstacle disturbance field | Qian and Koditschek, 2019 |
| 2.4 | Autonomous terrain ascent (Equation 15) avoiding disk obstacles (Equation 14) of sparse unknown placement | Point particle (Equation 35), or kinematic (Equation 44) and dynamic (Equation 51) unicycle mechanics with local range (Equation 26) and vestibular (Equation 55) sensing. | Global correctness for gradient-driven point particle abstraction (Thm. 3.2); more conservative guarantees for kinematic (Thm. 3.5) and dynamic (Thm. 3.9) unicycle | Safe reactive path to local peaks and ridges as an obstacle-policy-selected function of terrain slope (Figure 2) | Controller velocity or force commands driven by instantaneously sensed terrain slope mediated by obstacle-robot vector | Ilhan et al., 2018 |
| 2.5 | Planar navigation to a global goal avoiding familiar complex obstacles of sparse unknown placement (Figure 1) | Point-particle (Equation 14) or kinematic unicycle mechanics (Equation 18) with global position sensor and obstacle recognition and localization oracle (Equation 12) | Global correctness of obstacle-abstraction controller for point-particle (Thm. 1) and kinematic unicycle (Thm. 2) | Safe reactive path to global goal as a function of memory-triggered obstacle abstraction policy (Figure 4) | Controller velocity commands driven by instantaneously sensed goal-robot vector mediated by obstacle abstraction | Vasilopoulos and Koditschek, 2018 |
| 2.6 | Execution of deliberative assembly plan in planar environment (Figure 1) with sparse, unknown, complex, prox-regular (Def. 3) obstacles | Kinematic unicycle mechanics (Equation 1) with global position and dense local depth-map sensors (Equation 3) | Faithful assembly plan execution with obstacle avoiding excursions guaranteed to insure progress toward sub-goals (Thm. 1) modulo correct object manipulation modes (Sec. C.2) | Safe reactive paths to deliberatively sequenced sub-goals as a policy-selected function of obstacle boundary shapes (Figure 7) | Reference path tracking controller driven by path-error vector and obstacle boundary | Vasilopoulos et al., 2018a |
Where appropriate, we have specified the figures, theorems, and equations in the source material that correspond to the emergent, basis, and generative models, and the affordance exploited.