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

Authors: Randall T. Fawcett, Leila Amanzadeh, Jeeseop Kim, Aaron D. Ames, Kaveh Akbari Hamed · ICRA 2023

Licences

Open Access
Paper: CC BY 4.0

Everything below draws on the full paper under its CC BY 4.0 licence; its figure is credited to the authors.

TL;DR

A Hankel-matrix model of ball-joint-coupled quadrupeds, built from simulation data and split into per-robot QPs, plans forces and COM paths for 5 simulated and 3 real A1s.

Why it matters

A planning model learned from simulation data captures coupled multi-robot dynamics that are hard to model by hand, and it transferred to hardware with the same gains used in simulation. Splitting the planner by robot keeps each problem at 450 decision variables instead of 2250 for a centralised five-robot planner.

Problem

Quadrupeds rigidly joined through ball joints exert large interaction forces on each other, and template models such as the linear inverted pendulum or single rigid body become too complex to serve as reduced-order planning models as robots are added. Data-driven predictive control from behavioral systems theory avoids an explicit model, but its standard form adds decision variables that make it intractable in real time for teams of quadrupeds.

Proposed solution

Input-output data (contact forces in; standing height, COM velocities, roll, pitch and yaw rate out) is collected in RaiSim with random noise injected into the desired forces, then stacked in Hankel matrices to build a data-driven N-step transition matrix via a pseudo-inverse, which removes the g vector from the optimisation. The matrix is split into per-agent blocks and coupling blocks, each robot solves its own QP using the other robots' plans from the previous time step, and a 1 kHz QP-based virtual-constraint controller on each robot tracks the planned forces and COM trajectory.

Key insights

Behavioral systems theory represents a linear time-invariant system directly by its measured trajectories through Hankel matrices, without identifying state-space matrices.
Approximating the g vector offline with a pseudo-inverse turns data-enabled predictive control into a planner with far fewer decision variables, making real-time use possible.
Splitting the data-driven transition matrix into per-agent and coupling blocks, with a one-step communication delay, lets each robot plan on its own while keeping the coupling between robots.
Collecting data in simulation, where each robot can be modelled accurately, sidesteps the hard part, a physics-based reduced-order model of the coupled team, and the resulting model transferred to hardware.

Main results

Simulation: 5 coupled A1 robots walk over uneven terrain with an unknown 10 kg payload at a commanded forward speed of 0.5 m/s and 0.26 m standing height.
Planner size: 450 decision variables per robot, against 2250 for a centralised five-robot planner.
The distributed planner updates every 40 ms (25 Hz) over a 250 ms horizon (Tini = 10, N = 25); OSQP solves it in about 15 ms on an Intel Core i7-1185G7 laptop, with solve times of about 30 ms also observed.
Hardware: 3 A1 robots joined by ball joints trot at about 0.4 m/s over unstructured wooden blocks with a 4.5 kg payload, and over loose gravel.
Hardware: the team tracks a time-varying joystick trajectory on flat ground with a 6.8 kg payload and stays stable under push disturbances.
The low-level QP-based virtual-constraint controller runs at 1 kHz on each robot.

Limitations

The robots must form a complete graph with no relative translational motion; formations with limited freedom, and larger numbers of robots, are left to future work.
The underlying theory covers linear time-invariant systems; the authors note there are no proofs yet for a broad class of nonlinear systems, so the legged case rests on experimental validation.
Solve times of about 30 ms were observed against a typical 15 ms, which forced a 40 ms planner update period.
The low-level controller ignores the interaction wrenches between robots and assumes the data-driven model accounts for them.
The model is built from simulation data only, and each robot plans with the other robots' solutions from the previous time step.

Field impact

Winner of the ICRA 2023 Outstanding Paper award and a finalist for the ICRA 2023 Outstanding Multi-Robot Systems Paper award, with 37 citations. The authors publish a video of the simulation and hardware experiments; the paper does not state a code release.

Abstract

The aim of this work is to define a planner that enables robust legged locomotion for complex multi-agent systems consisting of several holonomically constrained quadrupeds. To this end, we employ a methodology based on behavioral systems theory to model the sophisticated and high-dimensional 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.

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