Distributed Data-Driven Predictive Control for Multi-Agent Collaborative Legged Locomotion

Abstract

The aim of this work is to define a planner that enables robust legged locomotion for complex multiagent systems consisting of several holonomically constrained quadrupeds. To this end, we employ a methodology based on behavioral systems theory to model the sophisticated and highdimensional structure induced by the holonomic constraints. The resulting model is then used in tandem with distributed control techniques such that the computational burden is shared across agents while the coupling between agents is preserved. Finally, this distributed model is framed in the context of a predictive controller, resulting in a robustly stable method for trajectory planning. This methodology is tested in simulation with up to five agents and is further experimentally validated on three A1 quadrupedal robots subject to various uncertainties including payloads, rough terrain, and push disturbances.

Distributed Planning of Collaborative Locomotion: A Physics-Based and Data-Driven Approach

“…Furthermore, we do not consider the use of reinforcement learning in this work and instead take a behavioral approach. Finally, this work extends our previous work [19] to model only the interaction force as opposed to an entire network of robots. In doing so, significantly faster solve times can be obtained in addition to a smoother gait.…”

“…Data-driven predictive controllers usually have very dense structures that reduce their computational effectiveness. However, the proposed method maintains a similar sparsity to that of linearized physics-based approaches, providing a significant improvement over our previous work in that we can solve the proposed trajectory planner more than 15 times faster than [19], which utilizes a purely data-driven approach. 3) Numerical simulation results are provided to show the efficacy of the proposed approach and improvement relative to using purely decentralized physics-based model predictive control (MPC).…”

“…Unfortunately, as the dimension of the system increases in size due to the addition of more agents, so too does the computational demand of the algorithm. It is therefore desirable to consider a reduced-order model, though this is often not sufficient and further necessitates the use of distributed control techniques [3]- [5], [18], [19]. Moreover, it is often the case that the reduced-order models commonly considered for multi-agent systems, such as a double integrator or unicycle model [15], [16], are oversimplified for use on quadrupeds.…”

“…, where µ denotes the friction coefficient. Remark 3: The distributed data-driven predictive control formulation in (10) has been used for multi-agent collaborative locomotion in our previous work [19] but also has some drawbacks. First, even with the approximations to (5), the planner is still relatively slow and runs at 25 (Hz).…”

“…where we have the future (i.e., predicted) outputs over the control horizon as y f = λ ∈ R N and the past outputs as y ini = λ ini ∈ R Tini , resulting in a direct mapping between the GRFs and the magnitude of the interaction forces. The data-driven model (19) can then be decomposed since the "previous" terms denoted by (•) ini are constant each time the model is used, and only the future vector of GRFs, i.e., ũ, is a decision variable. Furthermore, we define λ k to be the interaction force at time k, and G k will denote the k th row of the N -step state transition matrix G. In particular, the decomposed equations are given by…”