The gaits of locomoting systems are typically designed to maximize some sort of efficiency, such as cost of transport or speed. Equally important is the ability to modulate such a gait to effect turning maneuvers. For drag-dominated systems, geometric mechanics provides an elegant and practical framework for both ends—gait design and gait modulation. Within this framework, “constraint curvature” maps can be used to approximate the net displacement of robotic systems over cyclic gaits. Gait optimization is made possible under a previously reported “soap-bubble” algorithm. In this work, we propose both local and global gait morphing algorithms to modify a nominal gait to provide single-parameter steering control. Using a simplified swimmer, we numerically compare the two approaches and show that for modest turns, the local approach, while suboptimal, nevertheless proves effective for steering control. A potential advantage of the local approach is that it can be readily applied to soft robots or other systems where local approximations to the constraint curvature can be garnered from data, but for which obtaining an exact global model is infeasible.
more »
« less
Optimal Gait Families using Lagrange Multiplier Method
The Robotic locomotion community is interested in optimal gaits for control. Based on the optimization criterion, however, there could be a number of possible optimal gaits. For example, the optimal gait for maximizing displacement with respect to cost is quite different from the maximum displacement optimal gait. Beyond these two general optimal gaits, we believe that the optimal gait should deal with various situations for high-resolution of motion planning, e.g., steering the robot or moving in “baby steps.” As the step size or steering ratio increases or decreases, the optimal gaits will slightly vary by the geometric relationship and they will form the families of gaits. In this paper, we explored the geometrical framework across these optimal gaits having different step sizes in the family via the Lagrange multiplier method. Based on the structure, we suggest an optimal locus generator that solves all related optimal gaits in the family instead of optimizing each gait respectively. By applying the optimal locus generator to two simplified swimmers in drag-dominated environments, we verify the behavior of the optimal locus generator.
more »
« less
- Award ID(s):
- 1653220
- NSF-PAR ID:
- 10394234
- Date Published:
- Journal Name:
- 2022 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)
- Page Range / eLocation ID:
- 8873 to 8878
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
more » « less
Summary This article introduces a systematic method for designing a distributed nonlinear controller to achieve multiple distinct gaits, each of which is characterized by a prescribed oscillation profile and velocity, for a class of locomotion systems. We base the controller on the central pattern generator (CPG), a neural circuit which governs repetitive motions, such as walking and swimming, in most animals. First, we establish a general method for designing a nonlinear CPG‐inspired controller to assign a single gait for a linear plant; we show that this problem reduces to an eigenstructure assignment problem for which a solution has recently become available. We then extend the design to an adaptive, structured controller that can adjust the gait in response to variations in the environment. The essential problem becomes a controller design to satisfy different eigenstructure conditions for different plants; a computationally tractable formulation is provided for this problem. We provide two numerical examples using a link‐chain model as a plant representative of animals that move through undulatory motions, such as leeches or eels, to demonstrate the efficacy of this theory. In the first example, we employ an analytical condition for eigenstructure assignment to design an unstructured controller that assigns a single gait for the link‐chain model. The second example searches for a structured controller to assign two different gaits that can be switched using a higher level command.
-
In this paper, we present a set of geometric princi- ples for understanding and optimizing the gaits of drag-dominated kinematic locomoting systems. For systems with two shape vari- ables, the dynamics of gait optimization are analogous to the pro- cess by which internal pressure and surface tension combine to produce the shape and size of a soap bubble. The internal pres- sure on the gait curve is provided by the flux of the curvature of the system constraints passing through the surface bounded by the gait, and surface tension is provided by the cost associated with ex- ecuting the gait, which when executed at optimal (constant-power) pacing is proportional to its pathlength measured under a Rie- mannian metric. We extend these principles to work on systems with three and then more than three shape variables. We demon- strate these principles on a variety of system geometries (including Purcell’s swimmer) and for optimization criteria that include max- imizing displacement and efficiency of motion for both translation and turning motions. We also demonstrate how these principles can be used to simultaneously optimize a system’s gait kinematics and physical design.more » « less
-
more » « less
Abstract In animal and robot swimmers of body and caudal fin (BCF) form, hydrodynamic thrust is mainly produced by their caudal fins, the stiffness of which has profound effects on both thrust and efficiency of swimming. Caudal fin stiffness also affects the motor control and resulting swimming gaits that correspond to optimal swimming performance; however, their relationship remains scarcely explored. Here using magnetic, modular, undulatory robots (
μ Bots), we tested the effects of caudal fin stiffness on both forward swimming and turning maneuver. We developed six caudal fins with stiffness of more than three orders of difference. For aμ Bot equipped with each caudal fin (andμ Bot absent of caudal fin), we applied reinforcement learning in experiments to optimize the motor control for maximizing forward swimming speed or final heading change. The motor control ofμ Bot was generated by a central pattern generator for forward swimming or by a series of parameterized square waves for turning maneuver. In forward swimming, the variations in caudal fin stiffness gave rise to three modes of optimized motor frequencies and swimming gaits including no caudal fin (4.6 Hz), stiffness <10−4Pa m4(∼10.6 Hz) and stiffness >10−4Pa m4(∼8.4 Hz). Swimming speed, however, varied independently with the modes of swimming gaits, and reached maximal at stiffness of 0.23 × 10−4Pa m4, with theμ Bot without caudal fin achieving the lowest speed. In turning maneuver, caudal fin stiffness had considerable effects on the amplitudes of both initial head steering and subsequent recoil, as well as the final heading change. It had relatively minor effect on the turning motor program except for theμ Bots without caudal fin. Optimized forward swimming and turning maneuver shared an identical caudal fin stiffness and similar patterns of peduncle and caudal fin motion, suggesting simplicity in the form and function relationship inμ Bot swimming. -
Specifying leg placement is a key element for legged robot control, however current methods for specifying individual leg motions with human-robot interfaces require mental concentration and the use of both arm muscles. In this paper, a new control interface is discussed to specify leg placement for hexapod robot by using finger motions. Two mapping methods are proposed and tested with lab staff, Joint Angle Mapping (JAM) and Tip Position Mapping (TPM). The TPM method was shown to be more efficient. Then a manual controlled gait based on TPM is compared with fixed gait and camera-based autonomous gait in a Webots simulation to test the obstacle avoidance performance on 2D terrain. Number of Contacts (NOC) for each gait are recorded during the tests. The results show that both the camera-based autonomous gait and the TPM are effective methods in adjusting step size to avoid obstacles. In high obstacle density environments, TPM reduces the number of contacts to 25% of the fixed gaits, which is even better than some of the autonomous gaits with longer step size. This shows that TPM has potential in environments and situations where autonomous footfall planning fails or is unavailable. In future work, this approach can be improved by combining with haptic feedback, additional degrees of freedom and artificial intelligence.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1109/IROS47612.2022.9981871
